A111D3 llDMflD

NATL INST OF STANDARDS & TECH R.I.C.

A1 11 0311 0480

/Measurements of coettlclents o( dischar QC100 .U5753 N0.1264 1989 VI 96 C.I NIST OF COMMERCE

National Institute of Standards and Technology

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NIST Technical Note 1264 :";.'»38a&J-?«aia m<.

Measurements of Coefficients of Disctiarge for

Concentric Fiange-Tapped Square-Edged Orifice

l\/leters in Water Over thie Reynolds Number Range

600 to 2J00,000

James R. Whetstone, William G. Cleveland, George P. Baumgarten,

Samuel Woo, and M. Carroll Croarkin
NATIONAL INSTITUTE OF STANDARDS &

TECHNOLOGY

Researdi Information Center — Gaithersburg, MD 20899

rheNational Institute of Standards and Technology^ was established by an act of Congress on March 3, 1901. The Institute's overall goal is to strengthen and advance the Nation's science and technology and

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3

NIST Technical Note 1264

Measurements of Coefficients of Disctiarge for

Concentric Fiange-Tapped Square-Edged Orifice

l\/leters in Water Over tiie Reynolds Number Range

600 to 2,700,000

James R. Whetstone, William G. Cleveland, George P. Baumgarten, Samuel Woo

Chemical Process Metrology Division Center for Chemical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

and M. Carroll Croarkin

Statistical Engineering Division Center for Computing and Applied Mathematics

National Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

NOTE: As of 23 August 1988, the National Bureau of Standards (NBS) became the National Institute of Standards and Technology (NIST) when President

Reagan signed into law the Omnibus Trade and

Competitiveness Act.

June 1989

* "^^iIl^* /

U.S. Department of Commerce

Robert A. Mosbacher, Secretary

National Institute of Standards and Technology

Raymond G. Kammer, Acting Director
National Institute of Standards U.S. Government Printing Office For sale by the Superintendent

and Technology Washington: 1 989 of Documents

Technical Note 1264 U.S. Government Printing Office

Natl. Inst. Stand. Technol. Washington, DC 20402

Tech. Note 1264

546 pages (June 1989)

CODEN: NTNOEF
Measurements of Coefficients of Discharge

for Concentric Flange -Tapped Square-Edged Orifice Meters

in Water Over the Reynolds Number Range 600 to 2,700,000

James R. Whetstone, William G. Cleveland

George P. Baumgarten, Samuel Woo, and M. Carroll Croarkin

Abstract

Presented here is a description of the measurement procedures and

standards, data acquisition systems, and data bases developed in the

American Petroleum Institute (API) -sponsored orifice discharge coefficient data base project performed at the National Bureau of Standards

(NBS) primary water flow rate measurement facility. Measurements were performed on five orifice meter sizes, 2, 3, 4, 6, and 10 inches, over

the beta ratio range of 0.08 to 0.75. The measurement systems and

procedures were designed to provide full documentation of the relation

between the observations comprising the data base developed and U.S.

national measurement standards.

Data acquisition procedures were automated to minimize human error in

data recording, particularly for differential pressure observation.

Laboratory- quality transducers and pressure standards were used and data

acquisition was automated for observation of differential pressure,

flowing fluid temperature, collected mass of water, and time of

collection. Only a few parameter observations were made manually and

entered into the data base. A large data base stored in computeraccessible form has resulted. This data base consists of the recorded

raw data and the results calculated from them.

To realize the full potential of the transduction equipment used in the

project, appropriate working standards were incorporated into the

measurement systems to allow calibration of differential pressure

transducers, thermometers, length-measuring devices, and weigh scales.

These working standards were, in turn, calibrated against U.S. national

working standards over the course of the project and are described in

detail. Gravimetric measurement of the mass flow rate through the

orifice meters utilized the NBS primary water mass flow rate measurement

system. Documentation of the measurements, standards, and procedures

utilized in this project is given in an NBS report to be published

shortly. The data base will be available from NBS and API.

NOTE: On August 23, 1988 with the signing of the Omnibus Trade and

Competitiveness Act, the National Bureau of Standards (NBS) became the

National Institute of Standards and Technology (NIST) . Since this

report was written and reviewed before this change, references to NBS in

the body of the report have not been changed to NIST.

Ill-

Table of Contents

Page

Symbol List xvii

I . Introduction 1

II. Experimental Facilities and Measurement Systems 4

A. General Description of the Experimental Approach 4

B. Sensitivity Analysis of the Measurement System and

Variation of the Discharge Coefficient with Various

Observed Parameters 4

1. Sensitivity Analysis of the Measurement System .... 4

2. Discharge Coefficient Variation Due to Independent

Variable Variation 7

C. Water Mass Flow Rate Measurement System and Its

Uncertainty 10

1

.

General Description 10

2. Analysis of Diverter Valve Corrections 13

3. Diverter Correction Values for Each Weighing and

Timing System 15

4. Mass Measurement and Uncertainty 16

a. Measurement of the Mass of Water Collected .... 20

b. Scale Calibration Procedures and Mass

Standards 21

c. Uncertainty in the True Mass Value of Water

Collected 25

5

.

Mass Flow Rate Measurement Uncertainty 30

D. Differential Pressure Measurement Systems and

Standards 32

1. Differential Pressure Measurement Requirements .... 32

2

.

Differential Pressure Transducers 32

3

.

Pressure Transducer Mounting and Fluid Isolation

Interfaces 33

-V-
Page

4. Working Pressure Standards 39

5. Uncertainty in the Differential Pressure

Measurements 42

a. Uncertainty in the Pressure Developed by a Single

Deadweight Tester 42

b. Uncertainty in the Differential Pressure

Developed by the Working Pressure Standards ... 44

6. Differential Pressure Transducer Calibration

Procedures 47

7. Transducer Response Functions and Coefficient

Values 49

8. Estimation of the Uncertainty in the Mean

Differential Pressure Over the Period of a Flow Rate Measurement 50

9. Uncertainty in the Measurement of Orifice Meter

Differential Pressures 57

10. Transducer Surveillance Measurements 57

Temperature Measurement Instruments and Standards 60

1. Extension Cable Connection Effects 60

2. Uncertainty in Measured Temperature Values 62

3. Measurement and Calculation of the Density of

Water 63

Dimensional Measurements 65

1. Orifice Meter Installation 65

2. Orifice Meter Tube Geometry and Dimensional

Measurements 68

3. Meter Tube Surface Roughness Measurements 82

4. Orifice Plate Dimensional Measurements 82

Propagation of Error Analysis of Discharge Coefficient

Values 97

1. Uncertainty in the Mass Flow Rate, s» 98

-VI-
Page

2. Uncertainty in the Differential Pressure, s.- 98

3. Uncertainty in the Flowing Fluid Density, s 98

4. Uncertainty of the Orifice and Meter Tube

Diameters , s , and s^ 98

H. Uncertainty in the Reynolds Number 104

III. Working Equations and Dimensional Conversion Factors 106

A. Introduction 106

B. Derivation of the Coefficient of Discharge Relation

and Associated Units Conversion Factors 106

C. Derivation of the Reynolds Number Including Units

Conversion Factors Ill

D. Calculation of Differential Pressure Values:

Compensation for Drift in the Zero Differential

Pressure Response Values 112

E. Screening of the Differential Pressure Observations . .

.

115

IV. Data Acquisition and Control Systems 120

A. General Description 120

B. Data Acquisition and Control System Hardware 120

C. Data Acquisition and Control System Software 121

V, Calibration and Test Procedures 124

A. Differential Pressure Transducer Calibration 125

B. Meter Tube Installation 129

C. Orifice Meter Data Acquisition Procedures 130

D. Diverter Correction Calibration 136

VI. Archiving of the Data Base, Data Analysis Results,

and Statistical Analysis of the Results 139

A. Operational History, Final Data Base Definition, and

Archiving of the Data Base 139

B. Inventory of the Final Data Base 149

-Vll-
Page

C. Presentation of the Data Analysis Results 165

D. Statistical Analysis of the Final Data Base 410

VII . Acknowledgments 445

VIII . References 446

Appendix A. Operational History of the Project 447

Appendix B. Water Density Measurements 493

Appendix C. Differential Pressure Transducer Coefficient Values ... 497

Appendix D. Archival Data Base Format, Intermediate Reynolds

Number Project 505

Appendix E. Measurements of Orifice Plate Edge Sharpness 513

Appendix F. Velocity Profile Measurements 521

-Vlll-
List of Figures Page

Figure 1. Orifice Flow Rate Measurement System 5

Figure 2. Flow Measurement System/Orifice Meter Diagram 6

Figure 3. Diverter Valve Schematic Diagram with Timing

Circuitry 11

Figure 4. Hydraulic Mass Standard Loading Mechanism for

50,000-Pound Scale Calibration 24

Figure 5. Differential Pressure Transducer Manifold Schematic

Diagram 34

Figure 6. Schematic Diagram of Interface Sightglasses and

Five Valve Manifold for the Paros Type Transducers .... 35

Figure 7. Schematic Diagram of Interface Sightglasses and

Five Valve Manifold for the Ruska Transducer 36

Figure 8. Meniscus Height Setting Telemicroscope System 38

Figure 9. Differential Pressure Time Series Plot-0.4 psid 52

Figure 10. Differential Pressure Time Series Plot-1 psid 53

Figure 11. Differential Pressure Time Series Plot- 3 psid 54

Figure 12. Differential Pressure Time Series Plot-10 psid 55

Figure 13. Differential Pressure Time Series Plot-27 psid 56

Figure 14. Sprenkle Flow Conditioner Casing 66

Figure 15. Sprenkle Flow Conditioner Schematic Diagram 67

Figure 16

.

Orifice Meter Tube Assembly 69

Figure 17 . Internal Micrometer Used for Measurement of Orifice

Meter Tube Diameters 71

Figure 18. Orifice Plate Flatness and Thickness Measurement

Positions 87

Figure 19. Orifice Meter Installation in Pipeline -Formulation of

Working Equation for Coefficient of Discharge 107

Figure 20. Pressure Observations for a Test Run Showing 10

Standard Deviation Filter Bounds and the 3 Standard

Deviation Bounds Computed for the Filtered

Observation Set 119

IX-
Page

Figure 21. Differential Pressure Transducer Calibration Software . 126

Figure 22 . Orifice Meter Data Acquisition Software 132

Figure 23. Weigh Tank Diverter Calibration Software 138

Figure 24. Effects of Pumping System on Orifice Discharge

Coefficient 145

Figure 25. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-lABC 2 -Inch Meter Tube,

7 Orifice Plates , Final Data Base 182

Figure 26. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-2ABC 2 -Inch Meter Tube,

7 Orifice Plates , Final Data Base 199

Figure 27. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-3ABC 3 -Inch Meter Tube,

8 Orifice Plates , Final Data Base 218

Figure 28. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-4ABC 3 -Inch Meter Tube,

8 Orifice Plates , Final Data Base 235

Figure 29. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-5ABC 4- Inch Meter Tube,

8 Orifice Plates , Final Data Base 256

Figure 30. (A through D) Discharge Coefficient/Rejmolds

Number Plots, PE-6ABC 4 -Inch Meter Tube,

8 Orifice Plates , Final Data Base 277

Figure 31. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-7ABC 6 -Inch Meter Tube,

7 Orifice Plates , Final Data Base 293

Figure 32. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-8ABC 6 -Inch Meter Tube,

7 Orifice Plates , Final Data Base 309

Figure 33. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-9ABC 10 -Inch Meter Tube,

7 Orifice Plates , Final Data Base 327

Figure 34. (A through D) Discharge Coefficient/Reynolds

Number Plots, PE-OABC 10 -Inch Meter Tube,

7 Orifice Plates, Final Data Base 347

Figure 35. (A through E) Discharge Coefficient/Reynolds

Number Plots, DAN-4SS 4-Inch, Stainless Steel

Meter Tube, 9 Orifice Plates, Final Data Base 405

-X-
Page

Figure 36 (A through D) Standardized Residuals vs. Pipe

Reynolds Number for DAN-4SS, 8 Orifice Plates 415

Figure 37. (A through J) Discharge Coefficient/Reynolds

Number Plots , Plated and Unplated Results for

Two and Six Plates 424

Figure 38 . (A through E) Plots of Differences Between Observed

Discharge Coefficients and Those Computed from the

Stolz Correlation 436

Figure Al. Discharge Coefficient/Reynolds Number Plots,

4- inch Meter Tube, Beta Ratio 0.2 and 0.375

Orifice Plates , 1984 Observations 453

Figure A2 . Discharge Coefficient/Reynolds Number Plots,

4- inch Meter Tube, Beta Ratio 0.5 and 0.56 Orifice

Plates , 1984 Observations 454

Figure A3. Discharge Coefficient/Reynolds Number Plots,

4- inch Meter Tube, Beta Ratio 0.62 and 0.75 Orifice

Plates , 1984 Observations 455

Figure A4. Discharge Coefficient/Reynolds Number Plots,

2 -inch Meter Tube, Beta Ratio 0.375 and 0.75 Orifice

Plates , 1984 Observations 457

Figure A5 . Discharge Coefficient/Reynolds Number Plots,

10 -inch Meter Tube, Beta Ratio 0.62 and 0.75 Orifice

Plates , 1984 Observations 458

Figure A6 . Sanding Belt and Conduit Used in Rust Removal 462

Figure A7 . Corrosion Patterns in the FE-5B Meter Tube Section

After Testing with N-Sodium Silicate Treated Water .... 468

Figure A8 . Corrosion Patterns in the FE-5C Meter Tube Section

After Testing with N-Sodium Silicate Treated Water .... 469

Figure A9 . Photograph of Corrosion Nodules Around the Tap

Hole of FE-5B After Tests Using Oiled Surfaces for

Corrosion Inhibition 473

Figure AlO. Photograph of Corrosion Patches to the Side of the

Tap Hole of FE-5B After Tests Using Oiled Surfaces

for Corrosion Inhibition 474

Figure All. Photograph of Speckled Corrosion Pattern on FE-4B 480

Figure A12. Photograph of Speckled Corrosion Pattern on FE-4C 481

-XI-
Page

Figure A13. Topographic Traces of the Speckled Corrosion

Pattern in FE-4B 483

Figure A14. Topographic Traces Taken Immediately After

Electroless Nickel Plating of PE-6B 489

Figure A15. Photograph of the Tap Hole Region of PE-6B 490

Figure Fl. Horizontal and Vertical Velocity Profiles 523

-xii-
List of Tables Page

Table 1 . Weighing System Parameters 10

Table 2. Diverter Correction Computation of Weighing System 1

at 1583 . 222 GPM 17

Table 3. Diverter Correction Values for System 1 18

Table 4. Diverter Correction Values for System 2 18

Table 5. Diverter Correction Values for System 3 19

Table 6. Diverter Correction Values for System 4 19

Table 7. Diverter Correction Interpolation Function

Coefficients 20

Table 8. 50-Pound Working Standard Mass Values 23

Table 9. 500-Pound Working Standard Mass Values 25

Table 10. Uncertainty in the Observed Mass Value of Water 27

Table 11. Measurement Uncertainty of the NBS Water Flow Rate

Measurement Facility 31

Table 12. Pressure Gauge Mass Values, Maker Niomber 73520 40

Table 13. Pressure Gauge Mass Values, Maker Number 73521 40

Table 14. Relative Uncertainty in Individual Deadweight Tester

Pressures 44

Table 15. 20-Point Transducer Calibration Schedule 49

Table 16. Differential Pressure Transducer Surveillance

Measurements 59

Table 17. Thermistor Temperature Indication Relative to the

Calibrated Platinum Resistance Thermometer 61

Table 18. Thermistor Coefficients, Residual Standard Deviations,

and Experimental Locations 62

Table 19 . Measured Water Density Values 64

Table 20. Test Section/Orifice Meter Installation Chart 65

-Xlll-
Page

Table 21A. Orifice Meter Tube Diameter Measurements Before

thru 21D. Electroless Nickel Plating 72

Table 22. Orifice Meter Tube Diameter Measurements for the

4- Inch Stainless Steel Orifice Meter Tube Check

Standard 76

Table 23A. Orifice Meter Tube Diameter Measurements After

thru 23E. Electroless Nickel Plating 77

Table 24. Orifice Meter Tube Mean Diameters in the Plane of the

Tap Hole Center Lines (Axial Position 1) 81

Table 25. Orifice Meter Tube Interior Surface Roughness

Measurements 83

Table 26. Orifice Flange Center to Dowel Pin Inner Surface

Radii 85

Table 27. Orifice Plate Initial Dimensional Measurements 88

Table 28. Confirmatory Plate Diameter and Flatness

Measurements 92

Table 29. Tap Hole Diameters and Center Line Separation with

Respect to the Orifice Meter Flange Face 96

Table 30. Tabulation of Uncertainty Components 102

Table 31. Data Acquisition Filter Rejections 117

Table 32. Schedule of Differential Pressure Values for Flow

Rate Setting 136

Table 33. Meter Tubes/Orifice Plates Rerun in 1987 147

Table 34. Pump Crossover Between the 100- and the 20-gpm

Pumps in the 1987 Data Collection Period 148

Table 35. Archival Data Base Inventory, Bare Meter Tube

Tests Run Immediately Before Plating 151

Table 36. Archival Data Base Inventory, Test Runs Performed

on Orifice Meter Tube Assembly PE-lABC through

PE-OABC 152

Table 37. Archival Data Base Inventory, Test Runs Performed

on Orifice Meter Tube Assembly DAN-4SS 162

Table 38A. Orifice Discharge Coefficient Values

thru 38G. - Meter Tube PE-1 167

XIV-
Page

Table 39A. Orifice Discharge Coefficient Values

thru 39G. - Meter Tube PE-2 186

Table 40A. Orifice Discharge Coefficient Values

thru 40G. - Meter Tube PE-3 203

Table 41A. Orifice Discharge Coefficient Values

thru 41G. - Meter Tube PE-4 222

Table 42A. Orifice Discharge Coefficient Values

thru 42G . - Meter Tube PE- 5 239

Table 43A. Orifice Discharge Coefficient Values

thru 43G. - Meter Tube PE-6 260

Table 44A. Orifice Discharge Coefficient Values

thru 44G. - Meter Tube PE-7 281

Table 45A. Orifice Discharge Coefficient Values

thru 45G. - Meter Tube PE-8 297

Table 46A. Orifice Discharge Coefficient Values

thru 46G. - Meter Tube PE-9 313

Table 47A. Orifice Discharge Coefficient Values

thru 47G. - Meter Tube PE-0 331

Table 48A. Orifice Discharge Coefficient Values

thru 48S - Meter Tube FE-1 thru FE-0 351

Table 49A. Orifice Discharge Coefficient Values

thru 491 . - Meter Tube DAN-4SS 370

Table 50. Meter Tube and Plate Configurations 410

Table 51. Within and Between Standard Deviations from One -Way

Analysis of Variance 412

Table 52 . Tabulation of Test Runs Marked as Outliers 419

Table 53. Statistics for Testing for a Difference Between the

1987 Experiment and 1985 Experiment 422

Table 54. F Statistics for Testing for Differences Between

Unplated and Plated Meter Tubes 423

Table 55. Standard Deviations for Average Discharge

Coefficients at 27 psi Differential Pressure 441

Table Bl

.

Measured Water Density Values for Water Samples .... 494

XV-
Page

Table Cl. Response Model Coefficients for the Ruska Transducer

Serial Number 30827 Connected to the Upper Orifice

Meter Taps 497

Table C2. Response Model Coefficients for the Paros Transducer

Serial Number 13150 Connected to the Upper Orifice

Meter Taps 499

Table C3. Response Model Coefficients for the Paros Transducer

Serial Number 12200 Connected to the Lower Orifice

Meter Taps 502

Table El, Initial Orifice Plate Edge Sharpness Measurement

Results 514

Table E2 , Final Orifice Plate Edge Sharpness Measurement

Results 516

Table Fl. Summary of Relative Velocities and Positions and

Observed Mean Impact Pressures and Standard

Deviations of the Mean for Horizontal Traverses 524

Table F2 . Summary of Relative Velocities and Positions and

Observed Mean Impact Pressures and Standard

Deviations of the Mean for Vertical Traverses 529

XVI-
I. Introduction

For the last 2 decades it has been recognized in the flovTmetering

community that a need exists for well -documented, experimental data bases

of coefficients of discharge for orifice meters in order to achieve a greater degree of accuracy in custody transfer measurements . The

American Petroleum Institute (API) and the American Gas Association (AGA)

made an initial attempt to resolve the situation for flange -tapped

orifice meters in the mid-1970's; however, this attempt did not come to

fruition. A subsequent effort was made by API and the Gas Processors

Association (GPA) to develop a comprehensive and well -documented database of discharge coefficients for flange- tapped orifice meters spanning

their range of use. The three major parameters to be varied were the

Reynolds number, the meter tube diameter, and the ratio of the orifice

diameter to the pipe diameter (known as the beta ratio) . To accomplish

this objective a program consisting of three projects was planned.

Common to the program would be a set of orifice meters comprised of meter

tubes in five sizes with each size having sets of seven orifice plates

with a beta ratio range from 0.1 to 0.75. Each project would concentrate

on one region of the Reynolds number range by using a particular fluid

for flow tests. The fluids were selected on a practical basis and the

three projects were designed so that the data developed by any one project would overlap that developed by a companion project in the

adjacent Reynolds range. The low Reynolds number project would be performed using a moderate viscosity liquid and the smaller diameter orifice

meters. The intermediate Reynolds number project would use water as the

test fluid and would involve all orifice meters. The high Reynolds

number project would use natural gas and the largest orifice meters.

In 1981 the API and the U.S. National Bureau of Standards (NBS) entered

into a contractual arrangement to develop a well -documented data base of

discharge coefficients for flange -tapped orifice meters over the range of

Rejmolds numbers obtainable in the NBS water flow rate measurement

facility. The measurement devices, standards and procedures, data

acquisition methods, a condensed data base, and the results of this

extensive test project are described herein. The approach taken by NBS was to document all measurement procedures and standards and relate them

to U.S. national standards of measurement. This document describes the

experiments, procedures, instrumentation, measurement traceability

,

software documentation, and the resulting analysis used to develop the

orifice discharge coefficient data base reported here.

As with any data base development or research project, a set of initial

assumptions and conditions are necessary to form the basic framework

within which the project operates and its goals are accomplished. The

following is written to describe this framework. It is written with the

benefit of a considerable degree of hindsight developed over the 6 -year

period of the project's lifetime. During the course of the project some of the specific conditions, procedures and methods changed. In some facets of the project these changes were profound, strongly affecting the

manner in which it was finally completed. However, the basic framework

and objective of the project remained essentially constant.
The rationale for the configurations of the orifice meters and the

measurement system was the following:

(1) A primary condition was to develop a fundamental discharge

coefficient data base. Effects on the orifice meter from

sources extraneous to fundamental orifice meter configuration

were to be eliminated or their effect minimized.

(2) The complete set of orifice meter tubes in five sizes (2, 3, 4,

6, and 10 inches) would be used. Two duplicate meter tube

assemblies in each size were used. Flange taps would be used to

reflect the preponderance of U.S. commercial practice.

(3) Each meter tube size had two sets of orifice plates with beta

ratios ranging from nominally 0.1 to 0.75. The two sets were nominally identical in each size.

(4) The manufactured quality of the meter tubes and orifice plates

was to be of commercial quality in order to reflect a level of

variability normally seen in commercial metering installations.

Therefore, the meter tubes were constructed of seamless steel

tubing, and fitted with ANSI 600 psi steel flanges. (Although

rather low pressures were used in this project, the high

Reynolds project was to be done at gas pipeline pressures neces- sitating the use of the appropriate flanges.) However, a departure from commercial practice was made in the types of flange

seals. Rather than the compression gasket seals normally used

in commercial orifice metering, 0-ring seals were used. The use

of 0-ring seals provided a reproducible method for locating the

pressure taps relative to the orifice plate. This also

minimized any step in the diameter between the meter tube and

the orifice, and eliminated the question of the effect of

gaskets of variable thickness and diameter on the discharge

coefficients calculated from the data base.

(5) The maximum differential pressure would be approximately 800

inches of water or 28 psid. The minimum differential pressure

would be determined by the capability of the measurement system.

(6) Where feasible, state-of-the-art measurement techniques would be

employed.

(7) All measured parameters were to be referred directly to U.S.

measurement standards.

(8) Documentation of the measurement systems and procedures was to

be as complete as possible.

(9) In an attempt to isolate the orifice meter from effects caused

by the installation of the orifice meters in the test facility,

a flow conditioner and an approach tube (approximately 40

diameters long) were added to the normal commercial meter tube

configuration

.
In developing this data base it was decided at the beginning of the

project that the amount of data acquired manually would be minimized. In

particular the parameters observed for flow rate determination and in the

observation of differential pressure across the orifice meter would be

automated to minimize the incidence of human error. In the final system

used for data acquisition, automated logging of the observed parameter

values was used exclusively except for entry of the observed barometric

pressure. As a consequence, the rate at which differential pressure

values could be acquired was much higher than could have been possible

with manual observation and recording. Each of the differential pressure

values was recorded on magnetic media and became part of the total data

base which is quite voluminous . The entire data base is available in

computer readable form. The structures of this data base are given here

and the data base itself is available from the NBS and from the API.

The remainder of the report gives comprehensive descriptions of the

measurement systems used to acquire the observed data, descriptions of

the hardware, analyses of its performance, and the methods used to tie

each observed parameter to national standards. An analysis of the over- all uncertainty in the measurement of discharge coefficient values is

given. The data base is analyzed and the results tabulated and

discussed.

The magnitude of the data base is quite large and could not be

accommodated in a document of any reasonable length. Additionally, the

great majority of the data was collected by, stored in, and analyzed with

computers. Any analysis which one may wish to do is possible by obtaining the entire observational data base on magnetic tape either from the

NBS or the API.

The major difficulty encountered during the execution of this project was identifying, to some extent quantifying, and arresting the effects of

changing surface roughness of the meter tubes due to corrosion. The

efforts expended by the NBS and the API are summarized in Appendix A of

this report which gives the operating history of the project. Placing

this description in an appendix is done to encourage reading of the body

of the report first, since the operating history is written with the

assumption that the reader has an understanding of the various measure- ment systems and procedures used in the work. The final solution to

arresting corrosion induced effects on the results of the test data was

the plating with nickel of the meter tubes. The plating was done using

the electroless process to minimize the modification of the surface

finish of the meter tube, while inhibiting corrosion. Data collected

after nickel plating the meter tubes constitutes the final data base.

However, these data were collected after a substantial body of data had

been collected and analyzed. The data base which is archived contains

data taken for test runs beginning well before the nickel plating and

collection of the final segment of the data base. This has been done to

satisfy the wishes of the API that the complete record of the project be

well documented.

3-
The remainder of this report contains detailed descriptions of the

measurement systems and methods employed and the results obtained in

final data base. These may seem to be overly detailed at some points.

This was done intentionally to provide full documentation of this work

for the use of any future workers interested in its evaluation without

the aid of those involved, much as has been the case with the original

work of Beitler [1] , upon which much of current orifice metering practice

is based.

II. Experimental Facilities and Measurement Systems

A. General Description of the Experimental Approach

The experimental work was performed using the water flow rate measurement

facility of the NBS . Added to this facility was a system for automated

measurement of differential pressure, diversion timing, mass, and temperature. The measurement systems are shown schematically in figures 1 and

2. Included in the measurement and data storage system (fig. 2) is the

provision for periodic calibration and surveillance of the differential

pressure transducers and the scales used for flow rate measurement. The

general philosophy used in the development of the measurement system and

data base developed from it, was to tie each measured parameter included

in the data base to the national standards of measurement as maintained

by the NBS (see fig. 1) . Assessment of the magnitude of the effects of

each parameter on the total measurement uncertainty for the orifice

discharge coefficient was determined by a propagation of error analysis.

The work of Ku [2] provided the basis for this analysis, which was used

to determine the rigor with which each measured parameter was compared

with national standards. Efforts were made to minimize the primary

contributors to the error budget. The following sensitivity analysis is a tool to estimate the error contributions of the independent variables.

B. Sensitivity Analysis of the Measurement System and Variation

of the Discharge Coefficient with Various Observed Parameters

1. Sensitivity Analysis of the Measurement System

The total accuracy or uncertainty with which orifice discharge coefficients may be determined is dependent upon the combined uncertainty of

the independent variables from which it is computed. The magnitude of

the contribution of each independent variable's measurement uncertainty

to the discharge coefficient's uncertainty may be estimated by an elementary sensitivity analysis. The basis for this analysis is the

mathematical expression for the discharge coefficient which is given here

as eq (1) . This relationship is derived from fluid dynamic

considerations in section III.

-4-
CO +-• "O x> CO

1— i— <D

CO CO JD

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g^ E o D

c

CO T3

CO o

c

CO

E c

CO 0 E

(D E

m cQ o COc

CO

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CO o

c

CO

+-• CO

CO

CD

"D

CO o1— T3

CO (D

CO T3 -co

(D T3 E

3 CO a: <

=) 1X1 CO o

E

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CO

CD

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c

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k.

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CO

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oC

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CO ^14-1 *-' < < CO CO sz x: 03 CO L.D

"cO CO to

k—CD -C O-Q

Q. CO

a>"co

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CD DC oO

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CC CC •E a. z :^ ^ t

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cd

o

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o

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<uO

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-6-
C^ = m(l - /3^)^/2 /[Nd^ F^ (pAP)^/2] , (1)

where C, = discharge coefficient, m = mass flow rate,

d = diameter of the orifice,

F = orifice thermal expansion factor,

N = a units conversion constant dependent on measured parameters,

p = density of the flowing fluid, water in this project,

AP = the differential pressure developed across the orifice meter,

^ = d/D, the beta ratio, and

D = the diameter of the meter tube.

The relative magnitude of the variation in each parameter was calculated,

and the results used for selection of the procedures and hardware for

data collection purposes. Analysis of the sensitivity of the discharge

coefficient value to changes in the Independent variables may be investigated by differentiation of eq (1) with respect to each. Normalization

of each of these partial derivatives by the discharge coefficient results

in an expression for the relative change in discharge coefficient,

AC j/C J , due to relative change in the independent variable of Interest.

This method will be used to estimate the relative effect of variation in

each independent variable to quantify the rigor necessary in its

measurement

.

Each Independent variable is either a directly observed quantity or is

the result of observed values of two or more auxiliary observable

quantities . The two diameter values are directly measured quantities

,

i.e., the micrometers and measuring machines used gave their indications

in length units and were calibrated. All of the independent variables

require calibration procedures in order to make a direct tie to the U.S.

National Measurement System as maintained by NBS or are the results of

metrological work recognized as representing the most accurate data

available, e.g., the dependence of water density on temperature.

Discussions of the methods of calibration and measurement traceablllty

for each of these are given in subsequent sections of this report. In

this section we will discuss the effects of the measurement sensitivity

in the parameters appearing explicitly in the discharge coefficient

equation given above. The partial derivatives of interest and the

corresponding expression for relative variation of the discharge

coefficient due to relative changes in each parameter are discussed.

2. Discharge Coefficient Variation Due to Independent

Variable Variation

Am

m

The discharge coefficient varies directly as the mass flow rate varies

As will be discussed later the uncertainty in the mass flow rate as

Mass Flow Rate Variation

_ 1

•m

1 ac,d

C^d am <^d
determined by the NBS gravimetric water flow rate measurement facility

was initially expected to lie between 0.1 and 0.2%. This value appeared

to be a limiting one for flow rate measurement. Therefore, the magnitude

of this variation/uncertainty in the measurement of the discharge

coefficient was taken as an upper limit target for the other independent

parameter measurements.

Flowing Fluid Density Variation

1 3C, T AC, T. d 1 , d 1 Ap

C , dp 2p C; 2 p

Quite accurate values of the density of the flowing fluid, water, may be

obtained from temperature observations. The relative variation in the

water density values is 1 to 2 parts in 10,000 (0.01-0.02%). The effect

of this variation on the discharge coefficient is reduced by one -half

according to the above equation.

Differential Pressure Variation

1 «=d 1 ^"d. 1 A(AP)

c^ a CAP) 2AP =d 2 (AP)

The variation relation of the discharge coefficient with the differential

pressure developed across the orifice meter is similar to that of the

flowing fluid density. However, this measurement has traditionally been

one of the more difficult to make with a small uncertainty value. The

approach taken in this work was to make a large number of differential

pressure measurements, and to make them using state-of-the-art

transduction and calibration apparatus to attain a high degree of

accuracy. In this way the uncertainty in this measurement parameter is

minimized. The uncertainty in the measurement of the differential

pressure is constant over the pressure range. Therefore, the relative

uncertainty increases at the lower differential pressure values

.

Realistic estimates of the uncertainty in the differential pressure

working standards and transducers are on the order of 0.001 to 0.005 psid

(7 to 34 pascals, 0.02 to 0.1 inches of water). Taking the upper limit

of this range as the uncertainty in the differential pressure value and

the highest and lowest nominal differential pressure values used in the

testing procedures gives an approximate relative uncertainty range of

0.01% (diff. press, of 28 psid) to 0.63% (diff. press, of 0.4 psid). As

is the case with the measurement of mass flow rate, the contribution of

this pressure uncertainty component is a dominant and limiting one. The

measurement methods and techniques used here are considered to be stateof-the-art.

-8-
Orifice and Meter Tube Diameter Variation

1 ^^d^ -2 1

=d

-2 Ad

c^ad l-;8* d 1-^^ d

1 dC^a 2^* 1 ACd^ 2^^ AD

C^ 30 d

l-fi"* D =d l-yS^ D

The 2/(l-yS ) term in each of these relations Increases the relative

variation/uncertainty in the diameter measurements on that of the

discharge coefficient. The magnitude of this term ranges from 2 (for

fi = 0.1) to 3 (for fi = 0.75). Diameter measurement uncertainty was expected to be approximately 0.0002 inches (5 micrometers). The effect

of relative variation in the meter tube diameter, , on the discharge

ACd 4

D

coefficient, , is reduced by the ^ multiplier. Typical values are

given in the following table.

Meter Tube Orifice Beta

Diameter Diameter Ratio

(inches) (inches)

2.0 0.25 0.12

2.0 0.62 0.31

2.0 1.00 0.50

2.0 1.50 0.75

4.0 0.37 0.09

4.0 1.25 0.31

4.0 2.00 0.50

4.0 3.00 0.75

10.0 1.0 0.10

10.0 3.0 0.30

10.0 5.0 0.50

10.0 7.5 0.75

0.0002

0.0092

0.0625

0.3164

7.3x10"

0.0095

0.0625

0.3164

0.0001

0.0081

0.0625

0.3164

AC

d

(%)

0.16

0.07

0.04

0.04

0.108

0.032

0.021

0.020

0.040

0.013

0.009

0.008

AC

d-'

(%)

4.9x10

1.9x10'

0.001

0.009

7.3x10'

9.6x10'

6.7x10'

0.005

4.0x10'

3.3x10'

2.7x10'

0.002

-6

Orifice Thermal Expansion Factor

The effect of variations in the orifice thermal expansion factor, F , is

small due to the magnitude of the thermal expansion coefficient of the

orifice plate material, stainless steel. The thermal expansion of

stainless steel is of the order of 10 /°C, and for the temperatures used

in this work, 15 to 40 °C, errors in the measured temperature and

expansion coefficient are extremely small.

-9-
C. Water Mass Flow Rate Measurement System and Its Uncertainty

1. General Description

The NBS water flow rate measurement facility is a closed loop flow

system. Its general arrangement is shown in figure 2. The flow rate

measurement system is installed above the system's reservoir (or sump)

3 which has a capacity of approximately 60,000 U.S. gallons (230 m ).

Water flow rates are maintained in the system by four submersible, shaft

turbine pumps, three of which have 3,000 gallons/minute capacities. The

fourth has a 1,000 gallons/minute capacity. For flow rates below

approximately 50 gallons per minute the primary pumps were found to be

too large to produce stable non pulsating flow. Additional small submersible, turbine pumps of 20 and 100 gallons/minute capacities were installed and used at lower flow rates. All of these pumps are constant-speed pumps. Flow and back pressure at the metering device is

controlled through the use of two sets of valves . One set is located

near the pump discharge manifold and controls the amount of water passed

back to the reservoir directly without passing through the facility test

sections. The other set of valves is located downstream from the test

section. These are the primary controls for back pressure and flow rate

through the test sections of the flow rate measurement system.

Measurement of the flow rate of water through a meter under test is done

gravimetrically , i.e., through the use of the weighing and timing

method. (This method is often categorized as a primary flow rate

measurement.) As shown in figure 3 the apparatus consists of a wedgeshaped valve which diverts the flow, to and from a return chute leading

either to the reservoir or to a tank mounted on the deck of a weigh

scale. The NBS system utilizes four such weigh tank/scale combinations

based on load cell scales of varying sensitivities and sizes to cover

the 1 to 10,000 gallon/minute flow rate range used in this project. Each

weigh tank has associated with it a diverter valve sized according to

the flow rate range of the scale and weigh tank. The scale capacities

and sensitivities of each system are listed in table 1 with the

approximate flow rate range of each.

Table 1. Weighing System Parameters

Flow Rate Range

(Gallons/Min) (Pounds/Sec)

System Scale Scale

No. Capacity Sensitivity

(pounds) (pounds)

50,000 5.00 1,000 - 10,000 139 - 1390

6,000 0.50 250 1,400 35 - 194

2.000 0.10 40 400 5.5 55

400 0.05 40 0.1 5.5

Each of the scales is connected to an electronic multiplexing device

which allows manual selection of the scale to be connected to the

10-
Water

flow

i-5 volts

Additional

systems

DIverter

timing pulse

Scale

multiplexer/

Indicator

Optical

interrupter

switch

'ZZZ

Reservoir

Figure 3. DIverter Valve Schematic Diagram with Timing Circuitry

11-
electronic indicator unit. The indicator unit displays the mass value

from the selected scale and transfers this value and scale diagnostic

parameters, via an RS-232C interface, to the microprocessor-based data

acquisition and control system. The diverter valve position may be

controlled either manually from the flow measurement system control

panel or automatically by the microprocessor.

The method of measuring the time of diversion of the water flow into the

weigh tank uses an optical interrupter switch/flag mechanism to generate

a timing signal to control a universal counter/timer. An optical interrupter switch block is mounted on the stationary framework of each diverter valve. A metal flag is mounted on the movable portion of the diverter valve such that the flag interrupts the light beam of the switch

very near the mid-point of the valve's traverse. A schematic diagram of

the switching arrangement is given in figure 3. The collector of each

interrupter switch's output phototransistor is connected to the pull-up

resistor of the individual inputs of the four input TTL NAND gate electronic logic circuit. When the light beam is not interrupted, the

phototransistor is turned on, pulling the voltage at the gate's input to a logical (0 volts) . Light beam interruption forces the output of the

NAND gate to a logical 1 (+5 volts) . In the rest position each diverter

valve's flag places the corresponding input of the switch circuit in the

logical 1 state. During normal operation the output of the NAND gate is a pulse having a duration equal to the time that a diverter valve's flag

opens the light beam. This timing pulse was connected to the input of a Hewlett-Packard Model 5316A universal counter/timer [3] for measurement

of the duration of the pulse. The resolution of the counter/timer is

0.0001 seconds or less for periods of 10 to 10,000 seconds. The

measured diversion time value is transferred to the data acquisition

system from the counter/timer via an IEEE-488 interface.

In the gravimetric determination of mass flow rate realized in the NBS

flow facility the effective collection time is generally not equal to

the measured diversion time interval. With the diverter valve construction used in the facility, the water flow is actually split between the

chutes leading to the weigh tank and to the reservoir during the move- ment of the valve between its two positions. Pneumatic cylinders are used to actuate the valves . The time required to move the valve from

one position to the other is less than 1 second and varies somewhat with

the size of the diverter. Adjustment of the optical interrupter

switching flag was made to minimize, but could not eliminate, the

correction to the measured diversion times. Measurement and characterization of the diverter correction is necessary for each of the four

weighing and timing systems. Each interrupter switch flag is adjusted

so that the tip of the triangular section of the diverter valve is

located directly below the center of the rectangular chute carrying the

water flow into the valve. With the valve in this position, the interrupter switch flag is adjusted to partially interrupt the switch's light

beam and cause the switch circuit to change state to a logical 1.

Systems 1, 2, and 3 cover a flow rate range of approximately 10:1 with

sufficient overlap to allow measurement of flow rates in these regions

with two weighing/diversion systems, thereby allowing a comparison of

the system's performance. This type of system crossover checking was

-12-
done throughout the development of the data base. In the case of system

4 the diverter valve was modified to include a section of phosphor

bronze sheet which allowed the entrance chute of the diverter valve to

adjust to the flow rate of the water passing over it. The phosphor

bronze sheet thickness was 0.010 inches (0.254 mm). The elasticity of

the sheet causes the edge contacting the side of the diverter chute to

be drawn away from the chute's edge as the flow rate increases. In this

way the cross -sectional area of the water jet is maintained in a rectangular shape of variable thickness over a larger range of flow rates.

The sheet's ends were formed so that a close fit was achieved to eliminate the flow of water through spaces between them and the body of the

valve's upper chute. For this diverter valve the interrupter switch

flag's position corresponded with the chute edge contacting the phosphor

bronze sheet.

Various methods have been devised for adjusting the diverter valve's

switch/flag position or calculating corrections to the measured time or mass values [4,5,6]. The method of Jones [6] is used here for

calculation of the diverter correction and its variation.

The measured time interval is the period of diverter valve movement to

divert water to the weigh tank. This time is large compared to the time

necessary to switch the valve. Because the valve switching characteristics split the water flow between the weigh tank and the return chute, a correction must be made to either the observed time or mass in order to

account for this effect. The value of this correction must be evaluated

for each system. Estimates of the diverter valve correction value at one flow rate are obtained utilizing an auxiliary flow rate measurement

device (in this case a turbine meter) having short-term flow rate

measurement stability. Observations are made for a series of long and

short diversions into the weigh tank. The long observations fill the

weigh tank in a single diversion and are used to determine the turbine

meter's characteristics at the flow rate of interest and over the time

necessary to complete the measurement. Short observations are used to

fill the weigh tank a second time in several diversions. In this way

the cumulative effect of the diverter correction of several diversions

can be determined.

2. Analysis of Diverter Valve Corrections

Gravimetric measurement of the mass flow rate of water in the NBS flow

facility may be modelled with the following relation:

m = M , ^2)

(t + r)

where m = mass flow rate,

M = mass of water collected,

t = measured collection time, and

r = the diverter valve correction.

The time t + r is the effective collection time. The method of estimating the value of r is based on multiple diversions into the weigh tank

over short time intervals, short relative to the amount of time neces-

-13-
sary to fill the tank at the flow rate of interest. Typically 10 short

diversions are used to fill the tank. It is assumed that the value of t is constant for a given flow rate and independent of the diversion time.

Mass flow rate values for these short diversion times may be computed

using eq (2). Determination of the mass flow rate during the short

diversions must be obtained from an auxiliary flow rate measurement

device in the flow system, which has good short-term flow rate measure- ment characteristics. The approximate relationship between the indication of the auxiliary device and the mass flow rate must be known or measured. In this case turbine meters of the appropriate sizes were used because of their excellent short time reproducibility and high

resolution. The relation between the mass flow rate and the output

frequency of the turbine meter is assumed to be the following for each

flow rate

m == Cf

,

where C = turbine meter coefficient, and

f = turbine meter output frequency.

Each determination of the diverter correction is performed in the

following manner. After stabilization of the flow rate in the flow

system (determined by observation of the turbine output frequency)

,

estimates of C are obtained by diversions of the flow which fill the

weigh tank. The mass flow rate is calculated using eq (2) with r set to zero. These mass flow rate values are designated m , and the measured

diversion times, t . Then values of C are calculated using the

o ° relation: m = M /t = Cf , o o o o

where f is the observed turbine meter frequency.

After the first long diversion the weigh tank is drained, and then

refilled using n short diversions. It is again drained and refilled in

a single diversion. This constitutes an observation procedure. The

previously estimated value of C, the meter constant, is used to estimate

the mass flow rate value, m. , for each short diversion time, t. , i.e.,

i' 1 m.11= Cf. for each diversion. Substitution of this relation for the m.'s

1 into eq (2) yields the following relation for the diverter correction,

"i'

r^ = M^/Cf. - t.. (3)

Substitution into eq (3) of the number of turbine meter counts observed

during the diversion gives the working equation for the diverter correc- tion time.

"i t^(M^/N.C - 1), (4)

•14-
where N. = Number of turbine meter counts occurring during t.

.

These estimates are assumed to apply to the same flow conditions during

the series of diversions because once the flow rate has been set prior

to the initial long diversion measurement, the flow rate setting control

valves are maintained in the same position throughout the measurement

cycle. A check of the flow rate stability is made with a long diversion

immediately following the series of short diversions. The mean value of

C for the two long diversions is used to form the meter constant value

used in the computations described below. This also provides a means to

eliminate observation sequences in which the flow rate is not sufficiently constant. The observation procedure comprised the following:

one long diversion which filled the weigh tank,

drain the weigh tank n short diversions which also filled the weigh tank

drain the weigh tank, and

a final long diversion which filled the weigh tank.

Although this procedure yields a set of estimates for the r., it should

be noted that the initial estimate of the value of C is made using zero

as the diverter correction value, thereby introducing an error into the

values of the t.'s. To compensate for this an iterative procedure is

employed to determine the best values for the estimates of the r.'s.

The mean of the n estimated values of r , r , is used to recompute the

value of C using the following relation,

C = M /f^(t^ + r ). (5) o o o m

This new estimate of the value of C is used to recompute the estimate of

the r . values . This procedure is repeated until the difference in the

values of C calculated for two successive iterations is less than a fixed limit. The acceptance criteria were that the differences in

successively calculated values of the turbine meter constant differ by

less than approximately one half the number of digits of precision in

the total number of counts collected during the long diversion time.

Table 2 is an example of the data collected and of the computed results

for a set of diverter correction observations. The table contains three

sections, the short and long diversion parameters and the observed

parameter values. The mean correction time and its standard deviation

are listed below the short diversion parameter list.

3. Diverter Correction Values for Each Weighing and

Timing System

The diverter correction values and their standard error estimates are given in tables 3 through 6 for each of the four weigh tank/diverter

valve systems . For diverter system 1 a flow rate dependence is observed

in the diverter correction for which a quadratic function was fit to the

-15-
data using the least squares technique. This function is used to interpolate through the range of the diverter correction values for this

system. In the case of the other systems the dependence on flow rate is

smaller and the average diverter correction value is used. For each

system the range of the diverter tests has been set to span the flow

rate range. The interpolation relation for system 1 is of the form

r = Y +¥^111 + Y„m^

o 1 2

where m is the mass flow rate in units of pounds/second.

Table 7 lists the coefficients for the system 1 correction function and

the mean values for the other three systems. The residual standard

deviation for the system 1 fit is listed. The values listed in the

residual standard deviation column for the other systems are the

computed standard deviations for the data set.

For the upper flow rate range covered by system 1 the diverter corrections ranged from -0.11 second at 200 pounds/seconds to -0.061 seconds

at 680 pounds/seconds

.

The minimum diversion time for each weighing/diverter system was set at

30 seconds to minimize effects of diverter correction time uncertainty.

These effects are further reduced by using the largest weighing system

to increase the diversion time thereby reducing the relative error.

Tables 2 , and 3 through 6 indicate a contribution to random variation in mass flow rate measurements attributable to scatter in the diverter

correction values. In table 3 it is evident that the estimated value of

the diverter correction varied between days. While the correction for

system 1 was adjusted for the effect of flow rate, there were additional

between-day variations.

The diverter corrections listed in table 7 are average values. The

local diversion time correction applicable at run time cannot be

estimated directly. The residual standard deviations given in table 3 are not direct estimates of the contribution to random error attributable to diversion times, since they were derived from auxiliary

experiments with short diversion times. They do, however, provide a method for approximate estimates of the contribution from this source of

variability to the random error in mass flow rate measurements.

4. Mass Measurement and Uncertainty

Measurement of the mass flow rate using the gravimetric method requires

knowledge of the three quantities discussed above (1) the true mass of

water collected during a diversion, (2) the time of the diversion, and

(3) the switching characteristics of the diverter valve. All mass flow

rate values are stated on a true (vacuum) mass basis and not on an apparent mass basis.

16-
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l_ >* CO rj in o fO r^ in

<D rj rj to to 0«-CMtO>*m>ON-OOC>>0

-17-
Table 3. Diverter Correction Values for System 1

System Date\Time Flow Rate Diverter Std.

No. Correction Error

(Ibm/sec) (sec) (sec)

1 11/25/85-13:43 186.9518 -0.1106 0.0031

1 11/25/85-15:01 219.1919 -0.1152 0.0040

1 11/25/85-15:27 246.7773 -0.1087 0.0035

1 11/25/85-15:52 270.1524 -0.0976 0.0028

1 11/25/85-16:14 301.2940 -0.0959 0.0019

1 11/25/85-16:32 328.2265 -0.0944 0.0042

1 11/26/85-09:31 685.0880 -0.0595 0.0013

1 11/26/85-09:47 678.4531 -0.0580 0.0017

1 11/26/85-10:14 625.9438 -0.0624 0.0013

1 11/26/85-10:29 570.1273 -0.0691 0.0021

1 11/26/85-10:56 519.2268 -0.0720 0.0030

1 11/26/85-11:42 463.8214 -0.0786 0.0029

1 11/26/85-12:04 407.2061 -0.0842 0.0042

1 11/26/85-12:26 353.4898 -0.0880 0.0023

1 11/26/85-13:00 299.7684 -0.0954 0.0029

1 11/26/85-13:19 245.0634 -0.1038 0.0048

1 11/26/85-13:39 190.1348 -0.1175 0.0044

1 11/26/85-14:35 356.7263 -0.0936 0.0033

1 11/26/85-15:00 411.1569 -0.0784 0.0023

1 11/26/85-15:19 465.2753 -0.0750 0.0018

1 11/26/85-15:36 517.8587 -0.0739 0.0016

1 11/26/85-15:52 573.6771 -0.0694 0.0026

1 11/26/85-16:11 628.4513 -0.0667 0.0014

1 11/26/85-16:28 680.1666 -0.0635 0.0018

1 11/29/85-13:51 272.2335 -0.0994 0.0039

1 11/29/85-14:47 273.2980 -0.1037 0.0043

1 11/29/85-15:10 273.3920 -0.1054 0.0037

1 11/29/85-15:33 327.8049 -0.0885 0.0037

1 12/02/85-14:09 274.1538 -0.0989 0.0034

Tabl e 4. Diverter Correction Value s for System 2

System Date\Time Flow Rate Diverter Std.

No. Correction Error

(Ibm/sec) (sec) (sec)

2 11/25/85-11:14 192.4332 0.0274 0.0015

2 11/25/85-11:55 172.5101 0.0292 0.0016

2 11/27/85-08:50 171.1529 0.0272 0.0008

2 11/27/85-09:34 136.4090 0.0297 0.0013

2 11/27/85-10:20 100.6641 0.0336 0.0018

2 11/27/85-10:53 67.5246 0.0345 0.0022

2 11/27/85-11:57 54.8271 0.0289 0.0034

2 11/27/85-14:22 36.5908 0.0194 0.0034

2 11/27/85-15:53 171.7879 0.0297 0.0011

2 11/27/85-16:32 136.1678 0.0272 0.0019

2 04/15/86-22:14 35.9134 0.0262 0.0032

2 04/15/86-22:42 45.6147 0.0285 0.0023

18-
Table 4. Diverter Correction Values for System 2 -- Continued

System Date\Time Flow Rate Diverter Std.

No. Correction Error

(Ibm/sec) (sec) (sec)

2 04/15/86-23:02 55.7667 0.0265 0.0015

2 04/15/86-23:23 63.8362 0.0253 0.0025

2 04/15/86-23:43 74.0715 0.0262 0.0019

2 04/15/86-01:33 110.3024 0.0259 0.0014

2 04/15/86-01:55 128.9345 0.0231 0.0013

2 04/15/86-03:21 146.5766 0.0219 0.0006

2 04/15/86-04:18 165.6850 0.0218 0.0011

2 04/15/86-04:54 53.3422 0.0260 0.0027

2 04/15/86-05:14 36.4864 0.0258 0.0033

.2 04/15/86-05:32 73.1850 0.0251 0.0021

Table 5. Diverter Correction Values for System 3

System Date\Time Flow Rate Diverter Std.

No. Correction Error

(Ibm/sec) (sec) (sec)

3 04/16/85-11:49 7.9051 -0.0044 0.0020

3 04/16/85-12:16 8.9890 -0.0030 0.0016

3 04/16/85-12:40 8.9768 -0.0047 0.0015

3 04/16/85-13:01 10.3343 -0.0039 0.0011

3 04/16/85-13:20 10.3402 -0.0043 0.0011

3 04/16/85-13:37 5.7960 -0.0081 0.0019

3 04/16/85-14:04 5.1774 -0.0030 0.0024

3 07/22/85-08:55 49.3029 -0.0014 0.0030

3 07/22/85-09:15 36.7209 -0.0175 0.0037

3 07/22/85-09:37 36.7364 -0.0190 0.0054

3 07/22/85-09:57 25.6210 -0.0139 0.0018

3 07/22/85-10:13 14.8649 -0.0228 0.0032

3 07/22/85-11:14 15.0275 -0.0194 0.0051

3 07/23/85-15:50 4.0684 -0.0085 0.0036

3 07/24/85-08:14 49.5016 -0.0234 0.0075

3 11/29/85-10:28 18.2016 -0.0292 0.0079

3 11/29/85-10:48 36.7179 -0.0145 0.0011

3 11/29/85-11:08 55.0695 -0.0144 0.0006

3 11/29/85-11:44 18.2981 -0.0241 0.0058

Tabl e 6. Diverter Correction Values for System 4

System Date\Time Flow Rate Diverter Std.

No. Correction Error

(Ibm/sec) (sec) (sec)

4 04/15/85-16:08 1.4913 -0.0270 0.0119

4 04/15/85-16:31 2.6062 -0.0051 0.0060

4 04/15/85-17:02 3.7676 -0.0110 0.0036

4 04/15/85-17:17 5.2978 -0.0093 0.0015

4 04/15/85-17:35 6.0342 -0.0066 0.0011

19-
Table 6. Diverter Correction Values for System 4 -- Continued

System Date\Time Flow Rate Diverter Std.

No. Correction Error

(Ibm/sec) (sec) (sec)

4 04/15/85-17:51 1.5482 -0.0191 0.0041

4 04/15/85-18:10 5.1259 -0.0056 0.0019

4 04/15/85-18:22 5.9767 -0.0041 0.0008

4 04/15/85-18:32 3.6967 -0.0117 0.0017

4 04/15/85-18:43 2.6380 -0.0132 0.0019

4 04/25/85-09:16 1.6632 -0.0159 0.0046

4 04/25/85-09:37 1.6748 -0.0131 0.0030

4 04/25/85-10:14 1.3606 -0.0131 0.0061

4 04/25/85-11:42 1.1159 -0.0118 0.0047

4 04/25/85-12:09 0.9225 -0.0117 0.0070

4 04/25/85-12:43 0.7000 -0.0366 0.0204

4 04/25/85-13:23 0.4651 -0.0154 0.0108

4 07/24/85-00:05 1.6630 -0.0031 0.0031

4 07/24/85-00:22 1.3893 0.0007 0.0046

4 07/24/85-00:43 1.0771 0.0002 0.0069

4 07/24/85-01:06 0.9526 0.0001 0.0049

4 07/24/85-01:32 0.6874 -0.0011 0.0101

4 07/24/85-02:06 0.4638 -0.0084 0.0097

4 07/24/85-03:26 0.2356 -0.0044 0.0222

Table 7. Diverter Correction Interpolation Function Coefficients

System Y

o ^1 \

Residual

Std. Dev

(sec)

2 (sec /Ibm) (sec /Ibm ) (sec)

0.1529 2 .26229 xlO"^ -1.34741 X 10"•7 0.0030

0.0268 0.0035

0.0126 0.0087

0.0103 0.0087

a. Measurement of the Mass of Water Collected

Once the water has been collected in the weigh tank and the transients

associated with filling it have ceased (indicated by the scale indicator

through its scale motion index) , successive observations of the scale

indication are made by the data acquisition system, averaged, and the

average value is stored in the data base. The scale indicator was adjusted internally to indicate directly in mass value based on a

3 stainless steel mass scale of density of 8.0 g/cm [7] for three of the

four weighing platforms. These were system 2 (10,000-pound capacity),

system 3 (2,000-pound capacity), and system 4 (400-pound capacity).

This adjustment to the indicator was possible because these scales could

be loaded to near their capacity with a known mass standard. However,

this could not be done on system 1 (50,000-pound capacity). A calibration function was necessary, and was developed using the scale calibration procedures described below.

-20-
The observed mass of water in a weigh tank is an apparent mass value.

The true or vacuum mass value is computed by accounting for the buoyant

effect of the atmosphere upon the water. In the case of water, with a

3 nominal density of 1 g/cm , immersed in air, having a nominal density of

3 0.0011 g/cm , the effect of air buoyancy on the true mass value of water

has a relative magnitude of approximately 1 part in 1000. The buoyancy

effect acts to decrease the mass value observed by a weighing device

since the buoyant force of the atmosphere is oppositely directed to that

of the force of gravity. Therefore, the apparent mass of water is the

difference in the observed mass with the tank empty and filled. The

relationship between the apparent mass value and the true mass value is

the following:

M^ = M /{\ - p /p ), (6)

t app' a! w

where M = true mass value,

M = apparent mass value,

app ^^

p = density of the atmosphere, and

p = density of the water.

'^w •'

b. Scale Calibration Procedures and Mass Standards

Calibration of the weighing scales used a sequential, incremental

loading method based on working mass standards calibrated at NBS . These

working mass standards were calibrated using primary mass standards at

the 50- and 500 -pound level. Two sets of working mass standards were used for calibration and for checking of the operation of the weighing

scales. For all systems other than system 4 the calibration procedures

required the use of partial fills of each scale's weigh tank with water

to calibrate the full -use capacity of the scale. In the case of system

4 (400- to 600 -pound capacity) a sufficient number of mass standards

were available to complete the calibration without partial water fills.

The sequential, incremental method of scale calibration utilizes the

following operations:

1. Close the drain valve of the weigh tank and record the scale

indication.

2. Place the desired mass standard(s) on the scale and record the

scale indication.

3

.

Repeat step 2 until the scale capacity has been reached or all

of the mass standards have been used.

4. For systems 1, 2, and 3 remove the mass standards from the scale

and fill the tank until the scale indicator value is identical

to that obtained in the last iteration of steps 2 and 3. Care

must be exercised to match the value indicated when loaded with

the mass standards. Small additions or removal of water may be

necessary to achieve this. The weigh tanks of systems 1 and 3 were fitted with small drain valves for this purpose. System 2

21-
had easy access from the top of the weigh tank for addition or removal of small amounts of water.

5. For system 4 only steps 2 and 3 were used. Additionally, after

reaching scale capacity the mass standards were removed

sequentially and the indication recorded.

Scale calibration procedures were performed at various times during the

data collection phase of the project. The performance of systems 2 through 4 was such that the difference between the indicated mass value

and the true mass value of the standards was at most one unit of the

indicator. Checking of the scale performance was done each day of data

collection by placing a stack of the working mass standards on the scale

in use. The mass value indicated was stored in the data base. The

difference between the mass standard's mass value and the indicated

value was rarely greater than one indication unit.

Calibration Equation for System 1

As discussed above, the near equality between the indicated and actual

mass values achieved by the other scales was not the case for system 1,

since the scale could not be loaded with a standard of mass 40,000 to

50,000 pounds. Therefore, the indicator input channel for this scale was installed without second order response compensation as was the case

for the other scales. Coefficient values for a quadratic equation were obtained using the least squares method from scale calibration data.

This relation is given below:

M = -0.693 + 0.9957774 I + 7.86096 x 10

.2

where M = mass value, and

I = scale indication.

The residual standard deviation for the fit is 2.36 pounds. Three times

this value, 7.08 pounds, is taken as the uncertainty in the mass value

determination

.

50 -Pound Working Mass Standards

Two sets of mass standards were used for the scale calibration procedures. A set of 12 cast iron, 50 -pound weights were refurbished, given

numerical designations, and calibrated against the NBS primary 50-pound

mass standards using comparative methods. The mass values assigned to

these working mass standards are listed in table 8.

The comparative precision attained in the assignment of the mass values

to these weights is less than 0.0001 pounds. The uncertainty in the

primary mass standards is approximately 0.000005 pounds. Therefore, the

total uncertainty of the mass value assigned to one of these weights is

less than 0.0001 pounds. The uncertainty in the mass values of the

weights may be taken as the sum of these two uncertainties, or 0.000105

pounds for each weight.

22-
Table 8. 50-Pound Working Standard Mass Values

Weight True Mass Value Weight True Mass Value

Number (lb) Number (lb)

1 49.949 7 49.979

2 50.000 8 49.941

3 49.997 9 49.994

4 49.965 10 49.995

5 49.995 11 50.001

6 50.005 12 49.946

Mass Value of the 12 Weight Summation = 599.767 pounds.

Uncertainty in the Mass Value = 0.0012 pounds

For scale calibration purposes the uncertainty of interest is the total

uncertainty of the weights on the scale. An estimate of the maximum

uncertainty of the mass standards used for scale calibration is obtained

for the 600-pound summation of all 12 weights which would have an uncertainty of 0.0012 pounds at most. These working standards were used

for calibration of the scales in systems 2, 3, and 4. The uncertainty

value of 0.0012 pounds is at least 10 times smaller than the sensitivity

of the smallest scale used, system 4 with a sensitivity of 0.02 pounds.

Therefore, the contribution of the mass standards to the uncertainty of

the calibration procedure is not detectable by the scale and is negligible in its effect on scale calibration.

500 -Pound Working Mass Standards and Actuator System

A set of working standards each near the 500 -pound level were used for

calibration of the 50,000-pound scale of system 1. Nine of these stainless steel weights were incorporated into a hydraulically actuated

loading system permanently attached to the bottom of the scale's weigh

tank. The suspension arrangement is shown diagrammatically in figure 4.

The system consists of three stacks of three weights each placed S3rmmetrically around the frame of the scale. The hydraulic actuators and

the weight hangers become a permanent load on the scale and are attached

to the weigh tank bottom. The weight hangers are suspended so that,

with the actuators fully extended, the weight stacks rest fully on their

floor support and the hangers swing freely. Loading of the weights onto

the scale is accomplished by retracting the actuators with the hydraulic

pump mounted to the weigh tank. Mounting of the pump, actuators, weight

hangers and interconnecting hoses to the weigh tank, allows only the mass standards to be loaded and unloaded onto the scale. In this way

the movement of hydraulic fluid between the pump and actuators does not

constitute an unknown and variable, additional load on the scale during

calibration procedures.

The nine stainless steel working standards were assigned mass values

using the same double substitution weighing procedures employed in the mass value assignment of the 50-pound working standards. Four sets of

observations were performed on each weight over a period of several

days. The comparative device used was a 2,500-pound platform scale with

a mechanical dial indicator having scale graduations of 0.2 pounds.

•23-
Weigh Tank Bottom

<////// /// 7 / /////////////////y /Tl w?m

Weight Hanger

Hydraulic

Actuator

U-Joint Coupling

500 Pound

Mass Standards

Floor

Support

Figure 4. Hydraulic Mass Standard Loading Mechanism for

50, 000 -Pound Scale Calibration

24-
This scale was selected because these mass standards were to be used for

calibration and checking of the 50,000-pound scale which had an indication sensitivity of 5.0 pounds. It was desired to have a cumulative

uncertainty in the nine weight summation no greater than approximately

one half of the indication sensitivity. The mass values assigned to

these nine weights are listed in table 9 with the comparative precision

of each assignment procedure, which is three standard deviations of the

mean value. The uncertainty in the 500-pound standards used in these mass value assignment procedures is 0.01 pounds.

Table 9. 500 -pound Working Standard. Mass Values

Weight Mass Value Precision Weight Mass Value Precision

Desig. (lb) (lb) Desig. (lb) (lb)

16515 487.739 0.108 165165 489.298 0.056

165142 487.002 0.086 165173 487.843 0.192

165150 489.146 0.173 165174 489.230 0.074

165151 487.632 0.197 165176 487.814 0.105

165155 489.350 0.152

Mass Value of the Nine Weight Summation = 4,395.06 pounds

Uncertainty in the Mass Value = 0.44 pounds

The uncertainty in the mass value of the summation of weights is the

root sum of squares of the precisions of the individual masses.

c. Uncertainty in the True Mass Value of Water Collected

The analysis of uncertainty in the measured mass value of water is based

upon eq (6) . The elements contributing to the uncertainty of the observed true mass value are the observed mass value of the water collected and the density values of the atmosphere and water, which account

for the buoyant effect of the atmosphere in the weighing process.

Uncertainty in the Observed Mass Value

The uncertainty in the observed mass value is composed of (1) the

uncertainty in the scale indication itself and (2) the uncertainty in

the mass standards used in the scale calibration procedures . For this

project the objective of assignment procedures for the working mass standards was to obtain a total uncertainty in the assigned mass value

substantially below the minimum indication sensitivity of the scales.

The variation in the indication of the mass value of each scale is

modelled as a random process for these scales, which were sensitivitylimited, and, therefore, contributed finite levels of uncertainty to the

measurement process. The uncertainty assigned to the indication alone

is taken as the square root of 2 times the indication sensitivity based

on the following asstunption. For a fixed mass on the scale, its mass value has an equally probable chance of lying above or below the position within a particular indication interval at which the indication is

forced to the next interval, and is treated as a random effect. This

digitization effect accounts for a substantial portion of the total mass

•25-
measurement uncertainty in the case of systems 2 through 4 since these

scales were shown to be direct reading to a high degree. For the scale

of system 1 the fitting procedure used to obtain the scale calibration

equation's coefficients gives the indication uncertainty. The indication uncertainty for this scale is taken as three times the residual

standard deviation to the fit. This value (3 x 2.36 pounds or 7.08

pounds) also equals the scale resolution multiplied by the square root

of 2. It appears that this scale is also resolution limited. Additionally, one can conclude that the addition of water to the tank neces- sary to incrementally load the scale to capacity during the calibration

procedure introduces an undetectable level of variability into the calibration process. Otherwise the J2. multiplied by the indication sensitivity would be less than three standard deviations of the scale calibration fit.

The absolute uncertainty in the observed mass due to uncertainty in the

calibrating mass standards is dependent upon the magnitude of the load,

the calibration method, and the uncertainty in the summation of mass standards used in calibration. The mass used to load a scale during

calibration may be termed a virtual mass standard, which is composed of

the summations of the mass standards discussed above combined with an appropriate amount of water. The need for the concept of a virtual mass standard arises from the lack of mass standards of sufficient size to

fully load the scales with mass standards only. The virtual mass standard is considered to be composed of an integral number of summa- tions of the actual mass standard used. As described above in the

calibration procedures, this weight summation is applied to the scale

incrementally combined with a sufficient amount of water. Therefore,

the uncertainty in this mass value will be the uncertainty in the actual

standard weight summation, s , multiplied by the number of steps neces- sary to achieve the desired level of scale load. For example, using the

large summation listed in table 9 with scale 1, 10 summations yields a load of 43,950.5 pounds. The uncertainty in that value is 2.8 pounds,

i.e., 10 times the uncertainty in the mass standards themselves.

Of course, when the scale is used, integer multiples of the standard

mass involved in calibration are rarely encountered. Therefore, the

multiplier necessary to calculate the absolute uncertainty, s , in the

observed mass value, M, due to the calibrating weights is the ratio of

the observed water mass to the mass value of the calibrating weight

summation mass, M , i.e., 4,395.05 pounds for scale system 1 and 599.77

pounds for scale systems 2 and 3, as shown below:

s = s * (M/M ) . ma w ' s To facilitate the combination of the various uncertainty components in

subsequent discussions, each will be expressed as a relative value.

Therefore, the relative uncertainty in the observed mass of water

becomes

s /M = s /M . ma w' s Relative uncertainties in the observed mass values are tabulated in

table 10. Typical values of observed mass are used for each scale

system. The relative uncertainty in the mass value due to the scale

26
indication and to the mass standards are computed using the observed

masses (load) and indicator uncertainty, and the mass values of the

standards and their respective uncertainties.

Table 10. Uncertainty in the Observed Mass Value of Water

System Load Indicator Mass Std. Total

No. Sens

.

Uncer

.

Rel. Uncer. Rel. Uncer Rel. Uncer

(lb) (lb) (lb) (%) (%) (%)

1 40,000 5.0 7.08 0.018 0.008 0.026

2 5,500 0.5 0.71 0.013 0.0002 0.013

3 1,800 0.1 0.14 0.008 0.0002 0.008

4 350 0.02 0.03 0.008 0.0002 0.008

Calculation of the Densi.tv of the Atmosphere and Its Uncer taintv

The uncertainty in the buoyant effect of the atmosphere is dependent

upon that of the air and water density values. Due to the magnitude of

the ratio of the air density to the water density, the effect on the

total uncertainty of the weighing process may be made acceptably small

for the requirements of this work with only modest efforts in the determination of the individual values of the two. The atmospheric parameters of barometric pressure, air temperature, and relative humidity

were measured for calculation of the density of air. The density of air was calculated using the relation developed by Jones [8] , see eq (7)

below. Temperature of the water in the collection tanks was also

measured.

Calculation of the air density values was made using Jones' formula

which is given below.

Pm ^ m RH f P A P =_L{i -d - J! ) Ll], (7)

RT Z

'^ m 100 P

J a a

3 where p = density of air (kg/m )

,

Si P = barometric pressure (pascals)

,

Z = compressibility factor for air,

T = absolute air temperature (Kelvin)

,

a. RH = relative humidity (%)

,

P = saturation vapor pressure of water (pascals)

,

R = molar gas constant (8315.31 J/(K-kmole) )

,

m = 28.963 g/mole = molecular weight of air,

a. m = 18.0152 g/mole = molecular weight of water, and

f = enhancement factor.

e

The saturation vapor pressure is calculated from the following relation:

P = 1.7526 X lO-*-^ exp (-5315. 56/T ). S cL

-27-
The enhancement factor is calculated from the following relation:

f = 1.000 + 3.113 X lO'^P + 5.4 X lO"^ T^

e a The primary contributors to day-to-day uncertainty in the calculated air

density value are the measured values of temperature, pressure, and

relative humidity. The uncertainty in the air density value due to

uncertainties in the molecular weights of water and air, the enhancement

factor, and saturation vapor pressure of water, are thoroughly discussed

by Jones and combined contribute less than 0.05% to uncertainty in the

air density value.

Barometric pressure measurements were made using an aneroid barometer

which was kept in the flow laboratory during the course of the experiment. This barometer was checked against an NBS transfer standard

periodically and found to differ from the transfer standard by no more

than 0.2 millimeters of mercury, or approximately 0.03% of the

barometric pressure.

Air temperature measurement in the flow laboratory was made with a thermistor. This measurement and its uncertainty is discussed in more

detail in part E of this section. Due to the very local nature of this

measurement, the uncertainty of the measurement is estimated to be one degree Celsius. This value is considerably larger than that estimated

from its calibration, and has been increased to include the effects of

temperature gradients within the laboratory. This estimate corresponds

to a relative uncertainty in the air density value of 0.3%.

Measurement of the relative humidity of the air in the flow laboratory

was made with a hygrometer for which the estimated uncertainty was 5%

relative humidity. The table below provides a means to estimate the

effect of this uncertainty level. The density of air has been computed

using eq (7) for both the wet and dry gas cases. The saturated gas case

is given in the table and the percentage difference in the density

calculated for the wet and dry gas case is listed for each relative

humidity level. Inspection of the table for the relative humidity range

from 30 to 50% shows that an error no greater than 0.1% in the air

density value may result from an error in the relative humidity

measurement of 5% RH.

Air Density Values at 1 Atmosphere (760 mm of Mercury) and 20 °C,

Over the Range of Relative Humidity Values to 100% , Showing

the Effects of Neglecting Humidity in the Calculation

Relative Air Difference Relative Air Difference

Humidi ty Density Humidi ty Density

(%) (g/cm ) (%) (%) (g/cm ) (%)

0.0012045 0.00

10 0.0012034 -0.09 60 0.0011982 -0.53

20 0.0012024 -0.17 70 0.0011971 -0.62

30 0.0012013 -0.27 80 0.0011961 -0.70

40 0.0012003 -0.35 90 0.0011951 -0.79

50 0.0011992 -0.44 100 0.0011940 -0.88

28-
The compressibility factor, Z, is dependent upon the barometric pressure

and temperature and slightly dependent upon the CO^ content of the air.

Its value ranges from 0.9995 to 0.9998 for the ranges of pressure and

temperature encountered in this work. The levels of uncertainty for the

temperature and pressure discussed above are sufficiently small that

uncertainty in the air density value due to uncertainty in the compressibility value may be neglected.

The pressure, temperature, relative humidity, and gas molecular weight

error contributions are considered to be systematic in nature and are,

therefore, combined additively. The summation of these is no larger

than 0.5% in the air density value.

Uncertainty in the Value of the Density of Water

Calculation of the density of water uses the measured temperature of the

water in the weigh tank to compute the density of water using the relation of Kell [9]. A discussion of this method is given later in part E

of this section of this report and in Appendix B. The uncertainty in

the value of the water density calculated from the observed temperature,

including effects of dissolved minerals in the flowing water, is no greater than 0.02%.

Uncertainty in the Buoyancy Correction

The uncertainty in the buoyancy correction applied to the observed mass

of water arises from uncertainties in the density of the air and the

water. The relative uncertainty in the water density is given above as 0.02%, and that for the air density is 0.5%. Substituting eq (6) into

eq (2) and taking the partial derivatives of eq (6) with respect to the

density of the water, p , and of air, p , and dividing these by the

resultant expression for mass flow rate, gives the following

expressions. These expressions give the relative uncertainty values in

the mass flow rate due to uncertainty in the buoyancy correction term of

eq (6). Substitution of a nominal value for the density of air (0.00117

3 3 g/cm ) and of water (1.0 g/cm ) gives values for the relative magnitudes

of these effects.

1 3m -1 Am p Ap • = a a m p -p p

'^w ^a a

Am p Ap

; = ^a ^w

•m p -p p

"^w ^a w

m dp^ ^w-^a

1 dm

^^w

-Pa

•m ^w'^a

Water Density Contribution = 2.34 x 10

Air Density Contribution = 5.8 x 10

•7

29-
The magnitude of these effects combined additively or in quadrature are much less than the contribution of any of the other parameters affecting

the determination of the true mass of water collected. The magnitudes

given above will be combined additively to give a total relative uncer- tainty in the buoyancy correction for the mass of water as 6 x 10 ,6

parts per million (ppm) or 0.0006%.

The atmospheric parameters, i.e., barometric pressure, air temperature,

relative humidity, may vary during an experimental run and there may be

variable gradients within the laboratory. Thus the buoyancy correction

may not correct precisely for their effects, and the atmospheric effects

contribute to the random variations that are observed in differences

between repeated runs

5. Mass Flow Rate Measurement Uncertainty

The complete expression for the mass flow rate may be written

m = M/[(l - pjp^) (t + r)]. (8)

The uncertainty•^ in the mass flow rate, s» , is the combination of m

uncertainties in its independent variables which will be represented in

relative terms . Random and systematic uncertainties will be combined in

quadrature and additively, respectively. Each of the contributing

parameters in eq (8) has been discussed in preceding sections and is

tabulated in the following table.

Summary of Mass Flow Rate Uncertainty Components

Contributing Variable Random Systematic

Component Component

Observed Apparent Mass s^/Vl s /M

Diversion Time s /t

Diverter Correction s /t

r Buoyancy Correction 6 ppm

With this separation of error components into random and systematic

parts, the following expression may be written as the relative

uncertainty in the observed mass flow rate.

!m = [ (Sj/M^)^ + (s^/t)^ + (6 ppm)^ ] ^/^

m

s s.

M t

s where s = indication uncertainty, see table 10,

s = uncertainty in the mass standards, see table 10,

s = uncertainty in the diversion time measurement, taken as 0.0001 sec.

(9)

30-
M =

uncertainty in the diverter valve correction, see table 7,

three residual standard deviations are used for the value

of s , r total mass of water collected, and

mass of the standards used in calibrating the scale.

Substitution of numerical values for each term gives the following table

for the measurement uncertainty of the NBS water mass flow rate

measurement system. Each weighing system is treated individually with

30-, 90-, and 200-second diversion times used to give an estimate of the

range of uncertainty values.

Table 11. Measurement Uncertainty of the NBS Water Flow Rate

Measurement Facility

Sys Collected

Mass

(lb)

Diversion

Time

(sec)

Random

Uncertainty

(lb)

Systematic

Uncertainty

(lb)

Total

Uncertainty

(lb)

41,700^

50,000

50,000

30

90

200

0.020

0.015

0.014

0.010

0.010

0.010

0.030

0.025

0.024

5,800^

6,000

6,000

30

90

200

0.017

0.012

0.012

0.0005

0.0003

0.0002

0.017

0.013

0.012

1,650^

2,000

2,000

30

90

200

0.030

0.012

0.008

0.0005

0.0003

0.0002

0.031

0.012

0.008

165^

400

400

30

90

200

0.034

0.012

0.009

0.0006

0.0004

0.0004

0.035

0.013

0.009

Random variations

differences betwe

pheric variations

correction value,

variable than the

provides only for

uncertainty canno

final statistical

due to unknown

en repeated runs may not be prec

Also, the effe

measurement of

an average dive

t be estimated s analysis of obs

effects contribute indirectly as

, e.g., the correction for atmosisely reflected by the buoyancy

ctive collection time is more

time. The diverter correction

rsion time. These contributions to

eparately, but are included in the

erved discharge coefficients.

Maximum collected mass at the highest flow rate for this system

31-
D. Differential Pressure Measurements Systems and Standards

1. Differential Pressure Measurement Requirements

Measurement of the differential pressure at the orifice meter taps was

one of the primary measurements made during this project. The criteria

used in selecting the methods to be used for this measurement were:

(1) The method must significantly reduce or eliminate the need for

manual transcription of data, and therefore, the error rate

associated with it, and be compatible with the automated data

acquisition and storage techniques.

(2) The method must incorporate working standards of pressure for

in- situ calibration of differential pressure measurement

devices

(3) The method must be capable of an accuracy consistent with the

capability to measure the mass flow rate of water passing

through the orifice meter, or as best as can be achieved with

state-of-the-art instrumentation.

(4) The transduction devices must have the capability to maintain

this accuracy level between successive pressure calibrations.

2. Differential Pressure Transducers

Reduction of human error in the differential pressure measurement system

required replacement of the traditional flow laboratory differential

pressure measurement devices, i.e., water and mercury manometers, and

substitution of differential pressure transducers. These provided

compatibility with electronic data acquisition and storage technology.

In order to reduce the calibration interval of the transducers, and

satisfy requirement 3, high quality, laboratory type transducers were

used. These transducers were selected for their sensitivity and

stability of performance. Two types of transducers were used. Both

utilized quartz as the pressure -sensing material which gives excellent

stability and reproducibility in pressure measurements when applied

properly. Pressure- sensitive electronic quartz oscillator- type

transducers were connected to both the upper and lower pressure taps of

the orifice meter. A quartz bourdon tube instrument was connected in

parallel at the upper taps with the oscillator- type transducer. The

quartz bourdon tube transducer was a Ruska DDR- 6000 [3], and the quartz

oscillator- tjrpe transducers were manufactured by Paros Scientific [3].

The maximum working, differential pressure of the transducers was approximately 28 psid (800 inches of water, 193 kilopascals) . The

quartz bourdon tube transducer utilizes a force balance servo technique

and is capable of 100% overrange without damage. Due to this

overranging capability, the range of this transducer is selected to be

28 psid. The quartz oscillator- type of transducers were capable of a 20% overrange without damage. To minimize the possibility of damage to

these transducers the range was selected to be 40 psid. Both types of

-32-
transducers were used over the range of 28 psid in the flow testing

procedures

.

In the initial stages of the project a second set of quartz oscillator

type transducers were acquired and used, which had a range of 12 psid.

These devices were destroyed due to overranging and were not used for

the final data collection phase of the project.

3 . Pressure Transducer Mounting and Fluid Isolation

Interfaces

The differential pressure measurement system manifold is shown schematically in figure 5. Three transducers and two deadweight testers were incorporated in the final system. The two pneumatic deadweight testers

were the working standards of pressure for the measurement system, and

were used to calibrate the transducers used for measurement of

differential pressure developed across the orifice meter.

Two mechanical gauges were incorporated in the system for operational

purposes. The differential pressure gauge (marked AP gauge on the

schematic in fig. 5) was used for gross setting of the flow rate values

during flow testing, and a mechanical bourdon tube pressure gauge was used to maintain the back pressure at the downstream side of the orifice

meter near 41-psig. This was done to eliminate the possibility of

cavitation around the orifice itself. Previous experience at NBS had

indicated that in the case of turbine flow meters , cavitation at the

tips of the turbine blades causes erratic behavior of the turbine.

Therefore, as a precaution, a relatively high and fixed backpressure was used throughout the tests performed in this project. The pumping system

had the capability to produce a maximum of 90 to 100 psig. Therefore, a 41-psig pressure maintained at the downstream orifice tap was sufficiently low to attain the highest differential pressures planned

for the flow testing, and still suppress cavitation around the orifice.

Each of the differential pressure transducers was filled with silicone

oil to protect its sensing region from the corrosive effects of water.

As a result considerable complexity was added to the connection manifold

as is indicated in figure 5 . Each transducer had to be connected both

to the deadweight testers for calibration, requiring an oil to gas

interface, and to the appropriate orifice meter taps, requiring an oil

to water interface, for differential pressure measurement. As is shown

in figure 5 each transducer was connected to the rest of the pressure

transducer manifold through a five -valve manifold and a set of sight

glasses in which the interfaces were contained. Detailed schematic

diagrams of these manifolds are shown in figures 6 and 7 for the two

types of transducers. The five-valve manifold allowed the transducer to

be connected to pressures developed in either of the other two working

fluids, and the transducer's test and reference pressure ports to be

connected together, i.e., crossed over, to produce a zero differential

pressure condition at the transducer. An oil reservoir was placed in one side of the five -valve manifold/piping connections to each

transducer.

33-
gau

bO

•i-i a

•u

cdgo

eno

M-l •Ha

cd au

<uo

0)c

cd

5-1 H

a>u

CO

CO

a>u

cd

•i-t

<u

(4-4

in

bO

•i-l PE4

-34-
To sump

To

dead weight

testers

Air-oil

interface

-

I,^

Water-oil

interfaces-*

To orifices meter taps

To other

transducers

Bellows pump

Test

oil reservoir

pressure side

^

Air-oil

interface

PAROS

AP

transducer

Reference pressure side

Figure 6. Schematic Diagram of Interface Sightglasses and

Five -Valve Manifold for the Paros-Type Transducers

35-
RUSKA AP Transducer

To

dead weight

testers

y^

Air-oil

interface

^\

Bellows

pump oil reservior

Test pressure side

^

^

Air-oil

interface

Oil-water

interfaces

To orifice

meter taps

Reference pressure side

Figure 7. Schematic Diagram of Interface Sightglasses and

Five -Valve Manifold for the Ruska Transducer

-36-
This reservoir is composed of a screw- driven bellows having a capacity

of several cubic centimeters. Use of the reservoir with appropriate

setting of the manifold valves allowed oil to be moved around the

manifold/sightglass circuit to equalize the meniscuses in the two sets

of sightglasses of each transducer. Two arrangements of this type of

manifold were necessary to accommodate silicone oils of differing

density. The silicone oil filling the Ruska transducer had a density

less than water while that filling the Paros transducers had a density

greater than that of water. Therefore, the requirements of stable

oil/water menisci for the two required somewhat different physical

arrangements for the sightglass pairs.

The presence of these interfaces provides for the possibility of the

continuous introduction of systematic errors into the pressure measure- ment system through imbalance in the heights of columns of liquids of

differing density on the two pressure ports of a transducer. Such an error could occur either during transducer calibration procedures or during orifice meter differential pressure measurements. To minimize or reduce such an effect, a method was necessary to provide a stable and

reproducible horizontal reference plane relative to which each pair of

menisci could be compared and equalized. A specially designed rack was built to mount the differential pressure transducers incorporating a telemicroscope mounted on a travelling carriage to provide the horizontal reference plane necessary to determine and set the heights of each

pair of menisci. The carriage was mounted via ball bushings on two

precision-ground rods rigidly attached to the rack. Screw adjustments

of the rack allowed the rods to be maintained in a horizontal plane with

sufficient accuracy to make negligible the cosine errors in the heights

of the interfaces due to the separation of the two sightglasses forming

a set. These separations were approximately 3 inches (7.5 cm) for the

oil/water set and 6 inches (15 cm) for the oil/air set. The transducer

rack with the telemicroscope carriage is shown in the photograph of

figure 8. Precision machinists levels were used to maintain the plate

carrying the ball bushings in the horizontal plane.

Balancing the height of a set of menisci for a transducer was achieved

by adjusting the telemicroscope until its horizontal reticle was coincident with the bottom of the meniscus of the transducer's reference

port. The telemicroscope' s carriage was then moved until the meniscus

of the transducer's test port was in the telemicroscope' s field of view.

Adjustment of the meniscus height to the telemicroscope' s horizontal

reticle reference was made with the bellows pump. These balancing

procedures were used during both orifice meter testing and during

transducer calibration. The telemicroscope was used frequently to

monitor the positions of the interfaces during measurement operations.

The tubing used to construct the transducer manifold was nominal 3/8-

inch-diameter polyethylene tubing compatible with compression fittings.

As shown in figure 6, each side of the manifold could be bled through

two valves located above the manifold. This allowed elimination of air

bubbles in the manifold. Not shown were two 1/2- inch- diameter ball

valves located at the ends of the tubing connecting the manifold to the

37-
E

(U •uw

Qiaoo

COouua

0)

t-l

0) H

bOC

4-> a> w

bO

•r-l a>mow

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0)

5-1 bO

•i-i fa

-38-
orifice meter taps. These allowed the manifold to be isolated from the

orifice meter until flow had been established through the orifice meter,

producing a differential pressure near the desired flow rate set point.

Approximately 10 feet of the 3/8 -inch plastic tubing connected the

manifold to the orifice meter.

4. Working Pressure Standards

To calibrate the differential pressure transducers, pressure standards were configured to match the use conditions of the transducers as closely as practicable. Since the downstream orifice meter taps were maintained as near 41 psig as possible during data collection procedures

in flow tests, the working standards were configured to allow the

accurate setting of the 41-psig back pressure value on the reference

port of the transducers. This required two deadweight testers. These were of the ball type of pneumatic tester [10] and had the capability to

develop pressures up to 300 psig, although they were not used above

approximately 70 psig in this work.

Both deadweight testers were calibrated by the NBS pressure standards

group on two or three occasions. These calibration data produced an effective area for the ball and an uncertainty in its value. The

results of these calibrations showed the ball area values for the two

testers to be stable with time and use. Additionally, no pressure

dependence of the ball area was determined for either instrument. Mass

values were assigned to the weights, the ball, and the weight carriers

of each tester. These values coupled with the area of each ball, the

local acceleration of gravity (9.801018 m/s ) and the atmospheric

parameters (barometric pressure, humidity, and air temperature) were used to compute the pressure value developed by the deadweight testers

during transducer calibration procedures . Tables 12 and 13 list the mass values for the weights, balls and weight carriers for the two

working pressure standards. These mass values are the result of several

sets of weighings of each weight. The combined uncertainty in the mass standards and the weighing processes used was 1 part per million (ppm) or less. Therefore, the relative uncertainty in the mass values

assigned is 1 ppm.

Computation of the pressure values developed by the testers involved

computation of the density of the air using the measured atmospheric

parameters, the assigned area of each ball, and the total mass of the

weight stack. Since pressure is defined as the force developed per unit

area, the force exerted on the deadweight tester's ball must be

calculated for each stack of weights used in developing a particular

pressure value. The apparent mass value of the weights is computed

using eq (10). Equation (10) is similar in form to eq (6), discussed

earlier in determining the true mass of water weighed by the flow

facility's scales, but differs from it in that the apparent mass of the

weight stack is required in computing the force acting on the dead

weight tester's ball. The apparent mass is the mass value which

includes the effect of the buoyant force of the atmosphere.

M = M^ (1 - p /d ), (10)

app t ^ ^a' w' '

.

-39-
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a> 0> V

in (M «— J 3 q: CJ

•40-
where M = true mass of the combined weight stack,

M = apparent mass,

d ^^ = density of the weight material, and

p = density of the air surrounding the weight.

a. The weights were stainless steel having an assigned density of

7.8 g/cm . However, the materials making up the weight stack and

contributing to the generation of the force exerted on the ball were not

only the stainless steel weights, although these were the majority of

the mass, but also the ball itself and the weight carrier. The ceramic

ball was assigned a density value of 4 g/cm and the aluminum weight

carrier a density of 2.7 g/cm . Once the apparent mass value, M , for

the weight stack had been computed the pressure value was computea^using

the following relation,

P = M.T^T.g/^(l - "(T - 23)), app

where P = pressure,

g = local acceleration of gravity,

A = area of the ball, a = area thermal expansion coefficient for the ceramic

ball/stainless nozzle combination, and

T = temperature in degrees Celsius.

The relation includes a correction term for the thermal expansion effect

of the stainless steel/ceramic ball combination. The reference

temperature of 23 °C was the calibration temperature. Combining the

above relation with eq (10) gives the working equation for computation

of the pressure developed by a deadweight tester.

M g (1 - p /d ) P = ^ ^

(11)

A(l - a(T - 23) a Introduction of the appropriate units for each of the quantities in

eq (11) results in eq (11a) , which was used to compute the pressure

developed by both deadweight testers.

M (lb) X 0.4535924 (kg/lb) x 9 .80102(m/s^)

P = _!EE (11a)

A (m^) (1 + 0.000010 (T-23))

Equation (11a) provides pressure values in SI units of pascals. Many

customary pressure units other than SI units are in use. In this report

the pressure unit pound force per square inch (psi) is used. The

following lists some factors for conversion between systems of units

[11].

1 psi = 6894.757 pascals

1 atmosphere = 101325.0 pascals

1 atmosphere = 14.69595 psi

-41-
5. Uncertainty in the Differential Pressure Measurements

The uncertainty in the measurement of differential pressure is composed

of several components. Each of the components will be discussed and

used in developing an uncertainty statement for the measurement of the

differential pressure developed across the orifice meter. These

components are the following:

(1) The uncertainty associated with the pressure developed by a single deadweight tester;

(2) uncertainty due to fluid height differences in the two sides of

the transducer manifold;

(3) the uncertainty in the pressure difference between the two

deadweight testers;

(4) uncertainty due to the variability of the differential pressure

transducers ; and

a. Uncertainty in the Pressure Developed by a Single

Deadweight Tester

The statement of uncertainty in one of the working pressure standards is

composed of the following components:

(1) the uncertainty in the area assigned to the ball,

(2) the uncertainty in the buoyancy correction for the weight

stack,

(3) the uncertainty in the mass value of the weight stack,

(4) the uncertainty in the value of the acceleration of gravity,

(5) the uncertainty in the value of the thermal expansion

coefficient for the ceramic ball and the stainless steel

nozzle/ball retainer.

The uncertainty in the area assigned to the ball is obtained from the

calibration of each deadweight tester using the national working

pressure standards. In addition to the assignment of an effective area value for the ball/nozzle combination, the relative uncertainty in the

area value was assigned as part of the calibration procedure. Both

working pressure standards were calibrated over the course of the work.

One was calibrated three times and the other twice. The results of the

calibrations are listed below for both instruments.

Areas and Associated Uncertainties for Ball Gauge S/N 73520

Date Test No. Area \,

(x 10"^ m ) Random Uncertainty in

Variation Standards

June 1982 P-7802 1.425610 64 ppm 54 ppm

Jan. 1983 P-7869 1.425513 74 " 54 " Jan. 1984 P-7933

Mean

1.425540

1.425554

21 " 54 "

Pooled Standard Deviation 58 ppm

Total Uncertainty in the Assigned Area 112 ppm 1.60 10' m

-42-
Areas and Associated Uncertainties for Ball Gauge S/N 73521

Date Test No. ^^g^ o Random Uncertainty in

(x 10 m ) Variation Standards

June 1982 P-7803 1.425512 50 ppm 54 ppm

Jan. 1984 P-7934 1.425650 25 " 54 " Mean 1.425581

Pooled Standard Deviation 40 ppm _ _ Total Uncertainty in the Assigned Area 94 ppm = 1 . 34 x 10 m

The random variation in the two working standards is ascribed to the

inherent variation in the pressure generated during normal operation,

and is assessed from their calibration measurement data. Three residual

standard deviations of the fitting procedures used to determine the

effective area of each working standard gives a 99% confidence interval

for the estimate of the random uncertainty component in the area. Since

several assignments of the areas were made, the individual random

components of each assignment are pooled in quadrature. The total

uncertainty in the pressure developed by a single deadweight tester is

the sum of the random and systematic components . The systematic

uncertainty in the calibration of each working standard is the

uncertainty in the standard used to calibrate them. The relative

uncertainty in the national working standard used to calibrate the

deadweight testers is 54 parts per million of the assigned area value.

The uncertainty in the buoyancy correction for the weight stack arises

from uncertainty in the density of the air and of the weights. The

relative uncertainty in the density of the weights is taken to be 1%.

The relative uncertainty in the density of the air is taken from the

earlier discussion of air density calculation as 0.5%. Taking the

partial derivatives of eq (11) with respect to the density of the weight

material, d , and of air, p , and dividing these by the pressure leads

to the following expressions:

AP -p Ap

a a

(d - p ) p w ^a ^a

AP p Ad

'^a w

P (d - p ) d ^ w ^a^ w

These expressions give the relative uncertainty values in the

deadweight tester pressure due to uncertainty in the buoyancy correction

term of eq (11). Substitution of a nominal value^for the density of air

(0.00117 g/cm ) and for stainless steel (7.8 g/cm ) gives relative

magnitudes of these effects shown in table 14. Since the majority of

the parameters used to compute air densities are dominated by random

observation effects, this component will be taken as a random one. The

weight density uncertainty component is systematic.

43-
The relative uncertainty in the local acceleration of gravity is

obtained from Tate's [12] measurement, done at the NBS Gaithersburg

site, and is stated as 1 part per million.

The effect of the uncertainty in the combined thermal expansion

coefficient of the steel nozzle holding the ball and of the ball itself

is estimated to be approximately 10% of its value [13] . Since operation

of the deadweight testers was in the 20 to 25 °C range, the magnitude of

this effect on the uncertainty in the pressure is estimated at the 1

part per million level.

Combination of these components into a statement of total uncertainty in

the deadweight tester pressure will be done by combining the random

contributions in quadrature and the systematic contributions additively.

Table 14. Relative Uncertainty in Individual Deadweight

Tester Pressures

Ball Area Assignment (S/N 73520)

(S/N 73521)

Bouyancy Correction - Air Density

Bouyancy Correction - Weight Density

Weight Stack Mass Values

Acceleration of gravity

Thermal expansion coefficient

Total Component Uncertainty

Relative Uncertainty

(S/N 73520)

(S/N 73521)

(S/N 73520)

(S/N 73521)

Random Systematic

(ppm) (ppm)

58 54

40 54

0.4

1.5

1

1

1

58 59

40 59

58 + 59 = 117 ppm

40 + 59 = 99 ppm

These relative uncertainties correspond to uncertainty in the pressures

ranging from 0.0047 to 0.0079 psig for the S/N 73520 instrument and from

0.0041 to 0.0069 psig for the S/N 73521 instrument. For the time period

of the measurements reported in this report, June 1985 through February

1987, the reference pressure instrument was S/N 73521 and the test

pressure instrument was S/N 73520.

b. Uncertainty in the Differential Pressure Developed

by the Working Pressure Standards

The uncertainty in the pressure differential impressed upon the

transducers as developed by the two deadweight testers is composed of

two primary components: (1) uncertainty due to unequal heights of the

fluid columns in the lines connecting the deadweight testers to the

transducer manifold, and (2) the uncertainty in the pressure difference

itself.

44-
Uncertainty Due to Unbalanced Fluid Heights

The effect of unequal heights in the pressure fluids (silicone oil and

nitrogen gas) connecting the transducers to the deadweight testers is

treated independently for both fluids. The capability to set and

monitor the height of the silicone oil levels in the sight glasses is

determined by the capability of the operator to set the interface

menisci using the telemicroscope, and the incline to the horizontal of

the rails carrying the telemicroscope. The magnification and

translational sensitivity of the telemicroscope was such that any of the

operators could easily set the level of the menisci to 0.0005

centimeters. The sensitivity with which the telemicroscope was able to

maintain a horizontal plane was determined by the level used to monitor

and adjust the rail position relative to the horizontal plane. The

sensitivity of this level was tested and found to be capable of

reproducing the horizontal to within 0.002 inch per foot. The

sightglasses were separated by a maximum of 6 inches, therefore the

unbalanced height difference is taken as 0.001 inch (25 x 10 meters).

This value must be incorporated in the meniscus height setting

uncertainty, and are considered to be systematic in their effect on the

uncertainty, in the meniscus height difference. The sum of these heights

is 30 X 10 meters. Using a value of 950 and 1050 kg/m for the

density of the silicone oil filling the Paros and Ruska transducers,

respectively, the pressures generated by these unbalanced heights are 0.28 and 0.31 pascals (0.000041 and 0.000045 psi) for the two oils.

The unbalanced heights of the nitrogen columns above the sightglasses

were maintained to almost the same height. However, it was possible

that a maximum separation of 1 centimeter could have occurred. A

computation similar to that discussed for the unbalanced oil heights

yields a value of 0.6 pascals (0.00008 psi) at the largest operating

pressure value of 84 psia.

The sum of the two unbalanced fluid columns is 0.91 pascals (0.00013

psi) for the denser of the two silicone oils. To simplify the remainder

of the uncertainty analysis, this value will be used for the final

estimate of this component of uncertainty since the density difference

between the two oils is only a 10% effect in this value. For a pressure

difference of 0.4 psi the maximum relative uncertainty is 0.03%. At 28

psid this value is 0.0005% or 5 parts per million.

Uncertainty in the Difference Pressure Between the Deadweight Testers

The pressure difference, AP , between the two working standards is

AP = P^ - P . s t r The reference pressure P is maintained at a constant value during

transducer calibration procedures. The test pressure, P , varies to cover the differential pressure range desired for the transducer

calibration. For the tests discussed here the reference pressure was

always set to a nominal value of 41 psig and the test pressure values

ranged from 41 to 69 psig to cover the 28-psid operating range. Each

-45-
pressure contributes a component to the uncertainty in the difference

pressure.

The uncertainty in the reference pressure is that contributed by the

reference deadweight tester. During the period over which the data

reported here were collected, the deadweight tester having serial number

73521 provided the reference pressure. The total uncertainty in the

reference pressure of 41 psig is 0.0041 psi.

The uncertainty in the test pressure is similar to that in the reference

pressure. Since the two instruments were calibrated at differing times,

i.e., not simultaneously, it is assumed here that the systematic

uncertainty component of the national working standard could have been

in full effect, i.e., the systematic component of the uncertainty in the

national working standard is wholly a day-to-day effect. Therefore,

combination of the uncertainty components of the test and reference

instruments is done in the usual manner by combining both the random

components in quadrature and the systematic components additively. The

uncertainty in the differential pressure produced by the working

pressure standards, s , is computed in the following manner.

APs' [ (58 X lO'^P^)^ + (40 X 10 '^P^)^]-"-/^ + 59 X 10"^(P^+P^)

For the nominal values of the five differential pressures used in the

flow testing, s „ is evaluated below.

Uncertainty in the Differential Pressure

Due to the Working Standards for Nominal Flow Test Pressures

Differential

Pressure Random

(psid) (psid)

0.4 0.0029

1.0 0.0029

3.0 0.0030

10.0 0.0034

28.0 0.0043

^APs Relative

Syst. Unc^ertainty

(psid) (psid) (%)

0.0048 0.0077 1.9

0.0049 0.0078 0.78

0.0050 0.0080 0.27

0.0054 0.0088 0.088

0.0065 0.0108 0.039

Total Uncertainty in the Working Pressure Standards

The effect of unbalanced heights of fluid in the lines connecting the

transducers to the working standards is much smaller than any of the

other components contributing to the uncertainty in the calibrating

differential pressure, AP , by approximately an order of magnitude.

However, for the sake of completeness, it is included in the estimate of

the total uncertainty in calibrating differential pressure, s is expressed as follows:

AP

This

APc = s.^ + 0.00013

APs

-46-
6. Differential Pressure Transducer Calibration Procedures

Calibration of all operational transducers (at times the quartz bourdon

tube transducer was out of service due to periodic destruction of the

meniscuses) was generally done at the beginning of each day or each data

block. (For some of the testing associated with pipe wall surface

roughness effects, a data block extended over several days for which a single calibration was used. See Appendix A for a discussion of the

work and its results.) In this way the transducers were characterized

frequently, thereby reducing the impact of an undetected transducer

malfunction on the data base. Transducer calibration procedures were incorporated in the software of the data acquisition system's

microprocessor, to maintain a fixed and complete calibration procedure

over the period of data collection.

The calibration procedures were designed to emulate the operational

conditions of the differential pressure measurement system during flow

testing as closely as practicable. Since the downstream pressure taps

of the orifice were maintained as near 41 psig as possible, the

transducers were calibrated at 41 psig. Early in the project it was observed that all of the transducers showed small hysteresis effects

after they had been quiescent at zero differential pressure, i.e., with

the crossover valves opened, between measurement sessions. Also, during

measurement procedures, the transducers sensed time-varying pressures

(the inherent fluctuations of the differential pressure developed by the

orifice meter and the changes in differential pressure with flow rate

setting change) and the transducers were valved off and crossed over between flow rate settings during the flow testing to obtain zero differential pressure response values. To simulate these use conditions

calibration procedures were begun by exercising the transducers.

Transducer exercising consisted of placing approximately the full range

of differential pressure (28 psid) across the transducer manifold (at 41

psig static pressure), and manipulating each transducer's manifold

valves to alternately place zero or full range differential pressure

across all transducers.

The procedures for a transducer calibration are given below.

1. To begin transducer calibration both deadweight testers (DWT)

were loaded with weight stacks which produced nominally equal

pressures of 41 psig. The pneumatic pressure developed by

each of the testers was placed on one leg of the manifold as shown in figure 6. The crossover valve and the reference leg

valve for each transducer were then opened. This placed the

41 psig base pressure on both inlets of each transducer. This

response value was recorded as the zero differential pressure

value for the calibration.

2. The crossover valves were closed for the remainder of the

procedure and the test inlet valves were opened for each

transducer placing the DWT pressure difference across the

transducers. The transducer response values were recorded.

This value was the initial differential pressure calibration

point for the transducers. The pressure developed by the

-47-
deadweight testers was slightly different for nominally the same weight stack composition due to small differences in the

ball areas and in the true mass values of the weights.

3. The remainder of the differential pressure values (except for

the last point which was identical to that of step 2) were developed by adding or removing additional weights on the DWT

connected to the test-port side of the manifold. The DV7T of

the manifold's reference side remained at 41 psig throughout

the calibration procedure. Between each observation the

transducer's test and reference inlet valves were closed and

the crossover valves were opened to simulate transducer

operation during flow testing.

The pressure schedule for differential pressure transducer calibration

was ordered such that half the procedure consisted of successive

increases in the differential pressure value until the maximum value of

28 psid was reached. The remainder of the points successively decreased

the differential pressure until the near zero differential pressure

point of step 2 was reached. Several schedules were used during the

project. The number of points in them ranged from 14 to 31. Table 15

gives the menu displayed for the operators during a 20 -point calibration

sequence. The menu listed the weights comprising the weight stack of

the test port DWT, the pressure developed on the transducer's test

ports, and the differential pressure for nominal atmospheric conditions.

Variation in the number of points comprising a calibration pass was made

to determine a minimum number consistent with minimal degradation in the

procedure's quality. This quality was judged by the residual standard

deviations of the least squares fitting procedures used to determine

each transducer's calibration relation. During the period of time in

which the data on the nickel-plated meter tubes was collected, the 14-

point schedule was used. This required approximately 45 minutes to

complete. The barometric pressure and air temperature were recorded at

the beginning of the calibration observation sequence and stored with

the transducer calibration data base.

-48-
Table 15. 20-Point Transducer Calibration Schedule

Obs. Test Port DWT Diff. Test

No. Weight Designation Press. Press.

(psid) (psig)

1 66 77 88 0.00137 41.00708

2 66 77 88 13W 0.03744 41.04315

3 66 77 88 low 0.18173 41.18744

4 66 77 88 low IW 0.54246 41.54817

5 66 77 88 low IW 2W 0.90318 41.90889

6 66 77 88 low IW 2W 3W 4W 1.62464 42.63114

7 66 77 88 low 10 IW 2W 2.90372 43.90943

8 66 77 88 low 10 12 IW 2W 3W 4W 4.62543 45.63114

9 66 77 88 low 9 IW 2W 5.90474 46.91045

10 66 77 88 low 7 IW 2W 10.90617 51.91188

11 66 77 88 low 6 9 10 IW 2W 27.90986 68.91557

12 66 77 88 low 6 10 22.18685 63.19256

13 66 77 88 low 9 IW 5.54402 46.54973

14 66 77 88 low 10 12 IW 2W 3W 4.26471 45.27042

15 66 77 88 low 10 IW 2W 3W 3.26445 44.27016

16 66 77 88 low IW 2W 3W 1.26392 42.26963

17 66 77 88 low IW 0.54246 41.54817

18 66 77 88 low IIW 0.25387 41.25958

19 66 77 88 12W 0.07351 41.07922

20 66 77 88 0.00137 41.00708

Early in this project it was found that a characteristic of the

operation of the deadweight testers with the weight stacks stationary,

i.e., not spinning at a slow rate, was a small oscillation in the

pressure value. Due to the high sensitivity of these transducers, this

variation was easily detectable. This change in pressure was also

audible. The oscillation was minimized or eliminated by slowly spinning

the weight stacks. Once the weight stacks were placed on the testers

and the instruments were in a steady state, each weight stack was spun

and remained spinning through the time required for observation of the

differential pressure response of all transducers. Details of the

recording and storing of these values is given in the data acquisition

section of this report, section IV.

7. Transducer Response Functions and Coefficient Values

Upon completion of the observation sequence, the sets of response values

of each transducer were combined with the differential pressure values

to form the data pairs used in a least squares fitting procedure.

Generally a polynomial model having the response variables as the

independent variable and the differential pressure as the dependent

variable was used for interpolating through the range of the calibration

data. In the case of the quartz bourdon tube transducer a linear

dependence between its analog output voltage (V) and the applied

differential pressure (AP) was found to best represent its response.

-49-
The relation is

AP = C^ + C2V.

The response variable used in this fitting procedure was the voltage

difference V. - V , where V is the voltage observed with the transducer

at zero differential pressure immediately before the first observation

of the calibration procedure is taken, and V. is the voltage observed at

the ith step in the procedure.

A second order polynomial was used for the quartz oscillator- type

transducers. It includes a reduced range variable of the oscillator

period (T ) at zero differential pressure and the period at the sensed

differential pressure (T) . This relation is,

AP = Y + Y^x + Y^x,

where x = 1L°-- T >T. 2

o' Higher order polynomials were investigated for modelling the response of

the two types of transducers , but it was found that polynomials of the

first and second orders, respectively, were the best choice based on simultaneous minimization of the order and the residual standard

deviation of the least squares fit. The coefficient values and residual

standard deviations obtained from the least squares fitting procedures

for each transducer's response are tabulated in Appendix C.

8. Estimation of the Uncertainty in the Mean Differential

Pressure Over the Period of a Flow Rate Measurement

For each flow test, differential pressure observations were made with an observation period of slightly less than 1 second. The differential

pressure varies with time due to the fluid dynamic effects of the test

fluid passing through the orifice meter and to small changes in the flow

rate setting caused by slight changes in the flow control valve

mechanisms . The transducers sense these variations with a frequency

response characteristic to each transducer. The amplitudes of the

fluctuations were generally several percent of the mean differential

pressure. The transducers are read sequentially over the diversion

period and the observed values stored in the data base. To obtain the

best estimate of the mean differential pressure, one would like to have

the capability to measure the differential pressure with a temporal

resolution much smaller than the fluctuation period and with high

accuracy. Unfortunately the state-of-the-art in differential pressure

sensing does not allow both of these characteristics to be found in a single transducer. In this particular work it was decided to use transducers which had good measurement stability and sensitivity at the

expense of reduced frequency response characteristics. As a result the

frequency response of the transducers and associated connection lines is

of the order of several hertz.

Specifically, the quartz bourdon tube transducer (the Ruska transducer)

utilizes a servo loop which has a corner frequency near four hertz which

limits its frequency response. Its frequency response is further

limited by the silicone oil filling it. The analog output voltage is

50-
digitized for use by the data acquisition systems by a digital voltmeter

at 3 hertz. The quartz oscillator transducers (the Paros transducers)

had a similar digitization rate of four per second. The data

acquisition system was limited to transfer rates of approximately one set of observations per second, where a set of observations consisted of

a single value from each of the transducers. This limit was imposed by

software execution speed and was the controlling factor for data

acquisition rate.

In obtaining an observation set, the two Paros transducers were digitized simultaneously and the values transferred to the

microprocessor. The quartz bourdon tube transducer's output voltage was then digitized and transferred to the microprocessor. Although the

approximately 1- second data transfer/storage rate is thought to be

slower than the higher frequency, fluid dynamically- induced,

differential pressure fluctuations in the orifice meter, it is

sufficient to record low frequency components, and has considerably

greater temporal resolution than traditional manometry techniques.

An example data set for the three differential pressure transducers is

shown in figures 9 through 13. The data for these figures were taken

from a single day's observations on the 4- inch meter tube, PE-5ABC, with

the 2B orifice plate which has a beta ratio of approximately 0.37. Each

figure contains a time series plot of the differential pressure data

taken by the three transducers for the indicated test run. The five

nominal differential pressure values normally used in the testing, 0.4,

1, 3, 10, and 28 psid, are shown to illustrate the level of fluctuation

in the differential pressure data. A linear fit of differential

pressure as a function of observation time is shown as the curve through

the data for each plot. The differential pressure axis of each plot has

the same range to illustrate the difference in frequency response

between the quartz bourdon tube and quartz oscillator transducers. It

is quite evident that the bourdon tube transducer has a higher frequency

response then the other type of transducer. The amplitude of the

bourdon tube transducer is larger and its temporal variation suggests

that the frequency of the differential pressure signal may be higher

than the transducer's ability to follow it. The quartz oscillator

transducers have a lower frequency response than the bourdon tube

transducer. Inspection of the shapes of the three pressure signals

shows a close similarity between the Ruska and upper Paros indicating

that the transducers have similar capability to sense the low frequency

components of the differential pressure signal at the upper orifice

meter taps. The signal sensed at the lower taps has a similar shape in

the larger features.

Computation of discharge coefficient values from differential pressure

data arrays requires a mean value for the differential pressure.

Computation of the uncertainty in the discharge coefficient due to

uncertainty in the mean differential pressure requires an estimate of

the uncertainty in the differential pressure as sensed by each

transducer. The mean differential pressure is obtained in the usual

manner. Computation of the standard deviation is based on time series

analysis methods in order to properly account for any autocorrelation

51-
Differential Pressure Time Series Plots

Meter Tube PE-5 Orifice Plate 2B

Run 19

0.420 -1

tn

V)

0) ^ 0.410

Q

Upper Paros Transducer

^'%ff^f^'i^'^Wz-T-p^^

0.400 —

I—I—I—I—I—I—I—I—r~i—I—I—I—I—1

\—I—I—I—I—f~T—I—I—r-T—i—i—i""r~ 40 80 120

0.420 -1 Ruska Transducer

0.420 -1

V)

0)u^ 0.410

^-1

0.400

Lower Paros Transducer

'^^T^^^^^f^^^i'^^^]!;^^

n I I I I I I r~r"i i—r~r~T—i—i—i—r~T~T~"i i r~i ~ i ri r~r~] 40 80 120

Time (seconds)

Figure 9. Transducer Time Series Plots at 0.4 psld

52-
Differential Pressure Time Series Plots

Meter Tube PE-5 Orifice Plate 2B

Run 22

1.050

m

n

(U

Upper Paros Transducer

1.010 -j-TTT I I rr-r-T""|"'r "n~iT i r'i"r~[ i rr r~ri iri ir r t n-ri tt ] 20 40 60 80

1.050 -I

enen

(U &4

Ruska Transducer

1.010 I

I I I I I I I I rprr

20

1.050

tn

•1-1 Q

1.010

-r-TxrT-| I I n I I

I

I 1 1 I I ri I 1

I 40 60 80

Lower Paros Transducer

: '^

-^v"nVi/"'^'^V^

I I I I I I I I I

I I I I I I I I I rf"m~r i i i rrjn^rT-nrn^i -\ 20 40 60 80

Time (seconds)

Figure 10. Transducer Time Series Plots at 1 psid

-53-
Differential Pressure Time Series Plots

Meter Tube PE-5 Orifice Plate 2B

Run 28

3.150

CO

CO

0-« 3.050

Upper Paros Transducer

5S^,?v^,p2^y<«^y^

Q

2.950 -j I I I I I I I I I rn Mill! ~T~["T'-rT-"T-i~ri i i |-n"T-| i i i i t~i 50 100 150 200

3.150 Ruska Transducer

2.950 —I I 1 1 I 1 I |-rr"pi-i i i i i r-r-T-p-nr-n-r-r-rrTynn-^r-rr-t-r-T i 50 100 150 200

3.150 -1

V)

tn0)

O-i 3.050

tM

<+-(

2.950

Lower Paros Transducer

: •V^w'V^VA**'^^^'**^^

I I I I I I 1 I I 7"! I I I 1 I I 1 npr m-i"ttr-r-]-r7 'V rT"T-T-T-r-

]

50 100 150 200

Time (seconds)

Figure 11. Transducer Time Series Plots at 3 psid

•54-
Differential Pressure Time Series Plots

Meter Tube PE-5 Orifice Plate 213

Run 31

10.700 -I

mm

Qi ^ 10.200

«4-l

Upper Paros Transducer

9'700 —p-i—I—1—I—|—1—r—

I—1^1 I I I—I—I—

I—I—I—i~r~'—'—r~r~i~i—i—i

1~] 40 80 120

10.700 -,

CO

en

a; C^ 10.200 -

9.700

Ruska Transducer

"T—I—I I—T^i I —I—I

[—r"n—I—I—1—I—I —

I—r^i m—i—i—i i i i r"|

40 80 120

10.700

mm

(1) u^ 10.200

Q

9.700

Lower Paros Transducer

"I—

I—i~T

\r\—I—r~i—

I—r—1—i—r—r~i—i—i—i—| n—ri—

i—i~i i—i—i | 40 80 120

Time (seconds)

Figure 12. Transducer Time Series Plots at 10 psid

-55-
Differential Pressure Time Series Plots

Meter Tube PE-5 Orifice Plate 2B

Run 34

2B.300

cn

en(U

O-" 28.050

27.800

28.300

Upper Paros Transducer

I I I I I I I I I

I

I I I I I I I I I "pri-r~r~rT 'i i i

| i-n~r~i i i rj~]

20 40 60 80

Ruska Transducer

27.800

28.300

V)

cn

0) ^ 28.050

I 1 1 I 1 I I I T I 1 I I rrTT'TH" p~r~i i i i i i t "pi i i i i t i i n

20 40 60 60

Lower Paros Transducer

\r^A;^W'-'^^

27.800 I I I I I I I I

I I I I I I I I I II

I I I I I I I I "ry I I I I I ( I I I I 20 40 60 80

Time (seconds)

Figure 13. Transducer Time Series Plots at 28 psid

56-
effects in the data of each transducer. Autocorrelation effects are expected to be induced by the inability of the transducers to fully

respond to the full spectrum of frequencies in the differential pressure

signal. The method of Heidelberger and Welch [14] has been used to

compute the standard deviation of the mean, s.p .

9. Uncertainty in the Measurement of Orifice Meter

Differential Pressures

Descriptions of the methods used to compute the uncertainty in the

various components of the differential pressure values were developed

above. The uncertainty in observing the differential pressure developed

across the orifice meter with the differential pressure transducers is

the sum of the uncertainty in the working pressure standards used to

calibrate the transducers and the stability of transducer response to

calibration procedures. The estimate of the variation in the

transducer's response during calibration and use is given as the

residual standard deviation to the fit of the response functions to the

data for each calibration. In order not to underestimate the magnitude

of this variation, three residual standard deviations of the least

squares fit are used (99% confidence level).

The uncertainty in the estimate of the mean differential pressure value

for a differential pressure transducer is the sum of uncertainty

components due to the following:

1. s.p , the uncertainty in the differential pressure values

developed by the working standards used in calibrating the

transducers

.

2. s p^, the variability in the computed differential pressure

value due to random variation in each transducer (see Appendix

C).

3. s.p , the uncertainty in the mean differential pressure value

for each transducer over the interval of a test run.

Computation of the total uncertainty, s p, in the mean observed differential pressure for each transducer is the combination of the random

components in quadrature and the systematic components additively. The

mathematical expression for s is given in eq (12)

.

s^p = [(58xlO"^P^)2 + (0.0016 psid)2 + (3s^p^)2 + (3s^p^)^]^/^

+ 0.0048 psid + 59xlO"^AP (12)

10. Transducer Surveillance Measurements

A surveillance procedure was used to periodically test the transducer

performance data acquisition system during orifice meter data acquisition. These procedures were performed at the beginning of flow

testing data collection passes; each time that an orifice plate was inserted into the meter flange, a surveillance check of the transduction

57-
systems was made. These checks were incorporated in the data acquisition software to maintain a record of the transducer performance

Surveillance of the differential pressure transducer performance was

done using the deadweight testers in a manner similar to that of

calibration. A nominal 5.2 psi differential pressure was generated at

41-psig static pressure, the weight stacks spun, and an observation

sequence initiated by the operator. The means of the observed values

were converted to pressure units, using the most recently determined set

of transducer coefficients, and the results stored in the data base.

This procedure checked several things: (1) the computer/transducer

interface hardware and software, (2) the values of the coefficients

determined in the calibration procedures and used in the calculation

software for run- time values of differential pressure, and (3) the

stability of the transducer response after calibration and over the

period of data collection. The computed differential pressure value for

each transducer was displayed on the console of the data acquisition

system. This gave the operator an immediate check of transducer operation with the option of stopping the data collection procedures should

there be a large discrepancy between the values displayed and the known

differential pressure. A number of the results of these checks are listed in table 16. The value of the differential pressure supplied by

the two deadweight testers is given for comparison. This value has been

computed for the atmospheric conditions present shortly after the observations were made and stored. The level of agreement between the

pressure values for each transducer is within the sums of the residual

standard deviations for the fits of the transducer response and agrees

with the calculated value of the differential pressure within

approximately 0.003 psi.

58-
Table 16. Differential Pressure Transducer Surveillance Measurements

Date Time DWT

Pressure

(psid)

Upper

Paros

(psid)

Lower

Paros

(psid)

Ruska

(psid)

06/03/85

06/03/85

06/03/85

06/03/85

06/03/85

04:33:36

06:49:14

13:31:32

17:29:17

21:18:41

5.1789

5.1789

5.1789

5.1789

5.1789

5.1786

5.1818

5.1776

5.1770

5.1766

5.1800

5.1830

5.1805

5.1799

5.1796

a

06/04/85

06/04/85

06/04/85

01:09:01

02:37:20

05:31:58

5.1789

5.1789

5.1789

5.1797

5.1786

5.1808

5.1826

5.1817

5.1829

07/02/85 09:57:38 5.1789 5.1810 5.1820 5.1820

07/05/85

07/05/85

11:30:49

14:16:24

5.1789

5.1788

5.1796

5.1804

5.1807

5.1806

5.1818

5.1834

07/08/85

07/08/85

07/08/85

09:24:50

10:34:10

14:18:55

5.1789

5.1788

5.1788

5.1806

5.1790

5.1799

5.1815

5.1804

5.1805

5.1823

5.1816

5.1821

07/09/85

07/09/85

07/09/85

08:49:36

13:17:44

17:22:42

5.1788

5.1788

5.1788

5.1810

5.1793

5.1797

5.1819

5.1804

5.1810

5.1826

5.1826

5.1838

07/12/85

07/12/85

07/12/85

09:30:17

11:38:36

14:34:41

5.1789

5.1789

5.1789

5.1804

5.1806

5.1797

5.1816

5.1822

5.1812

5.1821

5.1829

5.1818

07/15/85 16:28:14 5.1788 5.1801 5.1808 5.1815

07/16/85

07/16/85

11:10:59

13:45:39

5.1789

5.1788

5.1806

5.1812

5.1819

5.1815

5.1824

5.1829

07/17/85

07/17/85

13:12:00

15:33:32

5.1788

5.1788

5.1790

5.1796

5.1805

5.1805

5.1815

5.1824

07/18/85

07/18/85

10:51:43

15:13:49

5.1789

5.1788

5.1800

5.1782

5.1810

5.1786

5.1816

5.1813

Ruska transducer not in use

-59-
E. Temperature Measurement Instruments and Standards

Temperature measurements were made of the flowing fluid and of the

atmosphere surrounding the weighing apparatus using calibrated thermistor probes. The calibration of each probe has been tied to the

International Practical Temperature Scale of 1968 through a calibrated

platinum resistance thermometer (PRT) . These comparisons were made

using a small, thermostatically controlled bath filled with mineral oil

in which the PRT and the thermistor probes were immersed. The bath was made of brass with copper tubing soldered to its sides. Water from a temperature controlled bath was passed through the copper tubing to

stabilize the temperature in the oil bath. Observations of the PRT

resistance and the thermistor indications were made in a short time

interval of several minutes. The stability of the bath over such a time was approximately 0.002 °C or less. The PRT resistance was measured

using a Leeds and Northrup [3] Model G2 DC resistance bridge which has

been calibrated by the NBS Electrical Measurements Group. The PRT had

been calibrated by the NBS Pressure and Temperature Division. The

maximum error in the temperature measured by the PRT was 0.0015 °C.

Table 17 lists the temperature values for the PRT and those indicated for

the eight probes tested. All probes were calibrated over the range 15 to

40 °C. This range represents the major portion of the range of operation

of the flow rate measurement facility during the work reported here. The

indicator for the array of probes displayed directly the temperature value

in units of degrees Celsius and was interfaced to the data acquisition

microprocessor, allowing selection of one of eight probes.

The representation of the calibration information for each probe is a polynomial in the indicated value. An investigation of the proper

functional form was made by fitting the PRT temperature to a linear

function of the thermistor indication. Inspection of the shape of the

residuals to this fit, plotted against the temperature, indicated that a third-order polynomial would best fit the calibration data. Subsequent

fits to third- order polynomials showed that the third order fit

minimized both the residual standard deviation and the order of the fit.

The four polynomial coefficients, B. , the residual standard deviation of

the fit, and the location of the probe during the flow rate measurement

phase of this work are given in table 18. The thermistor labeled 775006 was not used since its behavior was not consistent with the third- order

model.

1. Extension Cable Connection Effects

Each thermistor probe was physically separated from the indicator

location by as much as 50 feet. Extension cables were used to connect

the probes to the indicator. The effect of these extensions was assessed by using one probe immersed in a constant temperature bath, and

successively connecting the probe through each of the extension cables

and directly to the indicator. The temperature differences observed

did not exceed 0.01 "C for any of the extension cables. A systematic

uncertainty of 0.01 °C for the observed temperature values is assigned

based on the use of the extension cables.

60-
Table 17. Thermistor Temperature Indication Relative to the

Calibrated Platinum Resistance Thermometer

775001 775002 775003 775004

PRT TEMP Ind. Diff. Ind. Diff. Ind. Diff. Ind. Diff.

CO (°C) (°C) (°C) (°C) (°C) (°C) (°C) CO

20.91 20.85 -0.06 *21.05 0.14 21.23 0.32 *22.12 1.21

25.42 25.52 0.10 25.41 -0.01 25.92 0.50 25.43 0.01

30.50 30.72 0.22 30.53 0.03 31.21 0.71 30.53 0.03

34.96 35.25 0.29 35.02 0.06 35.80 0.84 34.93 -0.03

40.23 40.52 0.29 40.31 0.08 41.17 0.94 40.12 -0.11

34.93 35.22 0.29 34.97 0.04 35.75 0.82 34.91 -0.02

30.05 30.26 0.21 30.06 0.01 30.71 0.66 30.06 0.01

25.03 25.11 0.08 25.06 0.03 25.49 0.46 25.01 -0.02

20.87 20.81 -0.06 20.93 0.06 21.19 0.32 20.90 0.03

16.41 16.22 -0.19 16.44 0.03 16.57 0.16 16.47 0.06

16.40 16.22 -0.18 16.44 0.04 16.59 0.19 16.48 0.08

39.34 39.61 0.27 *39.30 -0.04 *40.19 0.85 *39.05 -0.29

775005 775006 775007 775008

PRT TEMP Ind. Diff. Ind. Diff. Ind. Diff. Ind. Diff

(»C) (°C) (°C) (°C) (°C) (°C) (°C) (°C) (°C)

20.91 20.90 -0.01 20.99 0.08 20.85 -0.06 20.85 -0.06

25.42 25.41 -0.01 25.42 -0.00 25.52 0.10 25.52 0.10

30.50 30.48 -0.02 30.66 0.16 30.71 0.21 30.70 0.20

34.96 34.89 -0.07 35.14 0.18 35.25 0.29 35.22 0.26

40.23 40.06 -0.17 40.39 0.16 40.51 0.28 40.47 0.24

34.93 34.86 -0.07 35.11 0.18 35.21 0.28 35.18 0.25

30.05 30.03 -0.02 30.16 0.11 30.26 0.21 30.25 0.20

25.03 25.01 -0.02 *24.97 -0.06 25.11 0.08 25.10 0.07

20.87 20.87 0.00 21.06 0.19 20.81 -0.06 20.81 -0.06

16.41 16.43 0.02 16.85 0.44 16.23 -0.18 16.23 -0.18

16.40 16.44 0.04 16.87 0.47 16.22 -0.18 16.22 -0.18

39.34 39.15 -0.19 *38.54 -0.80 39.60 0.26 39.56 0.22

*Data points judged to be outliers and omitted from the final least

squares fits.

-61-
Table 18. Thermistor Coefficients, Residual Standard Deviations,

and Experimental Locations

Thermistor Location

Niomber

B B, B2 X 10 B^ X 10

-5

Res.

Std. Dev.

(°C) CO (°C) (°C)

-3

(°C)

775001 16" Line 0.,237 1,.031737 -2.,84753 4.,32345 0,.010

775002 Air Temp

.

-0.,240 0..993186 0,,50974 -0,,93988 0,.021

775003 Tank #3 -0,,277 1,.049786 -3,.33100 4.,20485 0,.015

775004 Tank #2 -1,,130 1,.125176 -4,.63631 5,.70436 0,.018

775005 Tank #1 -0,,776 1,.091856 -3,,61436 4,.80412 0,.014

775007 8" Line 0,,194 1,.035789 -2,.97816 4,.47874 0,.011

775008 4" Line 0.,263 1..027828 -2,.71054 4,.26491 .012

2 . Uncertainty in Measured Temperature Values

The components of uncertainty in the temperature values measured by each

thermistor are:

(1) Uncertainty in the platinum resistance thermometer

temperature. This value represents the combined effects of

the resistance bridge and the PRT itself and is taken as 0.0015 °C.

(2) The effects of extension cable connections (taken as 0.01 °C)

.

(3) The random uncertainty component in the temperature

measurement, characterized by the residual standard deviations

of the fit for each thermistor.

The three thermistors used for measurement of the flowing water

temperature, immediately downstream of the orifice meters, have residual

standard deviations no larger than 0.012 °C. Therefore, for the flowing

water temperature values, the uncertainty in that value is taken to be

the sum of three times the largest residual standard deviation

(0.036 °C) , the uncertainty in the calibration temperatures determined

by the PRT (0.0015 °C) , and the effect of the extension cable connection

(0.01 °C) . The total uncertainty value in temperature measurement for

the flowing water temperature is 0.0475 °C. The residual standard

deviation is the only random error component with the other two taken as systematic

.

The uncertainty in the air temperature is computed similarly and is

0.0645 °C. The air temperature measurement did not involve cable

extensions and this error is not included.

•62
3. Measurement and Calculation of Water Density

The density of water was calculated using the formulation of Kell [9] at

atmospheric pressure. The values calculated with Kell's formulation

(eq (16) in [9]) relate exclusively to the density of distilled water.

Kell's relation for computation of the distilled water density is the

3 following; the units of the density value are kg/m and those of the

coefficients are chosen accordingly.

p^ = (aQ + a^T + a2T^ + a3T^ + aj^ + a.^T')/a + CT) ,

where T = temperature on the Celcius scale,

a^ = 999.83952, a^ = 105.56302 x lO'^,

a, = 16.945176, a, =-208.54253 x lO"-""^, and

a2 = -7.9870401 x lO"^, C = 16.87985 x

10'^

a^ = -46.170461 x 10'^.

The water used in this experimental program was not distilled, but drawn

from the municipal water supply and placed in the facility reservoir.

Due to dissolved minerals in the water, the density values are offset

somewhat from that of distilled water. Periodically samples were drawn

from the reservoir of the system and their densities were measured near

20 °C. See Appendix B for a description of the measurement principle, a listing of the data collected, the results obtained and an analysis of

the uncertainty in the resulting values. The results of these

observations are given in table 19. The difference between the measured

values of the mineral -laden water samples and the distilled water

density values are uniform for all samples. The standard deviation of

3 3 these difference values is 0.039 kg/m with a mean value of 0.194 kg/m . This value will be taken as a constant offset to the density of

distilled water as computed using the Kell formula. The density of the

water flowing in the flow measurement facility is calculated using the

Kell density correlation with the offset value added to it to reflect

its mineral content. This method will be used for any other flowing

fluid density values given in this document.

-63-
Table 19. Measured Water Density Values

Sample Type Period

Value

PRT

Resistance

Temperature Density

(sec) (ohms) CO (kg/m^)

Dist. Water 38.67970 1086.06 22.191 997.728

Xylene 37.37086 1086.04 22.186 865.555

8/02/85 38.68136 1086.03 22.184 997.898

7/18/85 38.68145 1086.03 22.184 997.910

6/25/85 38.68142 1086.00 22.176 997.908

8/02/85 38.68142 1086.05 22.189 997.905

1/09/85 38.68109 1086.05 22.189 997.871

10/20/83 38.68174 1086.04 22.186 997.938

7/24/85 38.68140 1086.05 22.186 997.903

12/27/84 38.68212 1086.05 22.186 997.977

4/05/86 38.68224 1086.06 22.191 997.989

Diff.

(kg/m-")

0.182

0.170

0.178

0.177

0.143

0.209

0.175

0.250

0.262

Computed Instrument Constant = 1.3278645

Average Diff. 0.194

Std. Dev. of the Diff. 0.039

The uncertainty in the flowing fluid density is the sum of the random

effects, which are dominated by the variation in the tap-water sample

densities, and the systematic effects largely due to the 0.12 kelvin

uncertainty in the thermometer used for temperature measurement. This

3 uncertainty contributes 0.034 kg/m systematically to give a total

3 uncertainty in the water density of (0.034 + 0.117) kg/m . Since the

variation in the water density is relatively small around a value of

3 1000 kg/m , the relative uncertainty in the water density is taken as 0.015%.

•64-
F. Dimensional Measurements

1. Orifice Meter Installation

There are three sizes of test sections in the water flow facility.

These are designated by the nominal pipe size comprising the test

section. The total usable length is approximately 55 feet (18 meters)

and varies somewhat with test section. The test section nominal pipe

diameters are 4, 8, and 16 inches (100, 200, and 400 millimeters). The

five sizes of orifice meters tested were installed in the test sections

as shown in table 20

.

Table 20. Test Section/Orifice Meter Installation Chart

(nominal sizes in inches)

Orifice Meter Test Section Manifold/Sprenkle

Diameter Separation

(inch) (inch) (Pipe Diameters)

2 4 60

3 4 30

4 4 20

6 8 10

10 16 1

The general installation of the orifice meter tubes and flow conditioner

in a flow facility test section was shown in figure 2. Conditioning of

the flow immediately upstream of the meter tube assembly was done using

Sprenkle [15] flow conditioners. Location of the flow conditioner/meter

tube assembly was arranged so that the maximum distance downstream from

the pump discharge manifold was obtained. In the case of the 10 -inch

orifice meters, a specially constructed container for the Sprenkle flow

conditioner was required since the normal casing would have made the

installed length longer than the available length in the 16 -inch test

section. The 16-inch flow conditioner casing consisted of a cylindrical

spool piece two pipe diameters long with a conical 16- by 10 -inch

reducing section fitted with appropriately sized flanges. A schematic

diagram of the normal casing is shown in figure 14. The schematic of

the Sprenkle flow conditioner is shown in figure 15. The flow

conditioner consists of three plates spaced one pipe diameter apart.

Each plate is perforated with a hexagonal pattern of holes. The hole

diameters and spacing depended upon the line size of flow conditioner.

Hole diameters and spacings for each line size are listed below.

Line Orifice Hole Hole

Size Meter Size Diameter Spacing

(inch) (inch)

4- inch 2, 3 0.242 0.330

6 -inch 4 0.410 0.470

10- inch 6 0.406 0.469

16 -inch 10

-65-
SPRENKLE FLOW

CONDITIONER CASING REDUCER

Flow

L2

Flow Conditioner Casing Specifications

4-inch

6-inch

10-inch

16-inch

Flange Sizes Lengths

Size Upstream Downstream Li (Inches) L2(lnches)

4-inch

6-inch

10-inch

16-inch

3-inch

4-inch

6-inch

16-inch

19-5/8

26-7/16

38

33

12

16-1/2

26

Reducer Specifications

Size Lengths

3x2 10-3/8 inch

4x3 11-7/8 inch

16x10 14-inch

Figure 14. Sprenkle Flow Conditioner Casing

•66-
SPRENKLE FLOW CONDITIONER

D

1/2 inch support

rods

3/8 inch dia.

holes on 1/2

inch centers

Figure 15. Sprenkle Flow Conditioner Schematic Diagram

67-
The flow conditioners were oversized relative to the orifice meters used

with them, as shown above. The plates were welded to four rods

S3nmnetrically spaced around the circumference of the plates. The

diameter of the plate/rod assembly was made such that the assembly fit

closely in its respective casing forcing the flow through the plate

perforations.

2. Orifice Meter Tube Geometry and Dimensional Measurements

The general geometry of each set of orifice meter tubes was the same. Three sections formed a set comprising a single meter tube. In all cases 600-pound ANSI flanges were used in all meter tubes. The Sprenkle

flow conditioner was bolted to the upstream flange of the approach tube

section, which was bolted to the upstream meter tube itself. (For the

3 -inch meter tube a 4 by 3 reducer was placed between the flow con- ditioner and the approach tube.) The orifice plates were pinned between

the downstream flange of the upstream meter tube and the upstream flange

of the downstream meter tube. These two flanges will be referred to as the orifice meter flanges in the remainder of this report. The arrangement of an orifice meter tube is shown schematically in figure 16. Also

one of the flange/meter tube sections is shown schematically in figure

16. This diagram is labeled with several reference positions which were used for measurements of the meter tube diameters. As shown, two dowel

pins were drilled in each orifice meter flange. Additionally, the

flange's joining the approach tube and the upstream meter tube were fitted with dowel pins which aligned the centerlines of the tube

sections. In this way any step between these tubes was minimized or eliminated.

The dowel pins in the orifice flanges provided mechanical constraint on

the position of the orifice plate centerline when installed between

them. The flange pairs joining sections A and B, and B and C (the

orifice flanges) were fitted with 0-ring seals. These are not shown in

the diagram. This was done to eliminate any interference that a normal

insertion type gasket may have caused should it not be positioned

correctly. Also the distances between the orifice tap holes and the

orifice plate faces were much more reproducible than would have been the case with gaskets which would have been used repeatedly and would have

changed thickness with time, thereby causing a continual change in the

distance between the plate faces and the tap holes. As will be

discussed in the operational procedures section of this report, the

separation between the dowel pins and the orifice plate was held to a small value throughout the project through the use of feeler gauges

during orifice plate installation.

-68-
Li L2 L3

-1

>v. ^ —

/ —

Lr Approach

-^ Upstream ^ r Downstream

Lj : Length of meter tube

Pj : Depth position of micrometer

A.B.C &D: Position of micrometer reference leg

Top tap hole

Bottom tap hole^ ^-^Dowel pin holes

Figure 16. Orifice Meter Tube Assembly

69-
Dimensional Measurements of the Orifice Meter Tubes

The schematic diagrams in figure 16 indicate several reference positions

and lengths associated with a meter tube set: the lengths of the three

tube sections and reference positions associated with the diameter

measurements. Diameter measurements were made with a set of internal

micrometers of the type shown in the photograph in figure 17 . This type

of micrometer, especially designed for the measurement of cylindrical

hole diameters, consists of three arms which center the micrometer in

the cylinder to be measured. The readability of each of the micrometers

was 0.0001 inches (2.54 micrometers). Each micrometer of the set was adjusted to read directly using proving rings traceable to NBS length

standards. The proving rings were also used to determine the

reproducibility of diameters using the micrometers once these were properly adjusted. Typical reproducibilities between operators was 0.0003 inches (7.62 micrometers) for diameters up to 6 inches. This

decreased somewhat (0.0002 inches (5 micrometers)) for the smaller

diameter meter tubes. For the 10-inch diameter meter tube the

reproducibility of diameter measurements increased to approximately

0.001 inches (25 micrometers) due to the considerably increased

difficulty in setting the micrometer lands in the meter tube.

The procedure used for measurement of the diameter of the meter tube

sections at the orifice flanges involved the four circumferential

positions labelled A through D and the three axial positions labelled P,

through P„ in figure 16 . Although only the diameter near the centerline

of the tap holes (position 1) was used in the calculation of discharge

coefficients (this being the customary position for stating the meter

tube diameter) , three positions along the length of each section were measured to characterize the contour of the tube near the orifice plate.

Both the upstream and downstream sections were measured. Position 2 was located in the region of the weld between the flange and tubing/pipe

forming the tube section. Position 3 was located approximately one pipe

diameter toward the interior of the meter section, from the weld. In

several cases this position was approximately two pipe diameters from

the flange face

Four measurements of the diameter were made at each of the three axial

positions, except for the 10- inch meter tubes. Diameters were measured

for the 10 -inch meter tubes only at positions 1 and 2 because the

micrometer could not be read reliably when placed in the third position.

At each of these depth positions four observations of the diameter were

made. One of the three arms of the micrometer was designated as the

reference arm and was aligned with one of the four circumferential

positions for each measurement. In this way an indication of the outof-roundness of the meter tube diameter may be detected in addition to

obtaining four independent measurements of the diameter for that depth

position. Position 1 coincided with the centerline of the tap holes.

To avoid the tap holes, measurements made at positions A and C were made

with the micrometer's reference arm positioned near the 1 and 7 o'clock

positions respectively. The results of these measurements are tabulated

in tables 21 through 24,

•70-
Figure 17. Internal Micrometer Used for Measurement

of Orifice Meter Tube Diameters

•71-
Table 21A. Orifice Meter Tube Diameter Measurements Before

Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-lABC

Surface Condition - BARE Observer - SW Date 05/17/85

Meter Tube Section Lengths

FE-IA 69,750 in. FE-IB 17.938 in. FE-lC 39.938 in.

Diameter Measurements - Meter Section - FE-IB

Position A B C D

1 2.0726 2.0725 2.0723 2.0721

2.0713

2.0732

2.0709

2.0673

2.0722

2.0767

2.0722

2.0742

Mean

2.0724

2.0716

2.0728

Diameter Measurements

Position A B

1 2.0709 2.0706

2 2.0718 2.0727

3 2.0689 2.0725

Meter Section • C D

2.0708 2.0713

2.0717 2.0700

2.0737 2.0678

FE-IC

Mean

2.0709

2.0715

2.0707

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-2ABC

Surface Condition - BARE Observer - GPB Date 07/17/85

Meter Tube Section Lengths

FE-2A 69.750 in. FE-2B 17.988 in. FE-2C 41.938 in.

Diameter Measurements - Meter Section - FE-2B

Position A B C D Mean

1 2.0721 2.0714 2.0716 2.0714 2.0716

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-3ABC

Surface Condition - BARE Observer - SW Date 05/17/85

Meter Tube Section Lengths

FE-3A 104.750 in. FE-3B 26.875 in. FE-3C 53.875 in.

Diameter Measurements

Position A B

1 3.0735 3.0727

2 3.0742 3.0712

Meter Section - C D

3.0732 3.0734

3.0737 3.0750

FE-3B

Mean

3.0732

3.0735

Diameter Measurements

Position A B

1 3.0755 3.0759

2 3.0721 3.0738

Meter Section - FE-3C

C D Mean

3.0756 3.0754 3.0756

3.0754 3.0736 3.0737

72-
Table 21B. Orifice Meter Tube Diameter Measurements

Before Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-4ABC

Surface Condition - BARE Observer - SW Date 06/04/85

Meter Tube Section Lengths

FE-4A 104.875 in. FE-4B 27.063 in. FE-4C 54.000 in.

Diameter Measurements

Position A B

1 3.0783 3.0778

2 3.0790 3.0800

3 3.0846 3.0825

Meter Section

C D

3.0780 3.0783

3.0731 3.0784

3.0781 3.0828

FE-4B

Mean

3.0781

3.0776

3.0820

Diameter Measurements

Position A B

1 3.0767 3.0765

2 3.0754 3.0760

3 3.0802 3.0724

Meter Section - C D

3.0769 3.0770

3.0757 3.0737

3.0761 3.0801

FE-4C

Mean

3.0768

3.0752

3.0772

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-5ABC

Surface Condition - BARE Observer - GPB Date 09/17/85

Meter Tube Section Lengths

FE-5A 139.750 in. FE-5B 35.875 in. FE-5C 65.875 in.

Diameter Measurements

Position A B

1 4.0485 4.0473

2 4.0503 4.0508

3 4.0381 4.0393

Diameter Measurements

Position A B

1 4.0368 4.0380

2 4.0306 4.0320

3 4.0321 4.0284

Meter Section - FE-5B

C D Mean

4 .0498 4.0456 4.0478

4 .0515 4.0478 4.0501

4 .0382 4.0366 4.0381

Meter Section - FE-5C

C D Mean

4 .0402 4.0364 4.0378

4 .0322 4.0351 4.0325

4 .0346 4.0339 4.0322

-73-
Table 21C. Orifice Meter Tube Diameter Measurements

Before Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-6ABC

Surface Condition - BARE Observer - SW Date 05/17/85

Meter Tube Section Lengths

FE-6A 139.750 in. FE-6B 35.875 in. FE-6C 66.000 in.

Diameter Measurements

Position A B

1 4.0326 4.0349

2 4.0320 4.0349

3 4.0270 4.0396

Diameter Measurements

Position A B

1 4.0327 4.0313

2 4.0284 4.0287

3 4.0307 4.0334

Meter Section - FE-6B

C D Mean

4,.0296 4.0351 4.0331

4 .0335 4.0368 4.0343

4 .0399 4.0367 4.0358

Meter Section - FE-6C

C D Mean

4 .0315 4.0351 4.0327

4 .0275 4.0302 4.0287

4 .0329 4.0346 4.0329

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-7ABC

Surface Condition - BARE Observer - GPB Date 08/22/85

Meter Tube Section Lengths

FE-7A 209.750 in. FE-7B 54.000 in. FE-7C 90.000 in.

Diameter Measurements

Position A B

1 6.1200 6.1200

2 6.1197 6.1196

3 6.1198 6.1198

Diameter Measurements

Position A B

1 6.1183 6.1185

2 6.1195 6.1194

3 6.1200 6.1198

Meter Section - FE-7B

C D Mean

6 .1200 6.1200 6.1200

6 .1196 6.1197 6.1197

6 .1198 6.1200 6.1198

Meter Section - FE-7C

C D Mean

6 .1182 6.1184 6.1184

6 .1195 6.1197 6.1195

6 .1194 6.1198 6.1197

74-
Table 21D. Orifice Meter Tube Diameter Measurements

Before Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-8ABC

Surface Condition - BARE Observer - GPB Date 07/01/85

Meter Tube Section Lengths

FE-8A 209.75 in. FE-8B 53.875 in. FE-8C 90.00 in.

Diameter Measurements - Meter Section - FE-8B

Position A B C D Mean

1 6.0833 6.0833 6.0841 6.0861 6.0842

2 6.0823 6.0928 6.1039 6.0884 6.0918

Diameter Measurements - Meter Section - FE-8C

Position A B C D Mean

1 6.0790 6.0846 6.0837 6.0838 6.0828

2 6.0860 6.0891 6.0812 6.0914 6.0869

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-9ABC

Surface Condition - BARE Observer - GPB Date 05/13/85

Meter Tube Section Lengths

FE-9A 349.750 in. FE-9B 89.875 in. FE-9C 143.750 in.

Diameter Measurements - Meter Section - FE-9B

Position A B C D Mean

1 10.0829 10.0829 10.0830 10.8290 10.0829

Orifice Meter Diameter Measurements For Meter Tube Assembly - FE-OABC

Surface Condition - BARE Observer - GPB Date 09/24/85

Meter Tube Section Lengths

FE-OA 349.625 in. FE-OB 89.875 in. FE-OC 143.750 in.

Diameter Measurements - Meter Section - FE-OB

Position A B C D Mean

1 10.0246 10.0254 10.0266 10.0267 10.0258

75-
Tables 21A through 21D tabulate the diameter measurements made on each

mild steel meter tube before electroless nickel plating [16] with a thickness of between 0.0005 and 0.001 inches (12 to 25 micrometers).

The measurements given in these tables were abbreviated in several

cases, although all tubes had at least one measurement set at position 1

of the upstream meter tube section. Table 22 tabulates the diameter

measurements for the 4- inch (100 mm) stainless meter tube which was used

as a check standard for the testing program after nickel plating of the

mild steel meter tubes. Tables 23A through 23E tabulate the diameter

measurements taken on the meter tubes after nickel plating. For these

the full number of measurements were made. Table 24 tabulates the means

of the position 1 measurements on the upstream meter tube section.

These values were used in the calculation of the discharge coefficient.

The length of each meter section is given in both sets of tables.

The diameter measurements tabulated here are those taken after

approximately 4 years of effort in this project and represent the

culmination of considerable work to identify and eliminate the spurious

effect of surface roughness on the measurement of the discharge

coefficient (see Appendix A) . During the course of these efforts

numerous measurements of the diameters of the meter tubes were made.

The results of these observations are described in Appendix G for the

purpose of completeness of documentation for this project.

Table 22. Orifice Meter Tube Diameter Measurements for the 4- Inch

Stainless Steel Orifice Meter Tube Check Standard

Orifice Meter Diameter Measurements For Meter Tube Assembly - DAN-4SS

Surface Condition - BARE Observer - GPB Date 09/24/85

Meter Tube Section Lengths

DAN-4SS 239.875 in. DAN-4SS 40.0

Diameter Measurements

Position A B

1 4.0309 4.0302

2 4.0274 4.0283

3 4.0262 4.0254

Meter Section - DAN-4SS-U

C D Mean

4.0302 4.0310 4.0306

4.0268 4.0309 4.0283

4.0258 4.0256 4.0258

Diameter Measurements

Position A B

1 4.0238 4.0220

2 4.0271 4.0209

3 4.0258 4.0264

Meter Section - DAN-4SS-D

C D Mean

4.0225 4.0237 4.0230

4.0281 4.0269 4.0258

4.0244 4.0284 4.0263

76-
Table 23A. Orifice Meter Tube Diameter Measurements

After Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-lABC

Surface Condition - PLATED Observer - GS Date 07/29/85

Meter Tube Section Lengths

PE-IA 69.750 in. PE-IB 17.938 in. PE-IC 41.938 in.

Diameter Measurements

Position A B

1 2.0717 2.0723

2 2.0711 2.0708

3 2.0683 2.0651

Meter Section • C D

2.0716 2.0711

2.0709 2.0705

2.0752 2.0732

PE-IB

Mean

2.0717

2.0708

2.0705

Diameter Measurements

Position A B

1 2.0694 2.0693

2 2.0670 2.0678

3 2.0672 2.0711

Meter Section - C D

2.0689 2.0694

2.0680 2.0676

2.0694 2.0665

PE-IC

Mean

2.0692

2.0676

2.0686

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-2ABC

Surface Condition - PLATED Observer - GPB Date 08/02/85

PE-2A

Meter Tube Section Lengths

69.750 in. PE-2B 17.938 in. PE-2C 41.938 in.

Diameter Measurements

Position A B

1 2.0696 2.0694

2 2.0680 2.0676

3 2.0621 2.0620

Meter Section

C D

2.0694 2.0696

2.0671 2.0655

2.0613 2.0601

PE-2B

Mean

2.0695

2.0671

2.0614

Diameter Measurements

Position A B

1 2.0645 2.0648

2 2.0630 2.0644

3 2.0642 2.0620

Meter Section

C D

2.0646 2.0648

2.0652 2.0655

2.0642 2.0617

PE-2C

Mean

2.0647

2.0645

2.0630

-77-
Table 23B. Orifice Meter Tube Diameter Measurements

After Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-3ABC

Surface Condition - PLATED Observer - GS Date 07/23/85

Meter Tube Section Lengths

PE-3A 104.750 in. PE-3B 26.875 in. PE-3C 53.875 in.

Diameter Measurements

Position A B

1 3.0707 3.0716

2 3.0705 3.0689

3 3.0826 3.0648

Diameter Measurements

Position A B

1 3.0723 3.0719

2 3.0722 3.0712

3 3.0740 3.0737

Meter Section - PE-3B

C D Mean

3 .0729 3.0721 3.0718

3 .0713 3.0713 3.0705

3 .0678 3.0817 3.0742

Meter Section - PE-3C

C D Mean

3 .0725 3.0722 3.0722

3 .0721 3.0722 3.0719

3 .0741 3.0742 3.0740

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-4ABC

Surface Condition - PLATED Observer - GS Date 07/24/85

Meter Tube Section Lengths

PE-4A 104.875 in. PE-4B 27.063 in. PE-4C 54.000 in.

Diameter Measurements

Position A B

1 3.0739 3.0751

2 3.0747 3.0741

3 3.0850 3.0814

Diameter Measurements

Position A B

1 3.0741 3.0740

2 3.0735 3.0736

3 3.0762 3.0721

Meter Section - PE-4B

C D Mean

3 .0746 3.0751 3.0747

3 .0719 3.0751 3.0739

3 .0782 3.0833 3.0820

Meter Section - PE-4C

C D Mean

3 .0746 3.0745 3.0743

3 .0745 3.0726 3.0736

3 .0768 3.0791 3.0760

•78-
Table 23C. Orifice Meter Tube Diameter Measurements

After Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-5ABC

Surface Condition - PLATED Observer - SW Date 10/08/85

Meter Tube Section Lengths

PE-5A 139.750 in. PE-5B 35.875 in. PE-5C 65.875 in.

Diameter Measurements

Position A B

1 4.0426 4.0365

2 4.0485 4.0495

3 4.0375 4.0374

Diameter Measurements

Position A B

1 4.0473 4.0365

2 4.0337 4.0291

3 4.0332 4.0263

Meter Section - PE-5B

C D Mean

4 .0472 4.0416 4.0420

4 .0458 4.0460 4.0475

4 .0351 4.0344 4.0361

Meter Section - PE-5C

C D Mean

4 .0376 4.0366 4.0395

4 .0359 4.0372 4.0340

4 .0334 4.0328 4.0314

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-6ABC

Surface Condition - PLATED Observer - GPB Date 06/24/85

Meter Tube Section Lengths

PE-6A 139.750 in. PE-6B 35.875 in. PE-6C 66.000 in.

Diameter Measurements

Position A B

1 4.0325 4.0324

2 4.0292 4.0350

3 4.0267 4.0323

Diameter Measurements

Position A B

1 4.0318 4.0311

2 4.0279 4.0292

3 4.0296 4.0312

Meter Section - PE-6B

C D Mean

4 .0332 4.0342 4.0331

4 .0346 4.0344 4.0333

4 .0367 4.0309 4.0316

Meter Section - PE-6C

C D Mean

4 .0315 4.0332 4.0319

4 .0289 4.0310 4.0293

4 .0314 4.0325 4.0312

-79-
Table 23D. Orifice Meter Tube Diameter Measurements

After Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-7ABC

Surface Condition - PLATED Observer - GPB Date 12/04/85

PE-7A

Meter Tube Section Lengths

209.75 in. PE-7B 54.0 in. PE-7C 90.0 in.

Diameter Measurements

Position A B

1 6.1236 6.1238

2 6.1234 6.1236

Meter Section - PE-7B

C D Mean

6.1237 6.1237 6.1237

6.1233 6.1233 6.1234

Diameter Measurements

Position A B

1 6.1223 6.1223

2 6.1238 6.1237

Meter Section

C D

6.1222 6.1221

6.1237 6.1235

PE-7C

Mean

6.1222

6.1237

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-8ABC

Surface Condition - PLATED Observer - GPB Date 08/15/85

PE-8A

Meter Tube Section Lengths

209.75 in. PE-8B 53.875 in. PE-8C 90.00 in.

Diameter Measurements

Position A B

1 6.0830 6.0815

2 6.0809 6.0938

3 6.0850 6.0883

Meter Section - PE-8B

C D Mean

6.0824 6.0847 6.0829

6.0774 6.0885 6.0851

6.0893 6.0823 6.0862

Diameter Measurements

Position A B

1 6.0778 6.0835

2 6.0828 6.0895

3 6.0911 6.0885

Meter Section

C D

6.0843 6.0823

6.0797 6.0891

6.0829 6.0925

PE-8C

Mean

6.0820

6.0853

6.0888

80-
Table 23E. Orifice Meter Tube Diameter Measurements

After Electroless Nickel Plating

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-9ABC

Surface Condition - PLATED Observer - GPB Date 11/04/85

Meter Tube Section Lengths

PE-9A 349.750 in. PE-9B 89.875 in. PE-9C 143.750 in.

Meter Section - PE-9B

Position A B C D Mean

1 10.0814 10.0805 10.0814 10.0816 10.0812

2 10.0822 10.0817 10.0815 10.0825 10.0820

Meter Section - PE-9C

Position A B C D Mean

1 10.0909 10.0907 10.0907 10.0911 10.0908

2 10.0894 10.0900 10.0897 10.0902 10.0898

Orifice Meter Diameter Measurements For Meter Tube Assembly - PE-OABC

Surface Condition - PLATED Observer - GPB Date 11/04/85

Meter Tube Section Lengths

PE-OA 349.625 in. PE-OB 89.875 in. PE-OC 143.750 in.

Diameter Measurements

Position A B

1 10.0240 10.0240

2 10.0189 10.0272

- Meter Section - PE-OB

C D Mean

10.0244 10.0245 10.0242

10.0096 10.0174 10.0183

Diameter Measurements

Position A B

1 10.0286 10.0304

2 10.0401 10.0485

- Meter Section - PE-OC

C D Mean

10.0332 10.0352 10.0318

10.0456 10.0429 10.0443

Table 24. Orifice Meter Tube Mean Diameters in the Plane

of the Tap Hole Center Lines (Axial Position 1)

Meter Tube Diameter

(Inches)

Meter Tube Diameter

(Inches)

PE-IABC

PE-2ABC

PE-3ABC

PE-4ABC

PE-5ABC

PE-6ABC

PE-7ABC

PE-8ABC

PE-9ABC

PE-OABC

DAN-4SS

2.0717

2.0695

3.0718

3.0747

4.0420

4.0331

6.1237

6.0829

10.0812

10.0242

4.0306

FE-IABC

FE-2ABC

FE-3ABC

FE-4ABC

FE-5ABC

FE-6ABC

FE-7ABC

FE-8ABC

FE-9ABC

FE-OABC

2.0724

2.0716

3.0732

3.0781

4.0478

4.0331

6.1200

6.0842

10.0829

10.0258

•81-
3 . Meter Tube Surface Roughness Measurements

Meter tube surface roughness measurements were made to characterize the

condition of the interior surfaces of the meter tubes. Measurements

were made of the surface roughness before and after nickel plating. Two

instruments were used: a ProfHometer Peak Counter (PPC) manufactured

by Bendix, Sheffeld Division [3] was used for some of the initial

measurements, and a Surtronic 3 (S3) manufactured by Rank Precision [3] was used for the final measurements. Both instruments were compared

with a tablet of known surface roughness as a check of the instrument

indication.

For consistency, measurements were made at two locations. These were at

the 5 and 11 o'clock positions with respect to the pressure tappings in

the orifice flange. The upper tap hole defines the 12 o'clock position.

Since this type of measurement is obtained from a stylus -tjrpe of instrument which averages the roughness over a finite length, the position of

the middle of the stylus stroke was positioned near the plane of the tap

holes. The Surtronic 3 instrument was compensated for long-period

fluctuations in the surface roughness with three ranges of stylus move- ment and signal averaging, 0.010, 0.030, and 0.100 inch period length

filtering settings. All three of these settings were recorded when

using this instrument and are listed in table 25. The Profilometer Peak

Counter did not have this feature and only the single observation is

given. In each case for this device a range is given for the roughness

measurement as indicated by the values separated by a slash (/) . All

values are given as the RMS fluctuation in the surface profile in units

of microinches. Measurements were made on both meter tubes comprising

the orifice meter itself, i.e.. Sections B and C.

4. Orifice Plate Dimensional Measurements

Orifice plate dimensional measurements were made using a 3-axis coor- dinate measuring machine having a sensitivity of 0.0001 inch. The

measuring machine was operated in a room maintained at 20 "C +/- 0.5 "C.

A computer controlled data acquisition system allowed reduction of

coordinate data to yield various types of results.

Orifice Diameter and Plate Concentricity

The orifice diameter and the position of its center relative to the

physical center of the orifice plate were measured. This procedure used

observation of at least three coordinate points approximately equally

-82-
Table 25. Orifice Meter Tube Interior Surface Roughness Measurements

Meter

Tube

Instrum . Date Surface Rough

5 O'CLOCK

.100 .030 .010

(microinches RMS)

ness

-- 11

.100

O'CLOCK -- .030 .010

FE-IB

PE-IB

FE-IC

PE-IC

PPC

S3

PPC

S3

05/17/85

08/23/85

05/17/85

08/23/85

195

169

109/135

155

150/155

144

108

81

189

199

144/138

136

174/155

192

93

95

FE-2B

PE-2B

FE-2C

PE-2C

PPC

S3

PPC

S3

05/23/85

08/23/85

05/23/85

08/23/85

206

219

151/159

194

236/227

248

212

191

319

260

160/136

268

205/175

184

214

112

FE-3B

PE-3B

FE-3C

PE-3C

PPC

S3

PPC

S3

05/17/85

08/23/85

05/17/85

08/23/85

169

176

135/149

122

172/168

153

55

142

88

171

55/54

38

143/140

124

38

50

FE-4B

PE-4B

FE-4C

PE-4C

PPC

S3

PPC

S3

05/17/85

08/23/85

05/17/85

08/23/85

126

276

52/52

96

140/155

150

49

97

165

349

39/39

101

236/226

261

52

121

FE-5B

PE-5B

FE-5C

PE-5C

S3

S3

S3

S3

09/17/85

10/18/85

09/17/85

10/18/85

179

435

109

325

77

240

73

289

41

172

54

184

143

331

143

238

109

203

102

166

45

106

40

91

FE-6B

PE-6B

FE-6C

PE-6C

PPC

S3

PPC

S3

05/17/85

08/23/85

05/17/85

08/23/85

246

248

152/174

180

245/246

230

118

120

248

207

220/215

231

170/173

138

172

86

FE-7B

PE-7B

FE-7C

PE-7C

S3

S3

S3

S3

08/22/85

11/04/85

08/22/85

11/04/85

58

23

56

112

63

34

38

100

42

41

36

184

57

29

63

20

32

69

46

50

23

198

34

129

FE-8B

PE-8B

FE-8C

PE-8C

PPC

S3

PPC

S3

05/23/85

08/22/85

05/23/85

08/22/85

184

239

147/150

158

189/177

223

91

112

141

230

91/89

113

225/219

281

75

161

83-
Table 25. Orifice Meter Tube Interior Surface Roughness

Measurements - - Continued

Meter Inst. Date Surface Roughness

Tube 5 O'CLOCK - 11 O'CLOCK

.100 .030 .010 .100 .030

(microinches RMS)

010

FE-9B PPC 05/23/85 27/30 35/31

PE-9B S3 11/04/85 42 36 23 76 53 29

FE-9C PPC 05/23/85 23/24 21/20

PE-9C S3 11/04/85 93 61 85 224 230 137

FE-OB S3 09/26/85 257 257 154 242 195 130

PE-OB S3 11/04/85 335 206 108 246 212 230

FE-OC S3 09/26/85 264 201 155

PE-OC S3 11/04/85 244 240 173 384 293 176

spaced around the plate outer circumference. The data acquisition

system fit these points to a circle to calculate the plate diameter

value and to determine the circle's origin. The measuring machine's

coordinate axes were then reset to coincide with this origin. Next the

orifice circtjmference was obtained by making several (3 to 8) observations around the outer plate edge at equally spaced points. The

position of the orifice center relative to the coordinate machine axes origin and its diameter were then computed.

Of course, this measure of the concentricity of the orifice is relative

to the plate geometry only. Determination of the position of the

orifice relative to the meter tube axis relies on the two dowel pins

located in the orifice meter flanges against which the plate edge rests

when installed. Therefore, the positions of these dowel pins were

measured. The measured values of the separation of each dowel pin

mounting hole's surface nearest the meter tube center and the inner edge

of the meter tube are listed in table 26. The orientation of the

orifice meter is as if one were viewing the upstream face of the orifice

plate with the two dowel pins disposed to the left and right of the

orifice center.

The measured diameter values for the plated meter tubes were used to

express the position of the locating surfaces of the dowel pins as the

diameter of a circle centered at the meter tube axis. (This is similar

in concept to the bolt hole circle dimension commonly used in locating

the bolt holes in the orifice flange.) These diameter values are listed

in table 26 as the dowel surface diameter as are approximate means of

the orifice plates for comparison purposes. The concentricity tolerance

band prescribed by commercial practice [17] is also given for reference.

It is clear that the construction of the orifice meter flanges and their

locating pins was well within the prescribed acceptance band.

•84-
The dowel pin tap surfaces were designed to be in contact with the

orifice plate in the installed condition, thereby locating the center of

the orifice at the meter tube axis. In practice a maximum gap between

the plate edge and the dowel pin of 0.0015 inches was allowed when

installing a plate. Procedures used to achieve this are described later

in this report.

Table 26 . Orif Lee Flange Center to Dowel Pin Inner Surface Radii

Meter Nom. Right Left Dowel Surface Plate Cone

.

Tube Section Dia. Dowel Dowel Diameter Nom. Dia Band

(in.) (in.) (in.) (irt.) (in.) (in.)

FE-IB-D 2 1.150 1.153 4.372 4.378 4.372 0.06

FE-IC-U 2 1.157 1.155 4.386 4.382 0.06

FE-3B-D 3 1.410 1.405 5.892 5.882 5.872 0.09

FE-3C-U 3 1.410 1.401 5.892 5.874 0.09

FE-4B-D 3 1.402 1.400 5.879 5.875 5.872 0.09

FE-4C-U 3 1.403 1.399 5.877 5.872 0.09

FE-5B-D 4 1.537 1.534 7.116 7.110 7.122 0.12

FE-5C-U 4 1.540 1.538 7.122 7.118 0.12

FE-6B-D 4 1.542 1.538 7.117 7.109 7.122 0.12

FE-6C-U 4 1.544 1.544 7.121 7.121 0.12

FE-7C-U 6 1.881 1.888 9.886 9.990 9.873 0.18

FE-7B-D 6 1.879 1.886 9.882 9.896 0.18

FE-8C-U 6 1.896 1.902 9.875 9.887 9.873 0.18

FE-8B-D 6 1.895 1.897 9.873 9.877 0.18

FE-9B-D 10 2.087 2.084 14.255 14.249 14.250 0.30

FE-9C-U 10 2.099 2.102 14.279 14.285 0.30

FE-OB-D 10 2.112 2.111 14.248 14.246 14.250 0.30

FE-OC-U 10 2.109 2.116 14.242 14.256 0.30

Orifice Plate Flatness Measurements

Measurement of the plate flatness was done using the coordinate

measuring machine. The measurement procedure involved the observation

of the z or height position of the top surface of the plate at 12

points. All observation patterns were referenced to a line generally

bisecting the orifice and handle of the plate as shown in figure 18

.

The z-axis origin of the measuring machines' coordinate system was reset

to an arbitrary position at the top of one of the two machinists

parallels supporting the orifice plate. Four sets of three observations

were made. These are illustrated in figure 18 by the numbered points.

85-
The measure of flatness accepted in industrial practice [17] utilizes

the dam height of the orifice as installed. The dam height is that

portion of the plate which influences the performance of the orifice

meter defined as follows,

Dam Ht. = (D • d)/2

where D - meter tube diameter, and

d - orifice diameter.

Limits of acceptance for the plate flatness [17] correspond to 0.010

inches per inch of dam height. This upper limit is expressed as

Flatness Limit = 0.010 (D - d)/2.

This criterion is used as the basis for expressing the measured flatness

of the plates. The 12 observed position values taken on each plate were segregated into groups as shown in figure 18. A straight line was fit

to each set of values to determine the slope of the line over the width

of the plate measured. These slope values were then multiplied by the

dam height to obtain the flatness measure. Comparison with the flatness

limit of all plates for which the 12 point observation sequence was performed showed that all were within acceptable limits.

Measurement of the orifice plates were made through the course of the

project. In the large majority of the cases the initial measurements

performed on the orifice plates were made before the plate was involved

in flow tests. In a few cases this occurred after flow testing. These

initial measurements of the orifice diameters were the values used in

computing the results of the tests. In the initial round of

observations the orifice diameter was always measured, but the

concentricity, flatness, and plate outer diameter were not always

measured. Table 27 lists the results of the initial dimensional

measurements on the orifice plates, including

1. the orifice diameter,

2. the plate outer diameter,

3. the concentricity of the orifice relative to the plate's

outside diameter expressed as x,y coordinates,

4. the flatness of the plate using the eight point

observation method, and

5. the thickness of the plate.

For those parameters which were not measured, the table entry is zero or marked appropriately.

•86-
ORIFICE PLATE

DIMENSIONAL MEASUREMENT POSITIONS

* - Thickness measurement positions

1-12 - Flatness measurement positions

Figure 18. Orifice Plate Flatness and Thickness

Measurement Positions

•87-
Table 27. Orifice Plate Initial Dimensional Measurements

Plate

Desig,

FE-1/2-1A

FE-1/2-2A

FE-1/2-3A

FE-1/2-4A

FE-1/2-5A

FE-1/2-6A

FE-1/2-7A

FE-1/2-1B

FE-1/2-2B

FE-1/2-3B

FE-1/2-4B

FE-1/2-5B

FE-1/2-6B

FE-1/2-7B

FE-3/4-1A

FE-3/4-2A

FE-3/4-3A

FE-3/4-4A

FE-3/4-5A

FE-3/4-6A

FE-3/4-7A

FE-3/4-8A

FE-3/4-1B

FE-3/4-2B

FE-3/4-3B

FE-3/4-4B

FE-3/4-5B

FE-3/4-6B

FE-3/4-7B

FE-3/4-8B

Date

08/20/84

08/20/84

08/20/84

08/20/84

08/20/84

08/20/84

07/19/84

09/25/84

09/25/84

09/25/84

09/25/84

09/25/84

09/25/84

07/19/84

08/20/84

08/20/84

08/20/84

08/20/84

08/20/84

08/20/84

04/23/86

07/19/84

07/19/84

07/19/84

07/19/84

07/19/84

07/17/84

07/19/84

04/23/86

Orifice Num. Plate Concentricity Flatness Num.

Dia. Obs. Dia. X Y Obs.

(in.) (in.) (in.) (in.)

0.5000

0.7502

0.9996

1.1244

1.3750

1.5002

0.2498

0.5004

0.7502

0.9998

1.1248

1.3746

1.5004

0.2504

0.6248

1.1250

1.5000

1.7508

2.0006

2.2492

0.3757

0.2510

0.6247

1.1251

1.4997

1.7496

2.0001

2.2499

0.3756

0.2506

3722

3721

3719

3729

3727

3722

0.0000

4.3712

4.3728

4.3719

4.3722

4.3723

4.3727

0.0000

8728

8709

8715

8707

8730

8719

0.0000

5.8780

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

5.8731

0.0040

0.0040

0.0030

0.0042

0.0039

0.0036

0.0000

-0.0110

0.0040

-0.0040

-0.0032

-0.0040

0.0000

0.0000

-0.0046

-0.0045

-0.0045

-0.0053

-0.0049

-0.0023

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0006

•0.0002

•0.0004

0.0004

•0.0004

•0.0006

0.0000

0.0010

0.0006

0.0003

0.0003

0.0005

0.0000

0.0000

•0.0001

•0.0040

0.0021

0.0011

0.0008

0.0004

0.0000

0.0010

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0025

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

-0.0009

12

12

-88-
Table 27. Orifice Plate Initial Dimensional Measurements -- Continued

Plate Date Orifice Num. Plate Concentricity Flatness Num.

Desig. Dia. Obs. Dia. X Y Obs.

(in.) (in.) (in.) (in.)

FE-5/6-1A

FE-5/6-2A

FE-5/6-3A

FE-5/6-4A

FE-5/6-5A

FE-5/6-5A

FE-5/6-6A

FE-5/6-6A

FE-5/6-7A

FE-5/6-8A

FE-5/6-1B

FE-5/6-2B

FE-5/6-3B

FE-5/6-4B

FE-5/6-5B

FE-5/6-6B

FE-5/6-7B

FE-5/6-8B

08/20/84

08/20/84

07/18/84

10/25/85

10/28/82

10/28/82

10/28/82

10/28/82

10/28/82

10/28/82

10/28/82

10/25/85

0.8750

1.4991

1.9988

2.2491

2.6242

2.6244

2.9998

2.9998

0.3740

0.2513

0.8752

1.5002

1.9995

2.2496

2.6249

3.0000

0.3737

0.2476

8

8

8

8

8

8

10

8

3

3

3

1

1

1

1

1

1

3

7.1223

7.1224

7.1207

7.0000

7.1222

7.1221

7.1214

7.1210

0.0000

0.0000

7.1219

1238

1185

1244

1225

1208

1228

0.0000

0.0189

0.0179

0.0057

0.0202

•0.0044

•0.0035

0.0000

0.0166

0.0000

0.0000

0.0000

0.0006

0.0067

•0.0009

•0.0014

0.0010

. 0044

0.0000

-0.0033

-0.0024

-0.0198

-0.0013

0.0042

0.0017

0.0000

-0.0017

0.0000

0.0000

-0.0088

-0.0110

-0.0020

-0.0130

0.0014

-0.0079

0.0154

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

. 0000

0.0000

0.0014

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0034

12

12

FE-5/6-1C

FE-5/6-2C

FE-5/6-3C

FE-5/6-4C

FE-5/6-5C

FE-5/6-6C

FE-5/6-7C

FE-7/8-1A

FE-7/8-2A

FE-7/8-2A

FE-7/8-3A

FE-7/8-3A

FE-7/8-4A

FE-7/8-4A

FE-7/8-5A

FE-7/8-6A

FE-7/8-7A

FE-7/8-7A

FE-7/8-8A

06/03/85

06/03/85

06/03/85

06/03/85

06/03/85

06/03/85

06/03/85

05/11/84

05/11/84

05/11/84

05/11/84

05/11/84

05/11/84

02/07/84

05/11/84

0.8747

1.5012

2.0005

2.2503

2.6247

2.9998

0.3754

1.2494

2.2498

2.2501

3.0001

3.0005

3.4979

3.4990

3.9997

4.4992

0.6252

0.6250

1.2503

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0027

•0.0018

0.0014

0.0014

0.0008

0.0011

•0.0025

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

12

12

12

12

12

12

12

-89'
Table 27. Orifice Plate Initial Dimensional Measurements -- Continued

Plate

Desig.

FE-7/8-1B

FE-7/8-2B

FE-7/8-3B

FE-7/8-4B

FE-7/8-5B

FE-7/8-6B

FE-7/8-7B

FE-7/8-8B

FE-7/8-1C

FE-7/8-3C

FE-7/8-5C

FE-9/0-1A

FE-9/0-2A

FE-9/0-3A

FE-9/0-4A

FE-9/0-5A

FE-9/0-6A

FE-9/0-7A

FE-9/0-1B

FE-9/0-2B

FE-9/0-3B

FE-9/0-4B

FE-9/0-5B

FE-9/0-6B

FE-9/0-7B

Date Orifice Num. Plate

Dia. Obs. Dia.

(in.) (in.)

Concentricity Flatness Num.

X Y Obs

.

(in.) (in.)

02/07/84

06/13/86

09/03/85

09/03/85

09/03/85

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

05/03/84

1.2496

2.2499

3.0004

3.4999

4.0002

4.4997

0.6254

0.6234

1.2499

2.9994

3.9994

1.9987

3.7480

4.9985

5.7488

6.6241

7.4996

1.0001

9983

7480

9976

7488

6239

4997

0.9995

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

9.8731

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

o.oooo

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0017

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0055

0.0037

0.0018

0.0008

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

12

12

12

12

Orifice Plate Confirmatory Measurements

In order to obtain a set of complete and uniform measurements describing

the geometric parameters of the orifice plates and to more fully

document their geometrical characteristics, a confirmatory set of

measurements was made on all plates . These measurements were performed

using a uniform set of procedures and the 3-axis measuring machine used

in the original measurements . The results of these measurements are contained in table 28. Descriptions of the procedures used in making

the measurements for each characterizing parameter are given below.

Inner Diameter (ID) - The diameter of the orifice was measured

using either three or four observation points of the position of

the circumference.

Outer Diameter (OD) - The outer diameter of an orifice plate was measured using procedures similar to that of the orifice.

-90-
3. Plate ID to OD Concentricity - The difference in the positions

of the centers of the circles representing the OD and ID of the

orifice plate relative to one another gives the concentricity of

the two. The measurement procedures defined the horizontal or xy origin of the measuring machine's space coordinate system as the plate center from its outer circumference position

observations. The position of the center of the orifice in the

space coordinate system expressed in x and y coordinates is

listed in the concentricity column of table 28.

4. Plate Flatness - Measurement of the flatness of the plate used

the 12 point method described above.

5. Plate Thickness - Measurement of the plate thickness was done

using a conventional micrometer having a resolution of 0.0001

inches . Thickness measurements were made along the outer

edge of the plate at approximately equally spaced positions

marked A through D in figure 18. These observations are listed

under the thickness columns in table 28.

6. Ring Diameter - As a check of the performance of the measuring

machine during the period of the measurements, observations of

the inner diameter of a gauge ring were made as the initial and

final measurements of each series. The same ring was used for

all plates. Its diameter was 3.3999 inches at 20 degrees

Celsius. The mean of the observed diameters is 3.39988

inches with a standard deviation for a single observation of

0.0001 inch.

Tap Hole Geometry

Measurements of the distance from the orifice flange face to the tap

hole center line and the tap hole diameters were made using a dial

caliper, a telescoping type hole-gauge and a micrometer. The distance

from the tap hole edge nearest the flange face was measured with the

caliper. This value was added to half the measured tap hole diameter to

determine the distance of the hole center line from the flange face at

the inner surface of the meter tube. These values are tabulated in

table 29. The stainless meter tube was also measured and was found to

not satisfy the API standard 2530 requirements. However, this meter

tube was used only for statistical control purposes in this project and

is not presented as conforming with the normal industry specifications

for orifice meter tubes . The B meter tube section orifice flange is

upstream of the orifice plate and the corresponding flange of the C

section is downstream of the plate. The stainless steel meter tube

flanges are labeled U and D appropriately.

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94-
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III II I 11 1 III II I II I II I II

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UJ tij III III III III III

95-
Table 29. Tap Hole

with Resp

Diameters and Center Line Separation

ect to the Orifice Meter Flange Face

Meter

Tube

Tap Hole Diameters

(inches)

Top Bottom

Flange Face

Center Line

( inche

Top

to Tap Hole

Separation

iS)

Bottom

FE-IB

FE-IC

0.376

0.376

0.375

0.375

1.013

1.010

1.014

1.008

FE-3B

FE-3C

0.378

0.374

0.378

0.374

1.008

0.997

1.003

1.015

FE-4B

FE-4C

0.381

0.378

0.380

0.376

1.017

1.013

1.011

1.013

FE-5B

FE-5C

0.522

0.511

0.506

0.500

1.013

1.002

1.004

1.004

FE-6B

FE-6C

0.492

0.502

0.501

0.506

0.998

1.003

1.010

1.006

FE-7B

FE-7C

0.507

0.507

0.505

0.508

1.002

1.010

1.000

1.004

FE-8B

FE-8C

0.495

0.508

0.508

0.506

1.004

1.006

1.006

1.008

FE-9B

FE-9C

0.500

0.501

0.499

0.503

0.995

0.998

0.996

1.006

FE-OB

FE-OC

0.514

0.500

0.513

0.499

1.011

1.002

1.008

1.002

DAN-4U

DAN-4D

0.501

0.500

0.503

0.502

1.002

1.015

1.030

0.996

96-
G. Propagation of Error Analysis of Discharge Coefficient Values

The uncertainty in the discharge coefficient values is the result of the

combination of the uncertainties in the measured parameter values. The

analysis of the contributions of the parameter components contributing

to the uncertainty in C, was given in part B of this section.

Equation (1) is reproduced here for convenience in discussion of the

contribution of the various parameters to the uncertainty statement for

the coefficient of discharge.

C^ = m(l - )9^)^/^ /[Nd^F^CpAP)^/^], (1)

where C, = discharge coefficient,

m = mass flow rate

,

F = orifice thermal expansion factor

N — a constant whose value depends upon the units of the

measured parameters,

p = density of the flowing fluid, water in this project,

AP = the differential pressure developed across the orifice meter,

P = d/D, the beta ratio, and

d = diameter of the orifice.

Analysis of the uncertainty of the various measurands in the previous

sections has been done using the relative uncertainty in each. These

components will be combined here to develop a relation for the relative

uncertainty in the discharge coefficient resulting from the propagation

of errors in the observed parameters. For most parameters the numerical

value of the uncertainty is dependent upon the flow rate, orifice, or meter tube diameter, or flowing fluid temperature value of each test.

The relative uncertainty in each parameter has been given as a simple

mathematical formula. These will be combined to obtain an expression

for the relative uncertainty in discharge coefficient which may be used

to compute the uncertainty in the discharge coefficients calculated for

each test run in the data base reported in this document. As has been

the case in the development of the relations for the uncertainty for

each observed parameter, the random error components will be combined in

quadrature and the systematic error components will be combined

additively. The general expression for this combination of error

components is the following.

d n d n n d n

s , (13) ns

where x = nth parameter in eq (1)

s = random uncertainty component for the nth component

,

s = systematic uncertainty component for the nth component, and

s_ = uncertainty in the discharge coefficient value.

^d

•97-
The following gives the uncertainty expressions, random and systematic,

for each parameter from which the expression for relative uncertainty in

the discharge coefficient will be developed.

1. Uncertainty in the Mass Flow Rate, s»

Equation (9) gives the relative uncertainty in the observed

mass flow rate of water through the orifice meter, s»/m.

!m = [ (Sj/M^)^ + (s/t)^ + (6 ppm)2 ] ^/^

m

s s + _! + _ (9)

M t

s where s-j. = indication uncertainty of the scale, see table 10,

M = total mass of water collected in the weigh tank,

s = uncertainty in the diversion time interval

measurement, 0.0001 sec is taken as the value,

s = uncertainty in the diversion time measurement,

t = diversion time interval,

s = uncertainty in the mass standards, see table 10.

2. Uncertainty in the Differential Pressure, s „

The three contributions to the uncertainty in differential

pressure are dependent upon the differential pressure value

itself, and to some extent the conditions of the test. Both

types of uncertainty components are present. These components

are given as the actual uncertainty in eq (12) which is

reproduced below.

s^„ = [(58 x lO'^P )^ + (0.0016 psid)^ + (3s^„ )^

AP t

r / N APm

+ (^s-p^)^]"*"^^ + 0.0048 psi + 59 X lO'^AP (12)

3. Uncertainty in the Flowing Fluid Density, s .

The contribution of this component is taken to be systematic

with a magnitude of 0.00015 g/cm . The relative uncertainty

value may be estimated by assuming that the density of water is

1 g/cm . Therefore, the relative uncertainty in the density of

the flowing fluid is approximately 0.015%. In computing this

uncertainty component the actual flowing fluid density is used.

4. Uncertainty of the Orifice and Meter Tube Diameters, s, and s

Both of these uncertainties are taken as systematic and have

identical magnitudes of 0.0002 inches, with the exception of

the 10- inch meter tubes where the value is 0.001 inch.

98-
Expansion of the summations of eq (13) for the uncertainty in the discharge coefficient using the appropriate partial derivatives, and

recognizing that those components having only a systematic or random

portion remove terms from the corresponding summation term, yields the

following expression:

=Cd ^ ffl ^=dl2^.2 ^ fl «=dl2 2-11/2

d d 3m d

,1 d ,1 d , d + s« + s.„ + s C^ ;^ ""s C^ SAP ^^s di~ ^ d am d

'^

1 ^^d 1 ^"^d + s , + s_

Cj dd Cj ao

d d

where the subscripts s and r refer to the systematic and random parts of

the uncertainty for the two parameters having both, i.e., the mass flow

rate and differential pressure. The other terms are systematic only and

appear only in that portion of the expression. Evaluation of the

derivatives in the expression given above yields the following:

^Cd^

c -If 1

+

^^2

^AP ^2^1/2

AP -' -* d m

s»m "ap

=^ . [ 2 2AP 2p '^T „V M D

^ m

'^ 1-yS

Substitution of eqs (9) and (12) and appropriate terms discussed in the

preceding sections yields the following expression for the relative

uncertainty in the discharge coefficient value:

?^ = ^ tf^ <^''^«">^ ^ ^ [TM"^^)2

4AP

1/2 + (2.56xlO-Ssi^) + (3s^p^)2+(3s^p^)2 ]]

+

I J! + _^I + J_ (0.0049 psi + 59xlO'^AP)

^M t ^ 2AP

(14)

'^d D

^ + 0.00015(g/cm^)/2p + _^ -j;;; + ^f- 0.0002(in)

-99-
A tabulation of the various components contributing to the random and

systematic uncertainties in the discharge coefficient allows an analysis

of their relative magnitude. The results of such a set of computations

of these uncertainty components for selected test runs are given in

table 30, The major contributing parameters to uncertainty in the

discharge coefficient are the mass flow rate and the differential

pressure. Uncertainty components derived from the density and the

orifice/meter tube diameters also contribute, but are smaller in

magnitude.

Table 30 lists various components contributing to uncertainty in the

discharge coefficient, and contains four sections, one for each weighing

system. Each section contains examples covering the normal ranges of

collection times and differential pressures used in developing the data

base. (A detailed description of the operational and computational

methods used in collecting and analyzing the data base is given in

succeeding sections of this report.) Each line of table 30 is identified by the meter tube and orifice plate used and a test run number.

Column label notation is consistent with that used in uncertainty

analysis

The top tabulation of each table section lists the parameter values

contributing to the random and systematic uncertainty components of the mass flow rate measurement for one scale/diverter system. These values

are given in terms of the uncertainty in the discharge coefficient,

i.e., the values listed are individual or groupings of terms given in

eq (14) multiplied by the value of the discharge coefficient. The two

columns labeled S and S /Time contain the diversion uncertainty and its

relative magnitude respectively. This notation departs somewhat from

that used above. Where appropriate, parameters are labeled with the

proper units. The uncertainties in the discharge coefficient value due

to random and systematic uncertainty in the mass flow rate are listed in

the two right most columns.

The mass flow rate uncertainty is dominated by its random component,

which contains the effects of scale indication sensitivity and variability in the diversion valve. In systems 1 and 2 the indication

sensitivity dominates. For systems 3 and 4 the random uncertainty in the

diversion valve is comparable to that contributed by the scale

indicator. Generally, the uncertainty contribution to the discharge

coefficient from the mass flow rate is expected to be of the order of 1

to 2 parts in 10,000 or less.

As an example of the effect of overlap in the capabilities of the mass flow rate measurement, a flow rate crossover, i.e., observations taken

at the same nominal flow rate but using different scales, is given.

These two runs are test runs 44 (weigh system 2) and 25 (weigh system

3) taken on meter tube PE-6ABC with orifice plate 6C at mass flow rate

of approximately 47 pounds/second. For run 25 the diversion time is near

the desired minimum of 30 seconds, which results in a larger relative

uncertainty in the diversion variability. Switching to the larger scale

reduced this component by a factor of 4, reducing the random component

of the discharge coefficient by approximately 30%.

-100-
The second portion of each table section tabulates the uncertainty

components arising from the differential pressure measurement. The

values listed in the table are taken from the observations of the quartz

oscillator-type transducer connected to the top orifice taps. The

primary contributors to uncertainty in the differential pressure are the

components associated with the deadweight testers used in their calibration, i.e., the first two random terms of eq (12) and the two systematic

terms. The relative magnitude of this contribution is listed in the

Cal. Press, column and is given as a percentage of the differential

pressure mean value.

The last three columns of the second portion of each table section give

the discharge coefficient value for each test run and its random and

systematic components of uncertainty as derived from propagation of

error analysis. For the table entry on meter tube PE-OABC with orifice

plate FE-9/0-6A, test run 8, the random uncertainty in the discharge

coefficient is 0.00098. In relative terms this component's magnitude is

0.16% of the discharge coefficient value of 0.6006. The total

uncertainty in the discharge coefficient is the algebraic sum of the

random and systematic components. For the first table entry the total

relative uncertainty is 0.55%. This value reflects the capability to

measure the discharge coefficient at the lowest differential pressure of

0.4 psi. At the highest differential pressure values the total relative

uncertainty in the discharge coefficient measurement decreases to

approximately 0.1% for the examples given in table 30 and is typical of

the data base generally.

The API has selected ANSI/ASME MFC -2M- 1983, "Measurement Uncertainty for

Fluid Flow in Closed Conduits," as a reference standard for calculating

uncertainty of orifice flow discharge coefficients. However, in this

report the authors have chosen the propagation of errors method (to

estimate uncertainty in discharge coefficients) which differs from the

API recommended procedure. Additionally, the authors have performed a statistical analysis of the discharge coefficient/Reynolds number data

that are described in section VI. D.

101-
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co 0) o o o o o 0) a: • I 1 I CO <J D O O C3 O Ul o o o o

(D c c o o o o u £ 3 (D o o o o o o o o

(DO ^0 ^ vO o o o >* O >0 ^ vf

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CO o o o o o o ^ ^ ^ ^ o E »- «- (\J hO o o o o z

t- o o o o o o o o ' E •^ o o o o

<u +J o o o o 4-> CO • • E >0 »- >0 N.

tfl o o o o <U >* in «- o

>-

M »- o o o

CO ^N ro ro

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a.

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a. a. a. a. a. a. a. a. ( F o o o o o C CO

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-103-
H. Uncertainty in the Reynolds Number

The primary results of this work are pairs of discharge coefficient and

Re3niolds number values. Values for each are computed from a combination

of observed and calculated parameter values . The contributions of the

various independent parameters and their uncertainties to discharge

coefficient values have been discussed above. Those associated with the

Reynolds number are discussed here if not discussed previously,

specifically the kinematic viscosity of water.

The pipe Reynolds number may be written in the following form, which is

derived in section III.C,

%

4_ m (15) n puD

where D = pipe diameter,

m = mass flow rate,

p = density of the flowing fluid, and

1/ = kinematic viscosity of the flowing fluid.

The kinematic viscosity, i/ , is defined as the ratio of the absolute

viscosity, n, to the density of the flowing fluid. Computation of the

density of water and its uncertainty has been discussed previously.

Computation of the water's absolute viscosity and its uncertainty are discussed here.

Computation of the Absolute and Kinematic Viscosity of Water

Computation of the kinematic viscosity requires a method to compute the

absolute viscosity and the density of water. The computation of the

density of water uses the Kell [9] correlation which was discussed in

section II. E. 3. Computation of the absolute viscosity of water uses empirical equations developed by Kestin, Sokolov, and Wakeham [18] based

on a re -evaluation of the most recent data on the subject. This re- evaluation of the data reduces the uncertainty in viscosity ratio

values, i.e., viscosity at temperature, t, to that at 20 °C, to 0.1% or less for the temperature range of interest here, which is consistent

with the uncertainty of the measured value of Swindells [19] at 20 °C.

The combined uncertainty of the value of the ratio and the 20 °C value

is approximately 0.2%.

The empirical relations are :

for the 0° to 40 °C range

A* 4- on T" o fi 9 log

-^ = t, 'at {1.2364 - 1.37x10'-^ (20 - T) + 5.7xlO'°(20 - T)^}, MoQ i + yb

(16)

for the -8° to 150 "C range

104-
log

-^ = l^'cil {1.2378 - 1.303x10'^ (20 - T) + 3.06xlO'^(20 - T)^

o o (17) + 2.55x10 (20 - T)^,

where the temperature, T, has units of degrees celsius, and the

logarithm is to the base 10.

The Swindells 20 °C viscosity value is 1.002 centipoise.

Equation (16) is used for test run water temperatures less than 40 °C

and eq (17) for higher temperatures.

Uncertainty in the Reynolds Number Value

Parameters contributing to uncertainty in Reynolds number values are mass flow rate, which was discussed previously and summarized in table

11, pipe diameter, also discussed previously, absolute viscosity, and

density of water. The observed parameters, mass flow rate and diameter, are dominated by systematic effects. The uncertainty in the two

computed parameters are taken as systematic. Therefore, the uncertainty

in the Reynolds number is computed for all components being systematic

with negligible contribution from random effects. The contributions of

each are the following:

1. Mass Flow Rate - Inspection of table 11 shows the range of

uncertainty in mass flow rate to be 0.02% to 0.09%.

2. Pipe Diameter - Uncertainty in the pipe diameter values ranges

from 0.01 to 0.02%.

3. Water Density - Uncertainty in the density is 0.015%.

4. Water Viscosity - Uncertainty in the viscosity value is 0.2%.

Combination of the error components, which are considered to be all

systematic in the propagation of error analysis, results in an upper

bound for the uncertainty in Reynolds number of 0.32 percent.

105.
III. Working Equations and Dimensional Conversion Factors

A. Introduction

The formulations derived here are those used in the various computations

necessary to the various analyses used for development of results from

the observed values discussed in subsequent sections of this report.

These are not unique and may be found in several sources familiar to the

fluid metering community [20,21]. The purpose of their placement in

this document is one of completeness and contractual compliance.

Previous documents describing data bases upon which basic orifice

discharge coefficient values have been based have not described the

complete rationale used in generation of the published results. It is our intent to do so here.

B. Derivation of the Coefficient of Discharge Relation and

Associated Units Conversion Factors

Figure 19 illustrates schematically an exploded view of the arrangement

of an orifice meter placed in a pipeline with differential pressure

tappings located in the adjacent flanges. The parameters pertinent to

this derivation are shown in the figure. For the purposes of this

derivation the following assumptions are made:

1. the flowing fluid is incompressible,

2. the velocity profile is uniform (one -dimensional) with no boundary layers at the pipewall or the surface of the orifice

plate

,

3. the pipeline is horizontal and of uniform, circular

cross-section, and

4. no energy loss occurs between the pressure taps.

The parameters used here are defined as follows:

P, - pressure at the upstream orifice tapping,

V^ - velocity in the pipe upstream of the orifice plate,

A^ - area of the meter tube through which the fluid

flows

,

•m, - mass flow rate through the pipe,

P^ - pressure at the downstream orifice tapping,

V2 - velocity of the fluid through the orifice,

Ap - area of the orifice,

m« - mass flow rate through the orifice, and

p - density of the fluid flowing in the pipeline and the

orifice.

106-
a

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1-1

107-
The physical principles applicable here are expressed by the continuity

equation, which is an expression of the conservation of mass flow rate

through the orifice meter, and Bernoulli's equation, which is an expression of the conservation of energy applied to this case. The continuity

equation is the following:

m, = mj (18)

The mass flow rate of fluid passing through the meter tube or the

orifice may be expressed as a function of the average fluid velocity, V,

the area traversed. A, and the density of the fluid, p.

m = pAV. (19)

Substitution of eq (19) into eq (18) yields

^Vl = ^V2 (20)

Bernoulli's equation in SI units applied to the geometry of the orifice

meter is the following:

2 2 P V P V

1 1 2 2 _ + _+gZj^ = _ + _L+ gZ2, pi pi (21)

where Z, and Z„ are the elevations of the points at which the pressures

are effective, i.e., the pressure tappings, and g is the local

acceleration of gravity. With the assumption that the pressure tappings

are at the same elevation, the form of the equation becomes the

following:

V V,

(22)

Rearrangement of the terms in eq (22) yields

1 2

2 2 V -V

2 1

(23)

Obtaining the dependence of V.. on V^ from the continuity equation,

eq (20) , substituting and rearranging terms in eq (23) yields the

following relation between the pressure difference across the orifice

and the average velocity of fluid through the orifice.

P -P

1 ^2

2 2 2

(24)

Since the shape of the orifice and the meter tube is circular in cross- section, the areas will be expressed in terms of the diameters of the

meter tube and the orifice. Introducing the beta ratio as

108-
p = d/D, (25)

where d is the orifice diameter and D is the meter tube diameter,

eq (24) may be rewritten in the following form, using the beta ratio and

expressing V^ as a function of the mass flow rate through the orifice.

P^-P (1-^"^) . —— = {m^/pK^Y^)"-. (26)

P 2

The subscript for the mass flow rate can be eliminated to reflect the

conservation of mass in this system. Also the parameter F is

introduced and is the thermal expansion factor for the orifice area,

eq (26) has been rearranged in the following form to express the

theoretical mass flow rate as a function of the differential pressure

developed across the orifice meter, and the geometry of the meter,

expressed as the ratio of diameters.

(pAP)^/^ (27)

•m. =

^2 F

TT da

t

27 2 (l-;8^)^/^

Using SI units the theoretical flow rate given by eq (27) has units of

kg/s. However, most of the observational units are given in the

English, customary system of units. Since mass is a derived quantity in

the customary system, conversion between mass and force units must be

accomplished using the defining relation between force, F, mass, M, and

acceleration, a, M = F/a.

The value of acceleration is that of the acceleration of the earth's

gravity at 45°„latitude and sea level, which is 9.80665 m/sec or 32.1740 ft/sec . Therefore, one pound mass produces a force of 32.1740

lb- ft/sec . This value is the basis of a conversion factor for the

differential pressure values derived from the transducer calibration.

Substitution of the appropriate unit into eq (27) yields the following

relation,

•m =

TT ^2 ,. 2,F d (in ) a X

t

27 2 (1 - ^V^^

p (Ib/ft^) X 32.1740 AP (Ib-ft/sec^ - in^) x

•*- ^^

144 in^

1/2

Collection of the various numerical terms yields the final working

equation for the mass flow rate in the customary units system,

2 F m = 0.5250202 ^ ^ (p)"*"^^ (AP)^/^ (28)

-109-
where F , area thermal expansion factor for stainless steel orifice

plates , is given by

F = (1+0. 0000333 (T -T )), (29)

a w r

' with T being the water temperature in degrees Celsius and T is the

reference temperature

.

Computation of the flowing water density utilized Kell's correlation as discussed previously^ This correlation equation produces density values

having units of kg/m . Conversion of these values to the customary

system of units uses the following conversion factor,

1 (kg/m^) X 2.2046226 lb/kg x [0.0254 (m/in) x 12 (in/ft) ]^

= 62.42796 x 10'^ Ib/ft^.

The bar over the AP term in eq (28) denotes that the average of the

square roots of the differential pressure values are used during the

computation of the discharge coefficient. The average of the square

roots of the differential pressure values was obtained using the

following summation. - 1/2 = ^^^^

n

Equation (28) is a theoretical relationship based on the assumptions

given above. The development of this equation neglects the many real

effects which occur in actual orifice meter configurations, e.g.,

effects due to velocity profile non-uniformity, turbulence, frictional

losses, orifice edge sharpness, the finite thickness of the orifice

plate, pressure tap location, etc. The inability to realistically model

these effects results in a significant difference between the observed

mass flow rate through an orifice meter and that theoretically predicted

by eq (28) . Accommodation of these differences is obtained through the use of a correction factor. This may be defined as the ratio ^ of the

actual mass flow rate, m to the theoretical mass flow rate, m_. It is

3. t customary to denote this ratio as the coefficient of discharge, or discharge coefficient, C , . This ratio is ubiquitous to head class flow

metering devices irrespective of their shape.

C , = m /m^. (30) d a' t

The actual mass flow rate was defined previously as

m^ = • (31) ^ (t+r)

where M is the true mass of water collected in Ibm,

t is the flow diversion time in s, and

r is the diverter correction value.

110-
Furthermore, the true mass of water collected can be expressed as

M^ = M /{X-p /p ), (32)

t a' '^ a.' ^'w' ' ^ ' where M is the apparent mass value (gross weight - tare weight)

p is the density of air in g/cm , and

p is the density of water.

'^w ' Equations (31) and (32) can be combined to give

M

m^ = I . (33)

(l-/.^/p^)(t+r)

Combining eqs (28), (29), and (33), the discharge coefficient may be

expressed in terms of observed parameter values and the geometrical

parameters associated with the orifice meter in the following relation:

M y l-y8^

C^ = ! (34)

0.5250203 Fad^(l-p

a/pw

) (t+r) V / f^V r

Equation (34) forms the basis for the computation of discharge

coefficients presented in this report. Using the expression for actual mass flow rate as given in eq (33), we can write eq (34) in its

conventional form,

C^ = m (l-jS^)^/V[Nd^ F^(pAP)^/^], (35)

• • where m = m = actual mass flow rate,

a N = the product of units conversion factors (see eq. (28)), and

F = the orifice thermal expansion factor.

Equation (35) was given in this convenient form as eq (1) in section

II.B.l to perform sensitivity analyses of the orifice measurement

system.

C. Derivation of the Reynolds Number Including Units Conversion

Factors

The Reynolds number is a dimensionless correlating quantity used to

combine the effects of density, viscosity, and velocity of a fluid. It

is defined as

Rjj = VDA, (36)

•111-
where V is the velocity of the fluid in the pipe,

D is a characteristic length, in this case pipe diameter,

and

J/ is the kinematic viscosity, which is the ratio of

absolute viscosity, n, to density, p.

Since velocity may be expressed as the ratio of volumetric flow rate to area (V=Q/A) , and mass flow rate may be expressed as the product of

density and volumetric flow rate (m=/9Q) , the expression for Reynolds

number becomes

% = - — (37)

Expressing m in lb /sec, p in g/cm , u in centistokes, and D in inches,

which are not compatible units, a units conversion factor is needed.

The units conversion factor for the Reynolds number is

(2.54 cm/in)"-"- x (453.59237 g/lb ) x (0.01 (cm^s )/ (centistokes)

) ''.

In addition, a diameter expansion factor for the meter tube may be

expressed as

F^ = (1 + 0.000103(1^-20)), (38)

where T is the temperature in degrees Celsius and the linear, thermal

expansion coefficient for carbon steel at 20 °C [13] is used.

Multiplying eq (37) by the units conversion factor above and 4/7r and

introducing the expansion factor of eq (39) yields the non-dimensional

Reynolds number equation used to compute pipe Reynolds numbers,

•m

R^ = 22737.47 . (39)

puDFj^

D. Calculation of Differential Pressure Values: Compensation for

Drift in the Zero Differential Pressure Response Values

Although the stability of the differential pressure transducer was good,

small drifts were observed in the response of the transducers . A method

of drift compensation was used to reduce these effects. Two observations of zero impressed differential pressure on the transducers were added to the test run observation procedures to provide the means for

drift compensation. These were designated as no -flow and transducer

zero observations. Both were applied to each transducer's observed

value in its conversion to pressure units. The no-flow zero value was taken with the transducers responding to the differential pressure

across the orifice meter with no flow through it and with the line

pressure set to 41 psig. This observation was the first taken at the

112-
beginning of a set of test run groups for an orifice plate/meter tube

combination. Typically a set of test run groups were taken for the full

flow rate range for the meter tested for one mounting of the orifice

plate with several groups comprising a set. It was applied as a drift

correction for all subsequent differential pressure observations taken

on that orifice meter configuration. The rationale for this observation

was to develop a means of compensation for drifts in the differential

pressure measurement system not directly associated with the transducers

alone

.

The transducer zero observations were taken before each test run group,

where a test run group was generally a group of three successive

observations. These observations were taken with each transducer's test

and reference port connected together via the crossover valve of the

five -valve manifold. These observations were taken with the line

pressure set to 41 psig and each port's blocking valves closed. These

observations were taken to compensate for drift in transducer response

characteristics alone. The following discussion gives the mathematical

relations used in converting differential pressure response observations

for each type of transducer to pressure unit values.

Differential Pressure Calculation for the Quartz Oscillator Type

Transducers

As discussed in part D of section II, the response equation used for the

quartz oscillator type transducers is the following

P = Yq + Y^ + Y2 (40)

where x = 1 - T /T. The T term is the oscillator period at the

o' ^ differential pressure of interest and T at zero differential pressure.

The calibration coefficients, Y-^, Y^ , and Y^ , are those appropriate for

pressure units of psi and oscillator period of microseconds. As

discussed above T was found to exhibit small changes between transducer

calibration and subsequent use, therefore, it was necessary to adjust eq

(40) appropriately.

One approach to compensating for drift effects is to assume that the

ratio of oscillation periods in x are invariant. Investigation of this

adjustment to the model indicated that it was not particularly

effective. A second approach is the assumption that a shift in the zero differential pressure period, T , represents a translation and, thus, an

equal shift in the period, T, at non-zero differential pressures as shown in the following relations

.

T000' ' = T + dT , T' = T + dT (41)

o

These may be rearranged as

T000 = T ' - dT , T = T' - dT . (42)

o

113-
Taking the ratio, T /T, from eq (42)

T

o T ' o

T'

dT

o To T - dT T' o

- dT

o

(43)

This expression is used to compute the ratio of the drift or translation

in the period value of the transducer. To perform the calculation

requires the additional observation of the transducer's zero differential pressure response in its translated state. This cannot be achieved

ideally, but is approximated by the zero differential pressure observations taken before each group of test runs. The dT values used in

computing the effective response variable of the quartz oscillator type

transducers, x' , are the differences between the observed zero differential pressure values taken before each test run series and those

observed during the most recent calibration.

This algorithm was tested thoroughly prior to the formation of the final

orifice discharge coefficient data base and was found to provide a significant reduction in the effects of transducer drift which affects

the low differential pressure values to the greatest degree. The

compensated response equation has the same form as eq (40) , but uses the

effective response variable,

AP = Yq -f- Y^x' + Y^x''^, (44)

where x' = 1

T

o

T' - dT

o T = zero diff. press, response at the time of calibration,

T ' = zero diff. press, response for the test group, and

dT = T' - T

o o o

T' = observed response for the orifice meter diff. press.,

assumed to be translated.

Differential Pressure Calculation for the Quartz Bourdon Tube Transducer

As discussed in part D of section II, a linear response model was used for the quartz bourdon tube type transducer, expressed

algebraically as

AP = C^ -I- C2V, (45)

•114-
where V is the analog response voltage observed for differential

pressure, AP, and C^ and C„ are the two calibration coefficients. Since

the transducer's response is linear, drifts in the zero voltage may be

compensated by using the difference V - V to replace the voltage

variable in the linear term of eq (45) . V is taken as the zero differential pressure voltage observed at the time of the most recent

calibration. Subsequent drifts in the response voltage at zero or near

zero differential pressure are used for compensation.

No Flow Corrections

To compensate for small drifts in the differential pressure measurement

observations caused by changes in the piping configuration around the

orifice meter as plates were changed, an observation of differential

pressure at zero flow through the meter and normal operating pressure

was taken. These no -flow zero values were made for all transducers and were subsequently subtracted from each observation. Denoting these

AP ., the compensated values, API used in computation of the mean

differential pressure values were of the following form,

AP. ' = AP. - AP .

,

(46)

1 1 oi' ^

'

where AP. is the observed value.

1

E. Screening of the Differential Pressure Observations

As is the case with any large data base of experimental values , a small

incidence of individual observations not consistent with the body of the

observations is expected. A means to detect and reject these was used

in computing the mean differential pressure values for each test run of

the data base. Since the observed differential pressures are considered

to be derived from stable flow conditions through the orifice meter,

variations in observed values from a single transducer are assumed to be

generated by a random process. Therefore, certain characteristics of

the population of observed values may be made and its members tested for

conformity with those characteristics. Additionally, the experimental

conditions were such that the differential pressure values observed

should not be negative. Screening of the differential pressure

observations was based on these assumptions

.

Data Acquisition Filter

To deal with difficulties encountered with the interfacing procedures

between the differential pressure instruments and the data acquisition

computer in the initial phase of this project, two methods of

differential pressure observation testing and screening were employed.

The objective of both was the elimination of spurious observations. The

first filter was placed in the data acquisition system software used in

generating the data base, and was based on the assumption that no valid

differential pressure observation would be negative. In operation the

observed differential pressure values for each transducer were compared

115-
with the zero differential pressure response observed during that day's

calibration procedures. If an observation was less than that observed

at zero differential pressure, the observed value was replaced with

zero. This filter operated following each test run before storage of

the data on magnetic media. It was initially installed to reject values

which were incorrectly transferred between the instrumentation and

microprocessor interfaces. By the time of collection of the final data

base in 1985, the source of these incorrect transfers was substantially

removed. However, this filter identified 34 test runs not identified by

the operator as having operational errors. These test runs are identified in table 31. The number of rejected observations for each

transducer and the total number of observations are given. With the

exception of one test run this filter rejected only observations of the

Ruska (quartz bourdon tube) differential pressure transducer.

Outlier Testing and Rejection

The second screening procedure inspected each of the three arrays of

differential pressure observations for entries which were not

characteristic of the body of the observations. This procedure was based on the following assumptions:

1. flow through the orifice meter was under steady state

conditions or closely so, and

2. fluctuations in the flow rate, and therefore the differential

pressure, were only the result of the turbulent nature of the

flow in the meter.

Under these assumptions the population of differential pressure

observations taken over the period of a test run may be considered to be

a subset of a normally distributed population. Observations not

belonging to the population subset may be detected by computing the

deviation of an observation from an appropriate estimate of the subset

mean and testing this against an estimated width, i.e., the standard

deviation. To perform such a test a method for estimating the mean and

standard deviation was devised. Since the total population must be

assumed to contain a number of outlying members, the computation method

for the mean and standard estimates must exclude these.

The method used to compute an estimate of the mean and standard

deviation of the population used the middle two quartiles of the array

of differential pressure observations after sorting them in ascending

order based on their magnitude. The steps in the procedure performed

independently on each differential pressure array were the following:

1. Convert the observed instrument indications to pressure units

using the appropriate transducer calibration coefficients and

zero offset observations

.

-116-
Table 31. Data Acquisition Filter Rejections

Run

No.

1

10

16

17

18

20

23

6

8

12

20

22

23

6

10

11

3

4

5

8

9

23

7 11

12

17

7

18

13

2

54

43

48

Date Meter

Tube

07/29/85 PE-IABC

07/24/85 PE-3ABC

07/29/85

07/29/85

07/29/85

07/29/85

07/29/85

10/11/85

10/11/85

10/11/85

07/01/85

06/26/85

06/26/85

06/25/85

06/25/85

06/25/85

12/04/85

12/04/85

12/04/85

12/04/85

12/04/85

12/04/85

12/04/85

11/14/85

11/14/85

11/14/85

11/14/85

07/08/85

06/24/85

06/17/85

06/19/85

08/13/85

12/30/85

12/30/85

PE-4ABC

PE-4ABC

PE-4ABC

PE-4ABC

PE-4ABC

PE-5ABC

PE-5ABC

PE-5ABC

PE-6ABC

PE-6ABC

PE-6ABC

PE-6ABC

PE-6ABC

PE-6ABC

PE-7ABC

PE-7ABC

PE-7ABC

PE-7ABC

PE-7ABC

PE-7ABC

PE-7ABC

PE-OABC

PE-OABC

PE-OABC

PE-OABC

DAN-4SS

DAN-4SS

DAN-4SS

DAN-4SS

DAN-4SS

DAN-4SS

DAN-4SS

Orifice

Plate

FE-1/2-6A

FE-3/4-4B

FE-3/4-5A

FE-3/4-5A

FE-3/4-5A

FE-3/4-5A

FE-3/4-5A

FE-5/6-1B

FE-5/6-1B

FE-5/6-5B

FE-5/6-1C

FE-5/6-5C

FE-5/6-5C

FE-5/6-6C

FE-5/6-6C

FE-5/6-6C

FE-7/8-2B

FE-7/8-2B

FE-7/8-2B

FE-7/8-2B

FE-7/8-2B

FE-7/8-4B

FE-7/8-4B

FE-9/0-1A

FE-9/0-1A

FE-9/0-1A

FE-9/0-1A

FE-5/6-2C

FE-5/6-4C

FE-5/6-6C

FE-5/6-6C

FE-5/6-6C

FE-5/6-8A

FE-5/6-8A

Number 1st Filter

Obs . Ruska Upper Lower

198

200

200

80

81

164

142

200

155

200

180

191

191

119

168

167

178

50

51

178

178

156

158

200

150

150

192

161

88

200

165

161

136

147

3

6

1

5 10

4

4

1

1

2

721

1

4

5

24

3

51

8

2

29

1

1

5

8

11

13

•117-
2. Sort the array in ascending order,

3

.

Count the number of initial zero values inserted by the data

acquisition filter. Adjust the array size for the occurrence of

these zeroes.

4. Form the test mean and standard deviation of the middle two

quartiles of the adjusted array.

5. Test the minimum and maximum quartiles for values greater than

10 test standard deviations from the test mean and set to zero those which are greater.

6. Adjust the array to be continuous, i.e,, non-zero values are eliminated and the size of the array is reduced accordingly.

7. Compute the mean differential pressure and its standard

deviation using the method of Heidelberger and Welsh [14]

.

An example of the operation of the filter is given in the pressure trace

of figure 20. The array of observations for the quartz oscillator- type

transducer measuring the differential pressure at the upper taps of the

orifice meter are shown. The observations are connected by a line

sequentially to show the order of occurrence. The test mean obtained

from the middle 50% of the array after sorting in ascending order is

0.3995 psi and the standard deviation is 0.0033 psi. These give upper

and lower filtering limits of 0.4326 psi and 0.3664 psi respectively and

are shown by the outer, short dashed boundaries. At approximately 130

seconds into the test run an observation lying outside the filters

bounds occurred. This observation was rejected from the final

computation of the mean and standard deviation of the array. The longer

dashed boundaries are obtained using the mean and three standard

deviations of the filtered array. In this case the means differ by

0.0003 psi. This difference is considerably smaller than a single

standard deviation. Both the filter boundaries and the three standard

deviation (as derived from the filtered array) are shown in the figure.

The basis for outlier screening is steady flow through the orifice

meter. Differential pressure values considered to be outliers may have

been due to actual flow fluctuations. Therefore, all transducers would

exhibit similar behavior to that shown in figure 20. However, in

analyzing the data base no method was used to adjust the filter for non- steady flow effects during test runs. As a result systematic effects in

the results could occur. The result of the 10 standard deviation filter

is reflected in the tabulation of test results by listing the average

rnomber of rejections for each test run. The user of the data base may

wish to take such action as deemed appropriate for use of these results

or compute differential pressure and discharge coefficient values

without the use of this filter from the archival data base (see Appendix

D).

118-
u

4J

(0 C 5-1 O (U •H 4J

4.) fH

Oj -i-l >Q ^

U U

cd O

c

CO -O W •!-> O &I

r-l S

o bOU

i-i m

o C

4=

to

i-i 4-) u CO

0) •r-l H >

<u

cd Q

Vj t3 O U

<4-l cd w C

C CO o 4-)

•r-( I/l U

CO CO . > 4J u 0) <U

0) ^ OT

CO 4.) XI c o •d o c •H o CO 4->

>-l CO s CO >

CO T) U

CO C

<u 3 CO u O XI

Pli CO o

oCM

0)V4

:3bO

•H

(xsd) d Jinss 3jij -//(t (7

119-
IV. Data Acquisition and Control Systems

A. General Description

The data acquisition and control system used in this project consisted

of an 8 -bit microprocessor system interfaced to the NBS water flow- rate

measurement facility. The system included 64 kilobytes of random access memory (64K RAM), dual 8 -inch floppy disk drives, and a serial printer.

The microprocessor communicated with external devices using a 4-port,

parallel input/output (I/O) interface, an IEEE -488 interface, and an RS232C communications interface.

The system software consisted of compiled BASIC and data base management

software. A word processing software package was used for text entry,

primarily operator notebook entries, and an assembly language driver was written to acquire mass value and scale status indications from the

electronic scales. Compiled Basic was chosen because of the increased

speed afforded both measurement and computational functions. The data

base management software was a commercially available package which

allowed sufficient programming capability to maintain the data base

files generated by the system and to allow menu-driven operation of the

complete data acquisition software system.

B. Data Acquisition and Control System Hardware

The data acquisition and control microprocessor utilizes the S-100

microcomputer bus and a Z-80A central processing unit (CPU)

microprocessor. In addition to a 100,000 Day Clock used for time-of-day

information stored in the data base, three other interface boards were

necessary for data acquisition and flow system control.

The four-port parallel input/output interface was used for both data

acquisition and measurement system control. This interface consisted of

three 8 -bit input ports, one input port dedicated to software status

polling of the interface ports themselves, two 8-bit output ports, one magnetic relay output port, and one output port dedicated to software

enabling/disabling of the other three output ports. The magnetic relay

output port was used for automatic control of flow diversion. One input

and output port was used for acquiring temperature information from the

thermistor-based thermometer and controlling the selection of one of

eight thermistor inputs to the thermometer indicator.

An IEEE-488 interface was used to interface three universal

counter/timers and a digital multimeter to the data acquisition system.

The IEEE-488 interface is also known as the HP- IB or GPIB interface, and

is a widely available laboratory instrumentation interface. Two of the

universal counter/timers were used to measure the oscillation period of

the quartz oscillator- type , differential pressure transducers.

Typically the oscillation period was in the 25 millisecond range, and

the period was measured with a precision of 0.00001 milliseconds via the

counter/timer's internal 100 MHz clock. The third counter/timer was used to measure the diverter time

.

A four -port RS-232C asynchronous communications interface provided

input/output functions for the microprocessor system. In addition to

120-
ports for the system console and printer, one port was used to acquire

electronic scale readings from the switching and summing

module/Indicator unit of the electronic scales. This task was accomplished using an assembly- language driver, which read the data

output by the scale Indicator and stored the data In a predetermined

location In the microprocessor's memory for subsequent access by the

complied BASIC data acquisition program.

C. Data Acquisition and Control System Software

The data acquisition and control system software controlled the two

primary functions of the project, namely the differential pressure

transducer calibration and orifice data acquisition. The dlverter

calibration software was an adjunct to these operations. The software

system was designed to be user- friendly and to Involve as little

operator Intervention as practicable. In fact, the only data not

automatically acquired by the computer were the date, the barometric

pressure, and the relative humidity. The entire system was menu- driven

using data base management software as the command shell for program

control and data storage functions. The use of menus was decided early

In the planning of the project In order to alleviate the possibility of

operator error during data acquisition.

The software system was designed to minimize operator Intervention,

thereby reducing the number of entry errors for the various data Items

which were Input to the data bases. The software provided specific

Instructions displayed on the terminal to Instruct the operator In the

next step required by the current task at hand. In addition, most

repetitive Inputs were put Into look-up tables or disk files so that the

operator need only choose a menu Item or Input an abbreviated response

associated with the desired choice. However, a more Important function

of the software was the use of Internal diagnostic procedures which,

although transparent to the operator, continuously monitored the

Integrity of various components of the data acquisition system.

Pressure Transducer Calibration Procedures

During differential pressure transducer calibrations, the weight stack

compositions placed on the dead weight testers were stored In a file

called WEIGHTS.DAT. These were used by the operating program to

Instruct the operator which weights were to be placed In the weight

stacks for each pressure value. The mass values for the weights were stored Internally In the program using DATA statements In the program

(DWTCAL.COM) so that the differential pressure being applied was computed correctly. If the applied pressure was greater than 6 psld, the

program warned the operator to turn off the valves to the 6 psld range

Paros Scientific transducer when It was In operation. This step was removed after the 6 psld transducers were no longer used In the system.

Temperature Value Data Acquisition Procedures

Temperature measurements for both the transducer calibration and the

orifice data acquisition program were read using Identical software

procedures. The software used a decision process to determine whether

the temperature reading was steady by comparing the first and tenth

121-
readings of a 10 reading set. If these two values differed by more than

0.02 °C then another set of readings was made until this requirement was

met, at which point the tenth reading was assigned to the desired

temperature parameter. This process normally required about 10 seconds

to complete.

IEEE-488 Interface Bus Error Detection

Bus error detection for the IEEE-488 interface was used during all bus

operations . The subroutine to check for errors was provided by the

manufacturer and was used to check for the following errors:

1. Set-up error

2. No listener

3. Serial poll address error

4. Service request

5. Timeout error

6. ATN true

7. IFC true

8. Reset S-100 system.

During the entire phase of orifice meter testing, no such IEEE-488 bus errors occurred.

Orifice Flow Test Data Consistency Checks and Diagnostics

More extensive built-in checks by the software system were used in the

orifice data acquisition portion of the software. For example, the

active scale deck selection made at the scale system multiplexer was checked to be consistent with the information entered by the operator

from the console. If the software indicated that the wrong scale deck

was being used, then the operator was notified via the console and could

correct the error and resume data acquisition. Before the computer

accepted a value from the scale, motion in the scale deck was also

checked via its motion index character. Transmitted data were accepted

by the computer only after the motion indicator was in the off state.

In this manner, no erroneous data was sent to the system. The scale was also checked for an over-capacity reading which, if detected, caused all

data acquisition operations to halt. This problem occurred only if the

operator entered an incorrect flow diversion time, which caused the tank

to overflow.

A file look-up table (ORIFDIAM.TXT) was used in the orifice program to

find the orifice plate diameter for use in the program. In this manner

the operator need only enter the plate designation to obtain a diameter.

If he entered a designation not contained in the table, then the program

would ask him again for the correct designation until a match was found

in the table of values. This style of programming significantly reduced

the occurrence of operator errors.

There were times during orifice data acquisition when data collection

extended past midnight. The software would adjust the date so that the

correct date was recorded in the data base files. In addition, because

the clock board was used to control flow diversion timing by counting

-122-
seconds since the previous midnight, a delay near midnight was forced to

prevent overflowing the tank during data acquisition. This would happen

because the clock would reset to zero seconds at midnight.

An important part of the diagnostics capability of the orifice data

acquisition software was a data rejection routine which checked the

absolute value of the measured voltage for the quartz bourdon tube type

differential pressure transducer and the period for the quartz

oscillator type transducers against prescribed limits defined in the

program. If too many values were rejected by the routine, the operator

was notified via the console, and a diagnostics program which checked

the IEEE-488 bus was run. This program was called CHEKIEEE.COM, and its

purpose was to record and display the values for each of the three

pressure transducers for a period of 60 seconds (typically 80 to 90

measurements) . The results were displayed in volts for the Ruska

transducer and microseconds for the Paros Scientific transducers and

could be printed out, if desired, for examination by the operator. This

program was very useful in diagnostic tests of the pressure transducers.

This initial filtering of differential pressure observations was directed at identification of errors caused by a data

transfer/instrumentation malfunction. This filter was an aperture type

which passed values lying within a specified range. The bounds for the

quartz bourdon tube transducer were 0.0 to 11 volts. For the quartz

oscillator type of transducer, the bounds were 25 to 29 microseconds.

The normal ranges of transducer indication for the three transducers are 25.2 to 27.3 microseconds for the oscillator type transducers and 0.13

to 9.7 volts for the bourdon tube transducer. The period of oscillation

for the quartz oscillator type transducers was measured with an indication sensitivity of five decimal places, e.g., 25.65432 microseconds.

The analog voltage of the quartz bourdon tube transducer was digitized

with a sensitivity of four decimal places, e.g., 5.1234 volts.

-123-
V. Calibration and Test Procedures

In this section a detailed description of the procedures used during

calibration of the differential pressure transducers and acquisition of

orifice meter test data is presented. As discussed in section II. A of

this report the data collection procedures were automated to the

greatest extent possible, consistent with realistic operation of the

measurements systems. The initial objective of this approach was the

reduction or elimination of human error in the recording of the data.

As the system was planned and constructed it became clear that the

procedures necessary to collect the data could be made to be very

uniform in their execution. To this end a menu driven software system

was developed for controlling the greatest part of the data base collection activities. This approach utilized data base management, word

processing and customized software, written in both assembly language

and compiled BASIC language, modules.

Each of the major tasks was controlled from a main menu of operator

selectable tasks . For the production of the data base a relatively

fixed sequence of operations was executed. The data base was arranged

generally in data blocks which contained all of the information

developed during an arbitrarily selected time period. In the case of

the final pass of measurements on the nickel plated meter tubes these

blocks contained the data collected during a single day. During a portion of the period of time in which the tests were run, data collection procedures ran on a 16- or 24-hour basis. Data blocks were defined

to cover the time period of 1 day in all cases. Each data block was

begun, usually in the morning, with a full calibration of the differential pressure transducers, followed by orifice meter testing. For the

most part a single orifice meter tube was tested during one data block

with several data blocks necessary to complete the data for all orifice

plates to be tested for that meter tube. On several occasions the meter

tubes were dismounted and mounted in the same data block, thereby

causing the data block to contain data for two meter tubes.

The main menus for the various tasks performed daily were written using

the data base management system's command files. The menus as they

appeared for the operators on the console screen are shown in each of

the following sections. The last two items listed are common to each

menu. These items are necessary for the cataloging of data diskettes

and give the operator information about how much storage space remains on a diskette and how to properly back up a data diskette to insure no loss of data. One of the constraints in the selection of the length of

time of the data blocks was the amount of data which could be stored on

a 1 -megabyte floppy diskette.

-124-
A. Differential Pressure Transducer Calibration

Differential pressure transducer calibration procedures were executed

from the following main menu.

API ORIFICE METERING DATA BASE PROJECT

PRESSURE TRANSDUCER CALIBRATION MENU

(Note - This program diskette MUST be In drive A:)

- EXIT

1 - Calibrate pressure transducers (14 points)

2 - Compute transducer coefficients and

append data to the appropriate data bases

3 - Surveillance test of transducers (6 points)

4 - Data diskette status

5 - Back up a full data diskette In drive B: onto a floppy diskette In drive A:

Calibration of the differential pressure transducers using the

deadweight testers was performed on a dally basis, as the first

procedure of the morning. This task was accomplished using programs

DWTCAL and TRANCALC . DWTCAL controlled the calibration procedure Itself

and formed the data base containing the observed and auxiliary parameter

values. TRANCALC performed the least squares fitting procedures on the

data for each transducer and produced the coefficient data base for

them. The basic features of this particular portion of the software

system are shown In figure 21. The floppy diskette containing these

programs was placed In drive A of the computer disk drive and a data

diskette containing the accumulated data was Inserted In drive B.

The details of the operation of the two deadweight testers (DWT's) used

as working pressure standards for differential pressure transducer

calibration procedures were discussed In a previous section. The first

DWT, serial number 73520, was connected to the high pressure side of the

transducers, and the other DWT, serial number 73521, was connected to

the low pressure side. Transducer serial number 13150, labeled #2 In

the data base structures , always measured the differential pressure

produced at the bottom set of taps of the orifice meter. Transducer

serial number 12200, labeled #3 In the data base structures, and the

quartz bourdon tube transducer serial number 30827 always measured the

differential produced from the top set of pressure taps.

During transducer calibration procedures, DWT 73521 supplied the

reference pressure of 41 pslg to the transducers' low pressure ports and

DWT 73520 applied pressures ranging from 41 to 69 pslg to the

transducer's high pressure port. The following gives a description of

the transducer manifold operation during these calibration procedures.

•125-
PRESSURE TRANSDUCER

CALIBRATION

SOFTWARE SYSTEM

Program

Files

Data

Files

Database

Files

Data

File

DWTCAL

Uses WEIGHTS.DAT

(Menu item #1)

V

TEMPDBF

TEMPDWT

DWTREAD

TRANDWT

TRANDATA

TRANCALC

(Menu item #2)

COEFTRAN

TRANCOEF

Figure 21. Differential Pressure Transducer Calibration Software

-126.
Figure 6 is a schematic diagram of the five -valve manifold associated

with the Paros transducers.

Non operational transducer manifold settings and designations:

1. All valves closed except for the bypass in center.

2. Valves on the left of the bypass valve are high pressure.

3. Valves on the right of the bypass valve are low pressure.

The transducer manifold opening sequence is:

1. Open low pressure valve (right side).

2. Close bypass valve (middle valve).

3. Open high pressure valve (left side).

The transducer manifold closing sequence is:

1. Close high pressure valve (left side).

2. Open bypass valve (middle valve).

3. Close low pressure valve (right side).

The operator normally would select item #1 of the pressure transducer

calibration main menu for a complete calibration procedure for the

transducers. A file called WEIGHTS.DAT contained the list of weights to

be placed on the deadweight tester during the calibration. This

procedure was comprised of 14 differential pressure points for most of

the calibrations run in 1985. Prior to that, procedures having a greater nximber of points were used. The use of the external data file

WEIGHTS.DAT allowed the schedule of differential pressures to be changed

easily without changing the operating program, DWTCAL, in any way.

After manual entry of the date, barometric pressure, and relative

humidity, the operator was instructed to perform the calibration using

the weight designations read from WEIGHTS.DAT.

The first test point taken is observation of the transducer response

values to zero differential pressure at the reference pressure, 41 psig,

applied to both sides of the transducers. This was accomplished by

opening only the valves on the low pressure side of the transducer

manifolds at the air/oil interfaces with each bypass valve open. The

remainder of the test points were taken with the bypass valves closed

and both the high and low pressure valves open. The remaining test

point differential pressures were obtained by adding and removing the

appropriate weights to the high pressure side DWT (s/n 73520) as listed

below for the 14-point calibration schedule. The weight designations,

differential, and test pressures are also listed. The pressure values

listed are indicative of the numerical precision used in computation and

storage of these values.

-127-
14- Point Calibration Schedule

Diff. Test

bs. Weight Stack De signation Press. Press.

1 66- 77- BB- 0.00137 41.00646

2 66- 77- SS -lOW- IIW- 12W- 13W- 0.36207 41.36715

3 66- 77- SS-IOW- 9- 10- 12- 8.18395 49.18904

4 66- 77- 88-lOW- 7- 10.18463 51.18971

5 66- 77- 88-lOW- 7- 9- 12- 16.18635 57.19143

6 66- 77- 8S-10W- 7- 9- 10- 12- 18.18685 59.19194

7 66- 77- 8S-10W- 7- 8- 20.18704 61.19213

8 66- 77- S8-10W- 7- 8- 9- 10- 12 28.18927 69.19436

9 66- 77- 88-lOW- 7- 8- 9- 10- 27.18903 68.19412

10 66- 77- S8-10W- 7- 8- 10- 12- 23.18779 64.19287

11 66- 77- 88-lOW- 7- 10- 12- 13.18537 54.19046

12 66- 77- 88-lOW- 10- 12- 3.18247 44.18756

13 66- 77- 8S-10W- 12- 1.18196 42.18705

14 66- 77- 88- 0.00137 41.00646

The pressures listed above are representative values. These did change

slightly from day to day as atmospheric conditions changed. Before the

data were taken at each pressure the oil levels in each leg of the

transducer valve manifolds were balanced using the traveling

telemicroscope

.

The calibration procedure was quite straightforward. The operator was instructed by messages displayed on the the computer's console to place

each series of weight stacks on the deadweight testers to generate a known differential pressure relative to the reference pressure of 41

psig. The computer then acquired 25 readings from all of the pressure

transducers. These individual readings were stored in a file called

TEMPDBF.DAT for later inspection of any suspect data. The average

transducer indication along with temperature, weight stack designation,

and other information were saved in a file called TEMPDWT.DAT. Upon

completion of the calibration procedure, the ASCII data file TEMPDBF.DAT

was appended to data base file DWTREAD.DBF and the file TEMPDWT.DAT was appended to TRANDWT.DBF as shown in figure 21. At this point it was possible to mark data for deletion that were obviously incorrect in the

data base file TRANDWT.DBF so that they would not be used in the subsequent fitting procedures. It should be stressed, however, that these

deleted data were not lost, but merely marked for deletion. After

deleting any suspect data a new data file called TRANDATA.DAT was created for use in the least square fitting procedures, and then the

software system returned to the main menu.

The transducer calibration coefficients were computed using menu item

#2. The program TRANCALC computed a linear least squares fit of the data

for the Ruska transducer and a second order least squares fit for the

two Paros Scientific transducers. These calibration coefficients were stored in the data file COEFTRAN.DAT and were appended to the data base

•12S-
file TRANCOEF.DBF upon completion of the program,

then returned to the main menu. The software system

The choice of item #3 on the main menu allowed a six-point surveillance

test of the pressure transducers. This test was designed as a check of

the transducer performance between calibrations. This test compared

predicted results to measured results for the current calibration

coefficient values and presented these data in tabular form on the

console for inspection. If a problem was detected, the full calibration

was rerun (item #1 on the main menu). The test side DWT weight stack

composition for these tests is shown below with the computed

differential pressure value and typical results for the transducers

.

Six-Point Surveillance Test

Obs. Weight Stack Designation

1 66-77-88-

2 66-77-88-10W-11W-12W-13W3 66-77-88-10W-12-

4 66-77-88-10W-10-12-

5 66-77-88-lOW- 7-

6 66-77-88-10W-7-8-9-10-12-

Diff. Paros Paros Ruska

Press. 13150 12200 30827

(psid) (psid) (psid) (psid)

0.0014 0.0093 0.0080 0.0098

0.3621 0.3686 0.3612 0.3701

1.1820 1.1880 1.1867 1.1892

3.1824 3.2102 3.1914 3.1897

10.1847 10.1901 10.1886 10.1914

28.1896 28.1964 28.1953 28.1970

This surveillance testing proved quite useful in determining the

presence of any strange behavior in the transducers. However, it should

be stressed that any problems detected in the transducers were corrected

immediately, and then the transducers were re -calibrated before orifice

data collection procedures were resumed.

B. Meter Tube Installation

All orifice meters tested were always installed with the Sprenkle flow

conditioner upstream, meter sections A, B, and C, respectively, from

upstream to downstream, with the orifice plate mounted between the

orifice meter flanges of sections B and C. These were located near the

control console and pressure transducer rack near the downstream end of

the facility test sections. This arrangement gave the longest possible

upstream lengths of straight pipe between the upstream end of the flow

conditioner and the pump manifold. In the case of the 4-inch test

section of the water flow measurement facility, a 4 -inch in-line filter

was also permanently placed in the flow line immediately downstream of

the pump manifold. This filter was of the re-entrant type with a stainless mesh filter element having a mesh spacing of 150 micrometers

(0.006 inches) had the effect of preconditioning the velocity profile of

the water flow as it left the pump manifold. A bleed valve was attached

to the Sprenkle flow conditioner to release entrapped air. This valve

was generally open except when taking a no flow differential pressure

measurement. Each upper tap of the orifice meter was fitted with a small manifold, which consisted of a short length of 1/4- inch pipe

connected to a tee with a valve connected to the opposite side of the

tee. The orifice meter was mounted such that this connection piping in

-129-
the orifice taps was in the vertical plane. The valve was placed above

the tap hole and providing the means of bleeding air which may have

accumulated in either of the upper tap holes. The transducer

connections were arranged such that the lower orifice meter taps were connected to the lower transducer (S/N 12200) and the upper taps led to

the two upper transducers (S/N 13150 and S/N 30827). Ball valves were located in the lines leading to the transducers to allow these lines to

be isolated in the filled condition during changing of the orifice

plates or meters , and during changes in the flow rate during data

collection procedures. This was a very effective means of protecting

the transducers from differential pressure extremes , and allowed the

transducer manifold and associated tubing to be water filled at all

times. By using these valves the need to bleed air from the transducer

manifold and tubing was much reduced.

Once all the connections were made, an orifice plate was selected and

installed in the meter run. The orifice plate was installed with the

sharp edge of the orifice facing upstream. Before an orifice plate was installed it was washed in acetone and dryed with a soft cotton cloth.

Any discolorations were removed in this manner. After installing the

plate, the gap between the locating pins on both the east and west sides

of the meter were checked with a feeler gauge. These values were recorded in the notebook file maintained by the operating program,

ORIFICE. Generally, the acceptance limit for this separation was 0.0015

inches (37 micrometers) . Once the meter was installed, the power to the

flow system control bench was turned on. The pumps were turned on with

extreme care in order to avoid bending the orifice plate by keeping the

backpressure less than 41 psig and the differential pressure below the

maximum value noted for each plate.

C. Orifice Meter Data Acquisition Procedures

The main menu used to control data acquisition and storage functions for

orifice testing procedures is shown below.

API ORIFICE METERING DATA BASE PROJECT

ORIFICE DATA MENU

(Note - This program diskette MUST be in drive A:)

- EXIT

1 - Copy transducer coefficient file

from drive B: to A:

2 - Test orifice plates and append

orifice data to data bases

3 - Data diskette status

4 - Back up a full data diskette in drive B: onto a floppy diskette in drive A:

•130-
Figure 22 shows a block diagram illustrating the organization of the

software system used to acquire the flow measurement system data during

orifice discharge coefficient measurement operations. Following the

calibration of the differential pressure transducers, it was necessary

to transfer the calibration coefficient data file COEFTRAN.DAT to the

orifice data acquisition program diskette. This task was accomplished

using item #1 in the main menu, which copied the file from the data

diskette in disk drive B to the program diskette in drive A and was necessary to prevent any ambiguity between the files on either diskette.

Data acquisition during orifice meter testing was accomplished using

three programs, ORIFTEST, 0RIFICE2, and ORIFICES. Using the Microsoft

Basic "CHAIN" statement, these three programs were chained together due

to memory limitations of the computer system. The "%INCLUDE" compiler

directive was used with the file ODEF.BAS in order to declare common

variables, functions, and subroutines used by each of the programs.

Data acquisition was started by choosing item #2 in the main menu. This

choice loaded and ran the first of the three chained programs . It

should be stressed that the loading of these programs from the systems

disk was transparent to the operator, whose menu selections controlled

operations at any time

.

ORIFTEST is an initialization program. Its tasks were to initialize

variables, place the number zero in two data files, NUMBFILE.DAT and

ZEROFILE.DAT, which will be discussed in the following paragraphs, and

to read the transducer calibration coefficients from the file

COEFTRAN.DAT. The operator was also required to enter the date and to

answer whether or not the Ruska pressure transducer was in operation.

Finally, the operator's notebook file, COMMENT, DOC, was opened for

subsequent input.

The data acquisition software next chained to the program 0RIFICE2. This

program first recalled the previous meter tube, plate, and run number

information from the file 0RIFSTAT.DOC. After the operator entered the run number for the next run, he could change the meter tube and/or plate

combination. A table of orifice plate diameters (ORIFDIAM.TXT) was

searched- for the plate diameter. If not found, the program asked for

the corrected orifice plate designation and checked the table again.

At this point the response of the differential pressure transducers and

the electronic scales were checked against the appropriate check

standards. The deadweight testers were used to generate a known

differential pressure, in this case approximately 5.18 psid. This

pressure was applied to the transducers through the manifold in the same way that the transducers were calibrated. The oil/air menisci were

adjusted by the operator to equal heights, and the microcomputer read

the transducer response values after being given the command to do so by

the operator. Twenty- five consecutive, sequential observations were made of the three transducer indications. These values were stored in a disk file. Next a scale check was performed using a set of calibrated

weights. The following is a list of the detailed procedures displayed

on the console and followed by the operator to perform these tasks:

-131-
FLOWCHART

DATA ACQUISITION PROCEDURES

Program Files Data Files

ORIFTEST

Uses COEFTRAN.DAT

(Menu item #2)

0RIFICE2

Uses ORIFSTAT.DOC

ORIFDIAM.TXT

0RIFICE3

Yes

NUMBFBLE

ZEROFILE\

ZEROS*

ZEROFILE

OHEAD*

OPRES*

NUMBFILE

Database Files ORIFHEAD

ORIFPRES

ZEROES

Figure 22. Orifice Meter Data Acquisition Software

•132-
1. Starting with all manifold valves closed, open the air pressure

supply from the cylinder to the deadweight testers.

2. Place weights #10W and #9 on the high pressure side of the

deadweight tester.

3. Close the drain valve to the tank of the scale to be checked.

4. Open inlet valves on both deadweight testers to "HIGH RANGE".

This will levitate the ball and weight stack of each

deadweight tester.

5. Open outlet valves of the DWT's to "ON".

6. Open transducer manifold valves of the air- oil interfaces as the console screen instruction directs.

7. Load the specified check weights onto the scale. Gross weight

will be read upon a "RETURN" from the console. Remove the

weights from the scale deck.

8. The tare weight will be read on a "RETURN" from the console.

9. Gently spin the weight stacks of the deadweight testers.

Balance the air/oil menisci using the telemicroscope.

10. When the values stabilize on the differential pressure

transducer indicators, initiate reading of the transducer

values with a "RETURN" from the console.

11. Close the transducer manifold valves. The transducers should

indicate approximately 5.18 psid and the scale should indicate

within one count of the specified weight. If this doesn't

occur, redo Transducer/Scale check from the console.

An observation of the transducer response was next performed with zero flow through the orifice meter. The following procedure was used to

accomplish this task:

1. With the transducer manifold valves closed, open the upper and

lower transducer line valves at the meter.

2. Relieve any back pressure on the orifice plate by opening the

bypass valves and close the downstream outlet valve on the

meter run.

3. Adjust the bypass valves to set the backpressure to 41 psig.

4. Close all bleed valves, including the valve on the Sprenkle

flow conditioner.

5. Open the transducer manifold valves at the water-oil interfaces

and balance the menisci.

133-
6. Close the upstream inlet valve supplying the meter run. The

computer will read the transducer values (20 consecutive values

are read and stored) . The values should be near the following.

This message is displaced on the system console.

Upper Paros 25.215 Lower Paros 25.597

Ruska . 002

7. Close the transducer manifold valves.

8. Open the upstream inlet valve, open the downstream outlet

valve , and open the bleed valve on the Sprenkle flow

conditioner. If the transducer values are not as indicated

above, perform the zero flow measurement procedures again.

Finally, the program instructed the operator to perform a zero differential pressure measurement at a reference pressure of 41 psig.

This measurement was made with each transducer's crossover opened and

the two shutoff valves closed. The sequence of valve manipulations was

the following. The high side shutoff valve was closed, and the cross- over was opened. Finally the low side shutoff valve was closed. The

sequence insured that the static pressures at the transducers were near

41 psig for this observation. All of the individual readings of "no

flow" zeroes and deadweight tester zeroes were saved in files designated

as ZEROS*. DAT, where the * indicates ascending numbers from one up to

the number of times this measurement was performed in a single day.

This index was saved in the file ZEROFILE.DAT to aid in the appending of

this data to the data base file ZEROES. DBF,

ORIFICES was the final of the three chained programs and acquired the

orifice discharge coefficient data over the flow rate range. Each

orifice plate was tested at differential pressures of 0.4, 1.0, 3.0,

10.0, and 28 psid (or the maximum allowed for the plate under test,

whichever was lower) at a base pressure of 41 psig. (These pressures

were selected to approximately equal incremental changes in the Reynolds

number over the flow rate range.) The operator was first instructed to

adjust the flow rate for the desired differential pressure and do a manual filling of the weigh tank in order to determine a nominal value

for the diversion time. After entering this time from the console, the

operator entered the number of test runs the system was to execute at

this particular flow rate setting (normally three runs were chosen)

,

values for the barometric pressure, the relative humidity, and any

pertinent comments he might have about the current test. The software

system then controlled the data acquisition procedures until the

selected number of runs were complete.

The system closed the weigh tank drain valve and measured the tare

weight. The operator was given another opportunity to adjust the flow

rate, then the system read the system time-of-day clock and diverted the

flow into the weigh tank for approximately the prescribed amount of

time. During the time of the flow diversion, the data acquisition

system read the values from each of the pressure transducer indicators

sequentially. This reading loop was terminated with a reading of the

time-of-day clock to check if the diversion time interval had been

-134-
exceeded. If not, the transducer reading loop was executed again. This

loop was executed until the diversion time interval was completed. All

of the individual values of the differential pressure indications were stored for the entire run. The maximum number of transducer readings

which could be stored was 200. This number of observations was selected

based on the size of the data space available, and on the minimum time

interval between readings. For the majority of the data base the

approximately 1- second reading interval was used. The transducer

indicator reading loop was executed in somewhat less than one second.

For diversion times below 150 seconds this loop was executed as quickly

as possible. Above 150 seconds a variable delay loop was inserted into

this observation loop to keep the maximum number of transducer readings

near or below the limit of 200. In this way the differential pressure

observations were evenly distributed over the diversion time of the run.

The system measured the flow loop, weigh tank and air temperatures as well as the gross weight of the tank and diversion time after the

diverter valve switched the flow back to the reservoir. The weigh tank

was drained and this process continued until the desired number of

observation runs were complete. After the final flow diversion, the

data was computed and the results along with average values were

displayed on the console screen and output to the printer. Data files

OHEAD*.DAT and OPRES*.DAT were used to store the raw data. Again the * indicates ascending numbers from one up to the number of times the

measurement was performed in 1 day. The final number was saved in the

file NUMBFILE.DAT to aid in the appending of the orifice data to the

data base files ORIFHEAD.DBF and ORIFPRES . DBF.

At this point the software system chained back to 0RIFICE2 in order to

measure the transducer zero values against the deadweight tester. The

system continued in a cyclic manner between 0RIFICE2 and ORIFICES until

either the data acquisition for the day was completed or all flow rates

for an orifice plate were completed. Then the operator was instructed

to perform, at his option, a final transducer and scale check as well as a final "no flow" pressure measurement as described above before the

system stopped. Finally, the data were appended to the appropriate data

base files as described above.

After the data base files had been appended, the software system called

the word processor to append the file C0MMENT.DOC to a list of notes

kept during the course of the project called N0TEB00K.DOC. This file

contained not only comments from the operator as described above, but

also such data as the operator (s) initials, date, time, plate and meter

tube designations, scale check value, and transducer check values. This

notebook was an extremely useful tool for the operators as well as for

the managers of this program.

Selection of Flow Rate Values for Each Orifice Plate

The selection of the sequence of differential pressure values for a set

of observations for each orifice plate during a data block was done

using table 32 prepared by the NBS Statistical Engineering Division. It was used to minimize or eliminate the possibility that systematic errors would not be introduced into the data base through the use of a fixed

135-
sequence of differential pressures run on every orifice plate. This

schedule was originally developed for a set of tests involving a single

meter run and two orifice plates. It was later generalized for use throughout the testing program. The schedule for the first plate of a block was selected by the operator on duty such that it was not the one selected for the previous data block. Once the beginning point in table

32 was selected, successive sequences were used for the remainder of the

block. After the plate 16 schedule, succession began with plate 1.

Table 32. Schedule

Setting

of Differential Pressure Values for Flow Rate

Plate #1 2 3 4 5 6 7 8

10 3 1 1 3 3 10 28

.4 .4 3 28 .4 10 1 10

1 1 .4 10 28 28 3 .4

3 10 28 .4 1 1 .4 1

28 28 10 3 10 .4 28 3

Plate #9 10 11 12 13 14 15 16

3 28 28 3 .4 10 28 .4

.4 1 1 28 3 28 3 10

1 .4 3 1 1 3 .4 1

10 10 .4 .4 28 1 10 28

28 3 10 10 10 .4 1 3

This schedule was modified somewhat for more efficient use of scales,

i.e., all flow rates to be run on one scale were completed before

selecting the next scale , Randomization of the flow rates was attempted

for the majority of the data base collection within these constraints.

D. Diverter Correction Calibration

The data necessary for computation of the diverter correction values

were obtained through the use of the following menu.

API ORIFICE METERING DATA BASE PROJECT

DIVERTER CORRECTION MENU

(Note - This program diskette MUST be in drive A:)

- EXIT

1 - Calibrate diverter

2 - Re-compute diverter correction

3 - Data diskette status

4 - Back up a full data diskette in drive B: onto a floppy diskette in drive A:

•136-
Calibration of each of the four weigh tank diverters was accomplished

using the software system shown In figure 23. The program DIVERTER was

run by choosing Item #1 In the dlverter correction main menu. The

specific measurements are discussed In detail In section II. C. 2 of this

report. The results of the calibration were saved In a data file called

DIVERT.DAT, which was appended to the data base file DIVERTER. DBF upon

completion of the program. The system then returned to the main menu.

Item #2 of the main menu allowed recomputatlon of dlverter correction

values off-line so that thermistor calibrations or scale calibrations

could be Included In the data reduction at a later time . This feature

of the system allowed the operator to continue orifice data acquisition

while using another computer system to recompute data.

-137-
Flow Chart

Diverter Calibration Software

Program File

Data File

Database File

DIVERTER

(Menu Item #1)

DIVERT

DIVERTER

Figure 23. Weigh Tank Diverter Calibration Software

138-
VI. Archiving of the Data Base, Data Analysis Results, and Statistical

Analysis of the Results

The extent of the complete data base generated during the course of this

work is quite large. It is stored in computer readable form only and

available from either NBS or API. The bulk of the data base consists of

the differential pressure transducer observations recorded for each test

run, 40 to 200 values for each of the three transducers. The results of

the analyses of the final data base are much less extensive. However,

listing of all the intermediate parameter values for each test run is

not possible here. To keep the size of this report within manageable

proportions, the results for each valid test run are summarized in a single line of information. Plots of discharge coefficient vs. pipe

Reynolds number are given for each orifice meter. A brief discussion is

given of the operational events and the data collection procedures used

in collection of the final data base because these affect the test runs analysis

The final data base contains the normal operational malfunctions and

blunders encountered in obtaining any experimental data base. A detailed inventory of the runs in which malfunctions occurred is included.

A. Operational History, Final Data Base Definition, and

Archiving of the Data Base

A detailed operational history of this project from its inception

through completion of the major period of data collection in January

1986 is given in Appendix A. A brief description of the major events

shaping the structure and segmentation of the data base is given here to

provide the rationale for elimination of certain blocks of test data

from the analysis procedures. The complete data base generated by this

project is quite large and is clearly segmented into two parts. The

segment of the data base which will be referenced here consists of test

runs taken on June 17, 1985 and thereafter.

On June 17, 1985 the initial observation runs were taken on the fourinch stainless steel, meter tube which served as a check standard in

generating the final data base. Stainless steel was chosen as the meter

tube material to ensure that surface roughness effects induced by

corrosion of the meter tube's interior surfaces would be absent and have

no effect on the performance of the 4- inch orifice plates tested with

the tube. In this way the performance of the total measurement system

could be quantified over the generation time period using statistical

methods. As mentioned above, an extensive experimental program was necessary to unquestionably identify and, to some extent, quantify the

role that corrosion- induced surface roughness may play on orifice meter

discharge coefficient values when determined using water as the test

fluid.

The test run data taken before June 17, 1985 were contaminated by modification of the surface roughness of the meter tubes over time. This

139-
modification was shown by experimental work to be caused by the continual increase in the roughness of the surface induced by corrosion of the

mild steel. Previously published work [22] investigating the effects of

surface roughness on orifice meter performance was performed on meter

tubes generally smoother (30 to 60 microinches rms surface roughness)

,

with one exception, than those used in this work. The previous tests

were done in natural gas (no corrosion- induced roughness changes) and

concluded that smooth or honed pipe could be used in making orifice

meters with no adverse effect on discharge coefficient values. The

magnitude of the effects observed at NBS was unexpected, and was clearly

shown to be induced by surface corrosion near the end of the time period

of the project. The investigation to demonstrate and quantify these

effects, and then, to explore corrosion inhibition methods to control

them, is discussed in detail in Appendix A. This investigation ended in

mid- June 1985.

The investigations performed between January and June 1985 clearly

demonstrated the effect of increased meter tube surface roughness on discharge coefficient values. In February a method acceptable to the

API was devised to obtain a level of statistical control in the collection of the final data base through the use of a single four -inch,

stainless steel meter tube, designated DAN-4SS. It was similar to the

other 4- inch meter tubes, but did not conform to all geometrical

specifications of the AGA Report No. 3/API 2530 standard [17]. It con- sisted of a single upstream section 20 feet in length with a downstream

section 3 feet, 4 inches in length, and did not meet all industrial

standards criteria. It only was to provide a measurement systems performance reference that would not include effects of changing surface

roughness levels. Data were collected with this meter tube and one orifice plate set in the same manner as with the other meter tubes.

Observation repetitions were greater to provide a reasonably large

amount of data roughly scattered over the length of the data base collection period. These data formed the basis for a statistical analysis

of measurement system performance which will be given later in this

section.

In the late spring of 1985 NBS and the API, through its Orifice Database

Steering Committee, had agreed that any data base developed using water

flows must incorporate a method to eliminate meter tube surface corrosion. (It had been shown that relatively small levels of rust formed on

the meter tube were measurable in the discharge coefficient value with

the NBS measurement system.) Several inhibition methods were explored.

Finally, it was agreed that the electroless nickel plating process would

be used on one meter tube. In preparation for obtaining the data base,

each of the meter tubes was refurbished to restore its interior surfaces

to a level judged to be of commercial quality by the API. Because the

API's Orifice Database Steering Committee had expressed some apprehension that nickel plating would adversely affect and deteriorate this

level of quality, and, hence, the value of the discharge coefficients

derived from them, brief tests were conducted on the first refurbished

meter tube before the nickel was applied. These series, designated bare

140-
meter tube tests, were subsequently performed on all meter tubes. To

distinguish the data on the bare steel meter tubes from the data on the

nickel plated meter tubes, the bare or unplated tubes retained the designation FE-XABC, where X ranges from to 9 indicating the meter tube

size. The nickel plated meter tubes were designated PE-XABC.

On June 18, 1985, a bare meter tube test on the refurbished FE-6ABC

meter tube assembly with the largest beta ratio orifice plate (approx.

0.75) was run. This test run series consisted of 21 test runs completed

in approximately 4 hours. The meter tube was removed from the water

flow rate measurement facility, dried, and shipped to be plated with

approximately 0.001 inch thickness of nickel using the electroless process. Inspection of the tube upon removal showed little visible rust on

the tube surfaces . Upon the return of this meter tube a full set of

test runs was completed involving each of the eight orifice plates tested for this tube. No corrosion was observed visually in the meter

tube. The consistency of test result replication between the bare and

plated meter tube was within the bounds expected from the propagation of errors analysis, and, most importantly, did not show large between-day

differences. With these results in hand it was decided to nickel plate

the remainder of the meter tubes using the electroless nickel process.

Subsequently, each of the meter tubes used in generating the final data

base was tested before electroless nickel plating with the largest beta

ratio orifice plate and the 0.37 beta ratio plate. Because the largest

beta ratio plate (beta = 0.75) is the most sensitive to surface rough- ness effects, the smaller beta ratio plate was added to give a basis for

drift effects, should a significant difference develop between the plated and unplated results for the large beta ratio plate.

Archival Data Base Segments

The complete data base is archived in two segments . The segment of

interest for correlation equation development, such as in the currently

used Buckingham [17] and Stolz [23] equations, would appear to be that

segment not unduly influenced by corrosion induced surface roughness

effects . This is defined as the final data base developed on the plated

meter tubes. The remainder of the data base taken before June 17, 1985

is of limited practical utility, although it may have academic interest

to future workers in the flow measurement field. The archiving of the

complete data base in computer readable form is described in Appendix D

of this report. Only the final data base will be discussed henceforth.

Criteria For Marking Test Runs for Deletion

In archiving the data base all of the complete test runs recorded on magnetic diskettes are included, i.e., those marked for deletion and

those not. This archival method was required by the API. Test runs marked for deletion were excluded from the analysis. The criteria used

in marking runs for deletion are discussed below.

Marking test runs for deletion was based on the following criteria.

141-
1. Deletion based on facility malfunctions as observed and indicated by

the operators in the hand written notebook, the data acquisition

computer notebook, or the preliminary results sheets, or operator

mistakes in entering the necessary data into the computer during data

collection procedures. Typical examples are:

(a) air bubbles observed when bleeding orifice meter taps,

(b) improper positioning of transducer manifold valves,

(c) not opening the main shutoff valves to the transducers before

beginning a test run group.

(d) keyboard entry errors of the operators. In several cases the

simplest method of recovery without restarting the program was repetition of a test run series allowing a complete data acquisition cycle and start a new test run group. This second group

would be the actual test runs with the initial group marked as deleted. This method was much more time efficient than restarting the data acquisition procedures as was done for each newly

installed orifice plate. Typical keyboard entry errors were

incorrect entry of the diversion time or system number.

2. Improper setting of the pumping or flow control systems leading to

poor reproducibility in the test run observations, e.g., pressure

pulsations attributable to using pumps at orifice meter flow rates

well below the stable operating capacity of the ptomp

.

3. Runs never recorded on the magnetic storage diskettes due to data

acquisition computer malfunction, e.g., operating program errors before test run data were written to disk files, or operators inadvertently skipping a number in the run ntimber sequence.

Operator entry of specific descriptions of malfunctions into the computerized and handwritten notes did not always occur. Deletion of specific test runs or test run groups was made on the preliminary results

sheets printed by the data acquisition computer. In most cases the test

runs or groups of test runs so marked were repeated before the orifice

plate was removed from the meter tube in order to complete a full set of

flow rate settings on each plate installation. Operator indicated deletions are the basis for the subsequent marking of a significant number

of test runs for deletion and fall into the first deletion criteria.

Deletion based on the second criterion is applied to blocks of test run

data on specific orifice plates. These blocks generally include all

test runs made on a particular day on a plate. This criterion is used

to describe a difficulty observed at the lowest flow rates and Reynolds

number which occurred with the small beta ratio orifice plates of the

smaller diameter meter tubes.

•142-
Abnormal Behavior at Low Reynolds Numbers

As mentioned in the introduction to this report this project was one of

three which ran concurrently and covered overlapping or adjacent Reynolds niomber ranges. The API program manager, Mr. W. A. Fling, noted a discrepancy between the results obtained in this project and those obtained from the low Reynolds number project being conducted in a high

viscosity oil at Colorado Engineering Experiment Station, Inc. (CEESI)

[24] on the same meter tube/orifice plate combinations. As a result a collaborative investigation of the effects seen in the water flow

measurement facility was undertaken. The following is taken from the

report of that work, and is given here to describe the investigation,

its results, and its impact upon the data base.

The test results of the low and intermediate Reynolds number projects

using the same meter runs and orifice plates have shown good correlation for all meter tubes and plates tested with the exception of the 2-

inch meter tube with the small beta ratio orifice plates (0.1, 0.2, and

0.375 beta ratios). For these plates the discharge coefficient values

obtained in the low Reynolds nxomber project uniformly decreased with

increasing Reynolds number. The discharge coefficient values obtained

at NBS using water as the fluid exhibited an increase in discharge

coefficient from very low values (approx. 0.5) observed at lower differential pressures to values similar in magnitude to those predicted by

either the Stolz or Buckingham correlation. The objective of the investigation was to determine whether the differential pressure instrumentation of the two laboratories had systematic effects differing by a sufficiently large amount to explain this discrepancy and behavior.

Approach

The approach taken was to use CEESI 's differential pressure instrumentation in conjunction with those used at NBS-Gaithersburg to investigate

the behavior of the low beta ratio plates in the water flow facility.

The only changes in the NBS instrumentation or flow facility made were

to provide a means to connect the CEESI instruments to the data acquisition system. Also, CEESI brought a set (3) of diaphragm- type , differential pressure transducers of different range and the deadweight tester used by them. The deadweight tester was connected to the transducer

manifold of the NBS differential pressure transducer manifold to perform joint tests of the 2-inch meter run, PE-2, using primarily the 0.1

beta ratio plate. The three diaphragm- type transducers were connected

in parallel to the bottom taps of the orifice meter. These were then

connected in parallel with the lower Paros transducer used at NBS,

Initial tests were run with the 750 inch-of -water , diaphragm- type

transducer monitored by an independent data acquisition system. These

initial tests were run at 10 and 27 psid differential pressure and the

pressure values obtained by both sets of instruments agreed with only

minimal differences (less than 0.1% at these two pressures).

The remainder of the data was collected in a similar manner with the

143-
exception that the analog signal from the diaphragm- type transducer in use was fed to the NBS data acquisition system through the voltmeter

normally used by the Ruska transducer. This arrangement allowed the

diaphragm- type transducer response to be stored in the identical manner

as that used for the Ruska transducer. Also this allowed computation

of discharge coefficient values derived from the average differential

pressures observed by the diaphragm- type transducers for immediate

comparison of discharge coefficient values obtained by the two types of

instruments

.

Observations and Results

In general the differential pressure values obtained from both types of

transducers showed good agreement and the calculated discharge coefficients were similar with less than 2 parts in 600 difference between

them. The decrease in discharge coefficient values with decreasing

Reynolds number was observed to be reproducible with both sets of

instruments. After observing the characteristics of all the data collected, it was decided that the 1000 -gpm pump may be the source of

spurious differential pressure signals or that pulsations were caused

by throttling of the pumps for the very small flow rates involved

(approx. 1 to 10 gpm). As a final test another source of water was substituted. The municipal water supply was connected as a source to

the 2- inch meter run via a flexible hose and tests were run through the

differential pressure range obtainable with this source of supply. The

discharge coefficient values observed in this way showed a marked

difference to those observed with the normal pumping system. These

discharge coefficient values were in the 0.61 to 0.62 region and were consistent with the higher differential pressure points observed in

water flows and with all the data obtained with the high viscosity

fluid at CEESI.

Following these tests a smaller turbine pump (approx. 100 -gpm capacity) was installed in the water flow facilities' reservoir. This installation was completed on August 23, 1985. Test run series were repeated

using this pump on the smaller beta ratio orifice meters which had shown

a characteristic down turn in the discharge coefficient. This behavior

is illustrated in the graph shown in figure 24 for the 2 -inch meter

tube, PE-2ABC, with the FE-1/2-7B orifice plate (beta ratio of 0.1210,

orifice diameter approximately 0.25 inches) installed. The orifice

discharge coefficient is plotted as a function of the pipe Reynolds

number. The observations were taken on 4 days in August 1985. The

initial two day's data were taken on August 6 and 12, and the results

show good reproducibility at the higher differential pressure values of

10 and 28 psid. However, as the differential pressure and Reynolds

number decrease, the discharge coefficient values decrease as well until

at the lowest differential pressure, approximately 0.4 psid, the discharge coefficients have decreased substantially. This characteristic,

rapid decrease in the discharge coefficient value with decreasing Reynolds number was observed in several, but not all, of the small meter

tubes with the smallest beta ratio plates for test run results taken

-144-
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-145-
before August 23, 1985. The Stolz correlation is shown as the dashed

line. Reruns of meter tube/orifice plate combinations exhibiting this

behavior were rerun after installation of the smaller, 100 -gpm pump and

showed increasing discharge coefficient values with decreasing Reynolds

number and agreed well with the high differential pressure results obtained previously in the low Reynolds number project.

Several groups of test runs were affected by the selection of a pump of too high a capacity, these were marked for deletion in the

final data base and were rerun with the smaller pump. Shown in the

inset of figure 24 is an expanded plot of the higher Reynolds number

points. The discharge coefficients at approximately 2,200 Reynolds

number are clearly affected. Values around Reynolds numbers of 4,000

and 8,000 are in two groups and are near the pipe Reynolds value for

which these effects appear to cease. The high Reynolds number values

taken at 27 psid appear to be consistent with the results taken with

the higher capacity pump. Certainly a pumping system dependence is

evident

.

It was expected that use of the 100 -gpm pump would eliminate these

effects, and did so for many meter tests taken in the lowest flow rate

range. However, similar behavior to that shown in figure 24 was observed at the lowest flow rates . As was the case previously at low

flow rate settings, this condition was observed intermittently. Substitution of the municipal water supply, as had been done in the diagnostic testing described above, for the 100- gpm pump mitigated these

effects. However, large variations in results continued to appear

intermittently. These were attributed to uncontrollable pressure fluctuations in the municipal water supply. To some extent these were avoided by taking the test run observations after normal working hours.

Due to the press of the operating schedule however, this could not

always be done, and a portion of the results for test runs taken at

these low flow rates show a degree of scatter either greater than or near that predicted by the propagation of errors analysis.

Collection of Additional Data on Selected Orifice Meter Configurations

Data collection procedures for the bulk of the data base were completed

on January 6, 1986. However, upon further analysis of the data base

certain of the orifice plate/meter tube combinations were rerun. The

primary reason to rerun selected meters was significant scatter in

the discharge coefficient relative to the remainder of the data base.

As noted above this variation exceeded that expected from the propagation of errors analysis and was not consistent with the variation in

the spread of results obtained at similar flow rates meter configurations. Most of those orifice meters rerun had been either wholly or partially run using either the municipal water supply or the low flow

rate end of the 100 -gpm pump's range.

For certain of the orifice meters chosen for additional test runs, the

discharge coefficient values exhibited characteristics similar to those

146-
discussed above and shown in the inset of figure 24, but to a lesser

degree. Generally the scatter in these discharge coefficient values

was near the level expected from the propagation of errors analysis,

although a significant number of them were greater than this level. To

check the possibility that this scatter could be due, in some degree,

to an oversize pump or to pressure fluctuations in the municipal water

supply, a smaller turbine pump (maximum capacity of 20 gpm developed at

a pressure of 95 psig) was installed in the flow facility's reservoir

in a manner similar to that used with the 100-gpm turbine pump installed in August 1985, and additional test runs were taken.

The meter tube/orifice plate combinations involved in this rerun schedule are tabulated in table 33. These orifice meters were rerun in

January and February of 1987 after installation of the 20 -gpm pump.

Additionally, test runs were taken on two 4- inch orifice plates installed in the stainless steel meter tube, DAN-4SS. These were to function

as the statistical control plates for the 1-month rerun period. These

were the FE-5/6-7C (beta ratio = 0.1) and the FE-5/6-4C (beta ratio of

0.56) plates, and were selected to span the flow rate range.

Table 33. Meter Tubes/Orifice Plates Rerun in 1987

Meter Orifice Nom. Beta Meter Orifice Norn. Beta

Tubes Plates Ratio Tubes Plates Ratio

PE-IABC FE-1/2-5A

FE-1/2-6A

0.67

0.75

PE-5ABC FE-5/6-7B

FE-5/6-2C

0.10

0.38

PE-3ABC

PE-4ABC

FE-3/4-7B

FE-5/6-2C

FE-3/4-7A

FE-3/4-8A

0.10

0.38

0.10

0.08

PE-6ABC FE-5/6-8A 0.06

PE-8ABC FE-7/8-7A 0.10

The 20-gpm pump was was assxamed to be correctly sized to remove effects

causing down turns in the results as shown in figure 24, and would

provide a stable operating pressure at the smallest flow rate settings.

The data collection schedule was planned, for statistical control purposes, for the initial and final test series to be taken on both these

plates in the stainless steel meter tube. However, due to difficulties

discussed more fully below, this objective could not be fully realized.

The FE-5/6-4C orifice plate mounted in the DAN-4SS meter tube was run on

the initial day of the data collection period, January 5, 1987. The FE5/6 -7C plate was tested the following day. Although the results of the

test runs taken on FE-5/6-7C were consistent with those taken in 1985,

results obtained at the lowest flow rate range were erratic. Diagnostic

tests indicated the possibility of resonance between the control valve

controller and the pneumatic pressure regulator controlling it in the

lowest flow rate range. To eliminate potential fluctuations, the pneu-

•147-
matic valve controller was disabled. Tests in this range of flow rate

were controlled with manual valve positioning for the remainder of the

test runs, i.e., all of the lowest flow rates up to a maximum of approximately 1.1 pounds/second (7.9 gallons/minute). Additionally, operating

procedures were modified to improve reproducibility of the measurement

system in the low flow rate range. These were:

(1) the time period before beginning a test run group was increased to

allow the system to stabilize to a greater degree than had been

done previously, and

(2) water and air were allowed to escape through a small gap created

between the orifice plate and the meter flanges . The flange bolts

were loosened to produce this gap which allowed much larger water

velocities in the meter tube, thereby sweeping any collected air

from the region of the orifice plate. This procedure was completed

by re- sealing the orifice flange with the securing bolts/nuts.

(3) replication of test point groups at low flow rate settings for

which both the 20- and 100 -gpm pumps were used.

Replication consistency of the discharge coefficient/Reynolds number

data pairs for most of the orifice meter configurations tested during

this period were considerably improved relative to the 1985 period.

A point of primary concern in performing this set of tests was demonstration of the level of consistency in replication of the discharge

coefficient/Reynolds number values obtained between observation days and

between the two smallest pumps used at the low flow rates. After modifying data acquisition procedures as described above, the day-to-day

variation in the observations was consistent with that of 1985 at the

higher flow rates. Frequent crossover checks between the two smallest

pumps were made and showed very good reproducibility. Table 34 gives an example of result replication for a pump crossover.

Table 34. Pump Crossover Between the 100- and the 20 -gpm Pumps in

the 1987 Data Collection Period

DATA TAKEN ON 01/08/87 AT 10:41:41 -- COMPUTED ON 01-09-87 @ 14:55:48

METER TUBE -- PE-5ABC WITH PLATE FE-5/6-7B

RUN COLLECT DIVERT OBS.MASS DIFF. PRESSURE DISCHARGE COEFF. REYN.

NO.

43

44

45

MASS TIME FLOWRATE UPPER LOWER

(Ibm) (sec)

181.75 165.550

181.53 165.048

181.61 165.007

(lb/sec)

1.098

1.100

1.101

mean mean

10.0085 10.0100

10.0447 10.0417

10.0605 10.0603

MEAN VALUES

UPPER LOWER NO

.

0.59965 0.59961 6436

0.59966 0.59975 6452

0.59958 0.59958 6461

0.59963 0.59965 6450

•148-
Table 34. Pump Crossover Between the 100- and the 20-gpm Pumps in

the 1987 Data Collection Period -- Continued

RUN COLLECT DIVERT OBS . MASS DIFF. PRESSURE DISCHARGE COEFF. REYN.

NO. MASS TIME FLOWRATE UPPER LOWER UPPER LOWER NO.

(Ibm) (sec) (Ibm/sec) mean mean

46 181.85 164.958 1.102 10.0917 10.0909 0.59968 0.59970 6560

47 181.87 164.725 1.104 10.1217 10.1211 0.59970 0.59972 6560

48 182.29 164.893 1.106 10.1494 10.1488 0.59963 0.59965 6565

MEAN VALUES 0.59967 0.59969 6562

General Operating Schedules

For a considerable time period through the summer and early fall of

1985 the testing program ran 24 hours a day for 5 days a week. This

schedule was only interrupted for equipment failures , or when no meter

tubes were in the NBS-Gaithersburg flow laboratory for testing. This

situation occurred occasionally due to the requirements of the schedule

for tube plating and the need to maintain a compatible test run schedule

with the other data base projects which were being conducted at that

time also. For many of the meter tubes the initial data collection pass

took 1 to 2 weeks with several orifice plate test run series being com- pleted in 1 day. A test run series consists of all test runs covering

the full differential pressure range (0.4 to 28 psid) made on a single

orifice plate for one installation in the appropriate meter tube. To

avoid damage to the small beta ratio orifice plates of the 4- and 6 -inch

meter tubes and to maintain systematic errors below the 0.1% level the

highest differential pressure setting was decreased. These upper differential pressure limits were computed using the method of Gorter [25]

.

This method allows computation of the differential pressure at which

elastic deformation of the plate would cause a systematic offset in the

discharge coefficient of 0.1% or less.

All test series were replicated at least once. Some were repeated for

selected meter tubes and plates where results showed unexpected characteristics. The previous test run data was marked for deletion as described above. As test run data was collected, discharge coefficient

and pipe Reynolds number values were printed, and the operators maintained plots of the preliminary results. In many cases values for test run groups or individual test runs which were inconsistent with previously collected data were rerun before ending the test series.

B. Inventory of the Final Database

The final data base consists of three sections:

1. The data collected on the bare metal or steel meter tubes

before plating, the bare tube section,

2. The data collected on the nickel plated meter tubes, the plated

tube section, and

149-
3. The data collected on the stainless steel check standard meter

tube, the stainless steel meter tube section.

The data base collected on the stainless steel meter tube provides the

means of assessing the long term performance of the measurement systems

used in developing the final data base. This section consists of the

repetitive test runs taken on the 4- inch orifice plates used with

the stainless steel meter tube designated, DAN-4SS. Groups of test

runs were made on several days on each of the orifice plates tested in

the meter tube. Typically the meter tube would be mounted in the flow

facility's 4- inch test section and a full set of test runs would be

taken on several or all of the plates.

The identification code is based upon a combination of the meter tube

and orifice plate designations, the date of the test run and the run number assigned to the test run. Except for a few cases, the run numbers for each meter tube/orifice plate combination were consecutive.

In some cases run number sequence was broken, i.e., the first test run

of a repetition was not consecutive with that of the last test run of

the preceding test run series. In a few cases the numbering sequences

are partially or wholly repeated. Gaps in the test run numbering

sequence are designated as run numbers skipped.

The inventory of the final data base is given in tables 35 (bare meter

tube tests) , 36 (plated meter tube tests) , and 37 (stainless steel

meter tube tests) . It contains a listing of all the test runs recorded

arranged by meter tube and orifice plate. Each page of the inventory

table has a listing of the test run blocks analyzed and those marked

for deletion. The causes for deletion are given in the comments

colijunn. Several causes were recurrent throughout the testing. These

have been assigned a character code which is given in the comments

column. These codes are listed below. Otherwise, specific causes are cited for the deletion.

Deletion Comment Codes

# - Keyboard entry error. Improper responses were given by

the operator to the data acquisition microprocessor

+ - Run numbering skip,

% - Delete due to improper pump selection or improper operation

of flow control valves.

* - Operator Indicated Deletion, no specific notation as to cause

! - Run Number block used for bare meter tube test runs

$ - Flow conditions not sufficiently equilibrated. This

condition observed in the 1987 data only.

•150-
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164-
C. Presentation of the Data Analysis Results

The results of the test run data analysis are presented in tabular and

graphical form. Tabulation for each test run is limited to a single

line where the information on that line is sufficient for computation of

the discharge coefficients and Reynolds numbers for the test run. The

precision used in listing each parameter value is determined from con- siderations of the propagation of errors into discharge coefficient or Reynolds number values, from the estimated uncertainties of the observed

parameters and from the total number of characters available for printing the tables. The intent is to allow calculation of discharge coefficient and Reynolds number values via auxiliary parameter values, e.g.,

water density and viscosity may be determined from the flowing fluid

temperature and the appropriate correlations or tables referenced in

other sections of this report. This approach allows for checking of the

values listed, while still maintaining the size of the tables within

manageable proportions. Those interested in a greater level of analytical detail may consult the archival data base.

The three data table sets are ordered by meter tube and orifice plate.

Tables 38-47 list the nickel plated meter tube results with each orifice plate's results contained in a subsection. The tables are ordered

according to the meter designation, beginning with the 2 -inch meter

tube, PE-lABC, and ending with the second 10-inch meter tube, PE-OABC.

Table 48 tabulates the results of the initial tests run on the unplated

meter tubes which were restricted to two orifice plates . Table 49 tabulates the results for the check standard, stainless steel meter tube,

DAN-4SS. Within each section of these tables the results for each orifice plate are given by plate designation in ascending order. The meas- ured diameter values for the meter tube and orifice plate and the re- sulting beta ratio are listed in the heading for each page of the table.

The contents of the table's columns are the following:

Run No

.

Date Code

Div. Time

Flow Temp.

Flow Rate

Number Obs

Niomber Rej

- Test run number

- Code designating the observation date. Code

definitions are given on the last line of each

table page.

- Diverter time (adjusted for the diverter

correction)

- Temperature of the flowing fluid (degrees C)

- Observed mass flow rate (includes buoyancy

corrections, scale calibration, etc.)

- Total number of observed differential pressure

observations

- Average number of differential pressure

observations rejected by the 10 standard

deviation filter for all transducers . These were not included in determination of the

mean differential pressure.

-165-
Differential

Pressure

Mean - Mean of the designated transducer observation

set (in units of psi)

SD - Standard deviation of the mean value of the

observation set corrected for autocorrelation

effects (in units of psi)

Discharge

Coefficients

CD - Discharge coefficient values

Rand. - Random uncertainty in the CD value taken from

the propagation of errors analysis. This

is the three standard deviation value.

Syst. - Systematic uncertainty in the CD value taken

from the propagation of errors analysis

Reynolds Number - Pipe Reynolds number

The total uncertainty in the discharge coefficient values is the sum of

the random and systematic components listed. The random components are three standard deviation values representing the 99% confidence level

estimate derived from the propagation of errors analysis discussed

previously. Refer to the statistical analysis for final uncertainty

estimates

The results of the analysis are also plotted for each orifice plate.

Only the discharge coefficients obtained from the upper pressure taps

with the quartz oscillator -type transducer are plotted. The plots are placed after the table section for each meter tube and are ordered

sequentially by beta ratio. In each of the plots is shown two curves which are derived from the correlation equations [17,23] currently used

for estimation of discharge coefficient values in the orifice metering

community. Both representations are based on the test results of

Beitler [1] and are a good indication of the behavior of the previous

body of knowledge in this field of flow measurement. As such these are given for the purposes of comparing the results of this work with that

produced previously.

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fMryCM CMCMCM CMCMCM CMCMCM CMCMOJ CMCMCM CMCMtO tOrOrO tOtOtO CMCMCM CMCMCM CMCVIOJ CMCMCM CMCMCM CMCMCM CMCMCM CMCMCM CMCMCM

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00 c , CO eo CO CM ,_ ,- >* «* vi- CM CM N* ,_ ,_ ,_ ,- CM CM vt vT vt lA 0» ?

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O o o o o o o o o O o o o o o o o O o o o « 1 >> o o o o o o o o o o o o o o o o o o o o o la u 1 (A o o o d d d d d d d d o d d o d d d d d o

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CM

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5?

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fC

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u. 1 >0 <o vO <o >o <o >o <o >o nO nO nO nO nO nO nO nO nO nO NO nO

fO CM ^ in in in

CM CM CM

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MM

O in »- «-

On

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N- l>^ 0>

CM »-

M >* vj- N»

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ooo ooo ooo

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0C30 ooo ooo

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nO *0 ^D N^ ^3 ^3 N^ N^ ^3 ooo OOC3 OOO

ininin »-«-»- eoeoiN- CMCMCM T-^»- vj-^vj- ooo ooo OOO OOO ooo

OOO ooo odd

ooo CMro«- si-Nt-4- «-«-«- ooo fMCMCM ooo ooo

ood ooo ooo

eorN>o OOOO cmo>no 00«- M>»>4 «-«-CM

CMCJCM .-.-.- CMCMCM

nO nO nO N^ ^Q ^3 N^ nO N^ ooo ooo ooo

ininin ^.-.- ooooh- r-i fMCMCM .-.-«- -4-vf>J- in ooo ooo ooo eo ooo ooo »«» >* ooo ooo ooo ov. ooo CMhO«- intn>* o> «-«-»- ooo CMCMCM O ooo ooo ooo 1 ooo ooo ooo </» o-ooon O'O'On v»fMh- ooo hOfOrt CMfMfM in CMCMCM «-«-^ CMCMCM OO

nO nO nO ^ nO ^ nO nO nO ^ • K> ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o

o> rOKICM OnCMO- vtO>4- OOfN-ON CMNICM CMOfN- vtmNO CM«-fM r^-stfO- inCMCM O ooo ineoeo o«-o >»-«-fM ooo »-«-«- ooo ooo r^rotn ooo ooo »-oo ooo oo»- ooo ooo ooo ooo «-cMo ooo I ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 3

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m

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infMfM o-inin >4-o«— «--4'fO CMfO«- fN-oOv* inoo*- eoS-oo niOnoq oo-o

o>onOn r^oo ooo>o oono «-«-»- ooo «-«-f\j ooo nooooo oon«-

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Ntoo oo»- ooo o«-o ooo roMin ooo ocao oo«- cm«-o

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Figure 25A. Discharge Coefficient/Reynolds Number Plots, PE-lABC

2 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

182-
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U.O 1 u —

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Figure 25B. Discharge Coefficient/Reynolds Number Plots, PE-lABC

2 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

-183-
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U.OAU —

\ FE-'1/2-4A

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\ \

07/30/85

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w 0.615 - \\

har 1

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1987

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Figure 25C. Discharge Coefficient/Reynolds Number Plots, PE-lABC

2 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

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2 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

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"O ^ ^ '^O ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 'O ^ ^ ^ ^ ^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

N.S.r«. N»>j-vj- iniAin ooo eoooco ooo ooo ooo oooooo ooo>o>n «-«-«- ooo ooo v*--«*-v» ooo N*vj->* -j-^i-vi- >*>*-* ooo ^T-^ \r\ ^OC} ooo ooo ooo ooo C300 ooo ooo ooo C300 00 ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo >*

o- ooo ooo ooo ooo ooo C300 ooo ooo ooo ooo o

m^>* roMto vtvtro Ntinro 'Oooo^ ^vi-<o ininin ininin eoooco in>o^ eo ooo ooo MMto ooo roiOM roKiM MKiM ooo .-»-^ o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 1 ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo M

(\jT-o co>oco o>o«- «-«-o inoro <oeQ%4' o«-o o>^^ oo^OO' ^<\j»-

'O^O'O ooo «-rsifM coo•^^ ^»*>*- oco^ o^ <y o- ooo>co roroio '>o<o>o in ^ ^ 'O ^ >0 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ >0 ^ ^ ^ 'O ^ ^ *0 ^ ^ ^ ^ ^ ^ ^v • . . • . ... ... ... ... ... ... ... . • in ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o

CO rvioKi coto>o co>oo> o>ooi^ t^ofM «-rjin o«-»- inoo> o>Q^ >oinoo o

rorvirj r>.>or>- «-o>i- ooo vtN-h- «-«-«- «-^«- o«-o h-eo>o pjcvjcj ooo T-oo «-«-o ooo ooo ooo ooo ooo ooo ooo i ooo ooo ooo ooo oo^ ooo ooo ooo ooo ooo

0C30 ooo ooo ooo ooo ooo ooo ooo ooo ooo

S«-ro >»«->o >*o<\i «->*>o N.>o«- eo>o<o oOns-^ foo«- oro»- inino co Onj- o-info eoQ>(\i h->Of'> oint^ m>»(\i rOMfvj o>o>o N.>*in roooo <u in^Oin ooooeo o>6>o ooo t^F-eo ooo ooo o>o>o tninoo "-r^NO "U ooo ... ... >»>*vt o.o>o> >j-v»>* -*«*-* roro>» oo>o> oo>o> o ... r^h.-t^ o>o>o ... ... ... ... ... ... ... cj «-«-«- <M<Mf\l »- ooo (MfMCJ ooo OOO OOO (\l<\Jt\J «-00

«-«-»- OO'ON- O>roho o>oot^ ooo>N- «-N»N. (Mcoro -Ot-o o^r>-r>- S-inO *' f^ r\i e\i «^>*eo «-o>» ooo vj-xo<o «-«-«- t-«-«- o«-«- vor^^o (njimim <a ooo «-oo «-«-o ooo ooo ooo ooo 0C50 ooo ooo a ooo ooo ooo ooo ooo ooo ooo 0C30 ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 3

at vtfNjoo oO'sto- t^fMM ooo>4' in<>o oo>OfO >f0^oo N-ro>* «->*•* oo«-o roineo on-nj- fMM>o o>N-in cm^)oo ro>»oj >oin>i- «-»-<m ^.>*^o N-inrvi *j '0>Oin oo>0> ooo ooo eooo9> ooo ooo ooo >OvO&. ^F»n. ca ooo ... ... >4'^>» 9>0>0> »*>*>* v»>»>j- vt%*-v» 0>0>9> 00>0> 9> ... ooN-r>- ooo I- «-«-»- (VJCMfM ^^^ ooo fM(M(M OOO OOO OOO CMfMfM «-00 '-' oO'Oin o>o>Q o>oor^ oooro .-^s. roino> oeo»- N.o>o O'Org c\iin>o

fvifvjcM fos-oo 0>«m »-fvj«- »»->oK- «-.-»- »-o«- oo«- >oin<o cnjpjpj OOO «-oo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo o^o ooo ooo ooo ooo ooo ooo

cooQoo oooN- ino^oo ^ooin ^i-ino >4'>4'N- N-^^-v*- coooo o^oo cj'Oh^ >I'0O oooin rjcMin ocooo ooo> >*-n.>» ininvt «-oro oor>-h- eoin[0

>0'0>o oo^o> ooo «-oo ooco<> ooo ooo ooo ^>oo> .-s-S- ooo ... ... Ntf-^f^ o>o>&> >t^>* ^ni->»- >*>*»* o>oct> oo-^ ... ooh>-r>- ooo ... ... ... ... ... ... ... «-«-«- (MCMCNJ «-»-«- OOO (MOJfVI OOO OOO OOO fVJfMfM «-00

OOO OOO OOO OOO <-oo OOO OOO OOO ooo ooo

SogcQ <-rMo oooo> ^o^o^ ooo>eo o^O^o^ o>oo^ (\j<-o ooO'O^ h-ooeo

>o<o oocooo rsjforvi mmin O^ o^ o^ rofiro K)-*ro ininin O^ o^ o- >0'0<o

•-(MvO «->*eo inroco MOin «-ofvi vf>oo t\i«-o co^0>0 vi-oki N-in-* inpo> «-eor^ fvjM<o vOino> roMin njin'O in>*co r'i«->0 r>-N-fO >»«-K» <of^-j- -*roro (McvjfM Mro»- >o>o>o (m<m«- «-«-o o>00> inin>o o^oin 0>0>0> fororo ... Kiroro fororo (m<m«\i ... oO'O^O • ininin «-»-.- ... ,-,-,- ... ... ... «-<-«- ... >0<0>0 tOKlW C\i(\I<M >*«4-s* «-T-«- >tNt^ >*>»>* >*^»*- «-.-«— ^^O

0>>*-eo »*^n^O opj-4- in^^ vtN-Os o>^(\j ^i'^in ooo^- O^o«— csJn*^

00O>O> C300 «-«-«- »-.-«- (\j(M(M (MKiro minin in>0<0 ^N-h~ N.N.r>.

(\ir\j(M rvirvjcM (vicvirvi cmojcm (VirMcu oooooo ooooeo eooooo ooeoeo MKito K»roixi roKiM toroM romro rofOfo Kiroio Mroro rofOfO toforo

o-"**- »-«-o> "-oin oroo o>eor>- ooin«- >o«\i(m oinoo ©•'O^*- >*-r^ro

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rvirsjro ininin >*>*-j- r^r>-t^ .-»-.- inv^«4- •-»-.- h.r^N. rotvitvi ininm «-«-«- »-^^ rvjcjcj >*^<* »-.-.- rvi(\i(\j .-^^ ^>4'>»' «-»-»- .-^»- ooo ooo ooo ooo ooo ooo ooo ooo oo^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

incjrvj >*N»>i- »-^rM «-&>o> f\jro«- ooo ro«-«- >otn>o cj»-»- >j-«*>» ooo ooo ooo ooo «-«-T- ooo rocjcj ooo ooo ooo ^»-.- ooo ooo cvjcoco ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ln^o^^ ooo>oo ooinr^ >os-ro oo^ro >oooco eo9>o> -^^o^ r^^ooo <-oo O>oo iMCJCo >i-inin r.>coco o^^o inmin o>o>o> h>eooo ooo rororo o»-»— «—«—«— »—«—«— «—«—«— oo^ «—«—»— ooo »-»-^- »-.— »— »— »-^- ^^>o ^^^ ^^^ ^^^ ^>o^ ^^^ >o^^ ^^^ >o^^ >o^^ o^^ ooo ooo ooo ooo ooo ooo ooo ooo ooo

rofvjrvj «-«-«-

ininin ^^.- >»->t>» rocjcj Kh»h>.

>*«*>»•

^-.-.-.-

r- t- in>»«* rocjco «-r-.- ^.-.- r..h.K rvicoco mmm >i--.*>d- »-«-.- ,-,-,- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

mcjro min-^ rororo incjtM cjro«- r- r- t- cj«-»- con-oo cjcjoj vt-*** ooo ooo ooo ooo «-•-«- ooo rororo ooo ^- x- t- ooo cjcjco ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

m'or^ ooo>o> O'>oco v**©*- co^'Cj >on-oo n-o-o^ r^o>r». >oinco «-oo> O^oo CJCJCJ N^-inin Kooco 9>0>0 mmm o>q>o> >o^-eo ooo rorocj 0«-«- ^r-i- ^^^ ^^,- 00«- .-»-^ ooo »-.-»- ^ r- r- ^ ,- ^ >0 ^ ^ >0 >0 ^ ^ ^ ^ >0 ^ >0 ^ >0 ^ >0 ^ ^ >0 >0 ^ >0 ^ ^ ^ ^ ^ ''O ^ ^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

rocjrvi mmm ^-*-* r^l>^>o ^^^ -*n»>» .-»-^ cor^N- cofvirM mmm i-i »-»^«- ooo v-«— ooo.- CJCJCO -*>»>» r- ,- X- CJCJCJ .-»-^ >*•>»>* ^»-^ r- T- r- in ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo CO ooo ooo ooo ooo ooo ooo ooo >» ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o>CO <omm ^»-^ >*mm ooKO> >0>0>0 «-»-^ cj»-«- ooo rocjco >*«*>»• co «-«-«- mmm •*>»-* r^^-^o ooo «-«-«- ooo rororo oocd ooo o ooo ooo r- rr- r- rororo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo C300 ooo ooo • ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo M

toovO mmr^ m«-ro >*<o«- r>.o>«- ror^r^ ooo>0> oooh- -omh^ oo>co ooo fvicjcj Nj-inm »oi>>-ro ooo mmm OOO cooOoo ooo rOCjcj

m 0«-»- ^«:-«- ^ T- T~ T- T- ^ 00«- ^ T~ r- ooo »-»-^ ^^»- t- t- r- CO ^ ^ ^ ^ ^ ^ ^ ^ >o ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo CJ>^

00 '>ocoo h«.r«.N» vo«-m vomvt roinm cj>*-r^ ^^o r^cjro ooo r^.v»ro o >ooro «-00 o«-o o»-«- «-oo coroo ooo <Mm>* ooo %»o«- oo^ ooo ooo ooo T-COO ooo COOO ooo ooo ooo I ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo % ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

0>00 oomco COOOOO 00ro»O mm>o «-^vO cooor^ mO»- oro«- cooo to Ov*r>- orof^ >}-cjo >ocoh>- m^oo m>oo «-«-m ocjcj -o tn ^ r>-r«-o « ooo o«-ro >o>om ooo ooo mm<o cor>-m ooo ooo >»->*m o ooo ooo Nj->»>*- ... ooo ... >t>4'N4' ... ooo o ooo cocoN- ... r^s.r^ ... ooo ... o «-»-»- rororo «-«-«- ooo cjcjcj »-.-^ cjcjco ooo »-»-.- rororo f«-coo ooooin •o»-<0 t>^mm rocjm roinoo >oor^ >OfOco oo«-«- ^^<0^ *-> mocj o«-o o«-«- «-oo «-coo ooo om-* ooo fo«-«- ooo to «-oo ooo ooo ooo «-cjo ooo »-oo ooo ooo ooo Q ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo c ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 3

inmoo mOs* >*ros» «-mN- >4-'OvO rvi^f^o <f-o«- ^m>i- «-mro .-co«- o>»^^ oco-o >*f>jo r*.coK- m<oo m<oo cocj>o «-ro<M >om>o coooo •m ooo o<-ro <o>om ooo ooo mm^o eor^m ooo ooo >t'>4'm to • •• ooo ooo >»•<*>* ... ooo ... <d'^>t ... ooo 0) ooo coooK ... r^s-N- ... ooo ... i- «-•-«- rororo r-^^ ooo rococo «-»-^ cocotvi ooo «-«-•- rororo •-• cor^o o>om <o«-m >om«- rocjN- -t in co ooooo <orocj <o«-'0 s-mco m«-cj •-00 o«-o o«-«- T-o«- «-ooo ooo comNj- ooo ro»-«- ooo ooo ooo ooo «-»-o ooo «-oo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

o<ocj ir\ ^Q o <ocoo mcooo •-co'^ oN-oo oooco r^iovt •-m»* ^-^N-

•-•^oo ro^o m>*»- ooom >ON.«- ^^o »-»->o Qscj(m >om>o 00«- ooo o«-cj <o>0>0 oo«- ooo mm>0 oof^m ooo ooo «*s»'m ... ooo ooo >»••*«* ... ooo ... rO'.4'>«' ... ooo ooo oooor^ ... r^r^s. ... ooo ... »-«-»- rororo «-«-»- ooo cjojrvi .-i-.- cjcjcj ooo «-«-»- rororo o«-o «-o«- (MOO oocj ooo o«-co ooo ooo ooo »-oo

«-«-«- ro^tro vO<o>o >o>o>o ooo >0'0>o ooo >o-onO «-»-«- ooo mmm %»>»>* rororo rororo ^>*-4- rororo mm>* rororo mmm *»*•*

>* >* CO o CJ ro ooo mmm

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426.36 426.02 426.31 750.45 754.75 749.70 1206.1 1206.2 1205.9 1206.1 1205.9 1206.0 300.06 300.13 300.21 1206.1 1206.1 1206.0 301.26 300.09 299.17 1206.1 1206.0 1205.8 426.35 425.97 426.02 903.15 903.11 902.94

«: % % % 4t % % % % % % % « « % MMM MMM MMM MMM MMM c3 d grCfi! fClSIC fSfcS r>. CO 00 00 CO oo in >o hoo CO 00 S8SS OOO >* in «0 OOO N-OOO00 O

198-
Meter Tube PE-2ABC

U.OAU -^ n FE-1/2-7B

^

- eo Beta = 0.1210

O o 08/27/85

<» 0.615 -

S 08/29/85

SJ ^

\ <

\ 9

\

•5 \

\ B

0,610 - B \ o O \

s \

t \

o \

- N

n RftK N. u.ouo 1 III 1 1 1 1

1 '

1 1 1 1 1 1 1 10 10' 10

Stolz

0.610

o

<» 0.605

r

0.600

0.595

10

Buckingham

FE-1/2-1B

Beta = 0.2418

o 08/27/85

08/28/85

1 1—I—I I I I

I 1 1—I—I I I I

Pipe Reynolds Number

10

Figure 26A. Discharge Coefficient/Reynolds Number Plots, PE-2ABC

2 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

•199-
Meter Tube PE-2ABC

0.610

O

Q)

0.605 -

0,600

FE- 1/2-23

Beta = 0.3625

o 08/27/85

a 08/28/85

Stolz Buckingham

0.615

0.600

10'

FE-1/2-3B

Beta = 0.4831

08/06/85

o 08/12/85

* 08/28/85

T I I I I TT 1 1 1 1—I I I I 10' 10

Pipe Reynolds Number

Figure 26B. Discharge Coefficient/Reynolds Number Plots, PE-2ABC

2 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

-200-
Meter Tube PE-2ABC

0.620

o

w 0,615 H

r

0.610 H

r

0.605

FE-1/2-4B

Beta = 0.5435

o 08/06/85

a 08/09/85

10'

1 1 1—I

\-l

Stolz Buckingham

0.620

o

«^

«» 0.615

o

^ 0.610

O

0.605 —

10

FE-1/2-5B

Beta = 0.6642

o 08/05/84

a 08/09/84

T- !

1 1—I I I I T r1 1 III!

10' 10

Pipe Reynolds Number

Figure 26C. Discharge Coefficient/Reynolds Number Plots, PE-2ABC

2 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

•201-
Meter Tube PE-2ABC

U,0/60 —

\ \ FE-1/2-6B

^

- \ \ Beta - 0.7250

Q> \ \

O

\ \ 8

08/05/85

«» 0.620 -

u 08/09/85

r - \\§i

rfS \ \

•5

\ \ oi

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Pipe Reynolds Number

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3 -Inch Meter Tube, 8 Orifice Plates

•218-
Meter Tube PE-3ABC

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Pipe Reynolds Number

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3 -Inch Meter Tube, 8 Orifice Plates

219-
Meter Tube PE-3ABC

y

FE-3/4-3B

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08/02/85

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Pipe Reynolds Number

Figure 27C. Discharge Coefficient/Reynolds Number Plots, PE-3ABC

3 -Inch Meter Tube, 8 Orifice Plates

220-
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3 -Inch Meter Tube, 8 Orifice Plates

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m>0«0 'OOO'O <oir>iri in>*-'^ eoo>^ KiroM mniv* 'Oin>* f^N-r^ f^J.-.- roroM .-^^ r- ^ ^ ooo ooo ooo ooo ocso ooo •-«-»- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

«-«-ro ooop> t>-(>>o .-r\j»- -c -Q \r\ fowro «ON-^ K>K>m u-<in>o ineoN ^^^ oof^h- r^pi-eo inmm vO'O^O >*>»>» >*•*>» inmin >o^<0 ^-^-r«- OQO ooo ooo OOQ QOO OQO OOO OOO QQO OOO

OOO ooo ooo OOO OOO OOO OOO OOO ooo OOO

coo>o> ^>.^o^o r>.h.r^ >*>i->s- h>.h-r«. rororo rotoKi >»>*•«»• r^r>-N. ^^^.^. ,-, MtOrO T- ^ w- ^- T- ^ OOO OOO C30C3 C3C30 0C30 OOO t- ^ w- in ooo OOO ooo ooo ooo ooo ooo OOO OOO ooo ooo ooo eo ooo ooo ooo ooo ooo ooo ooo ooo >s • • • • . . ... ... ... ... ... ... ... ... in ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o

>*«*>*• >or^in N»inin >»>*in ^eoeo firott toro^t inin«* t^^O'O fM»-fNj o roK>ro ^.-^ ^^^ ooo ooo ooo ooo ooo ooo ^»-»- o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 1 ooo ooo 0C30 ooo ooo ooo ooo C30C3 OOO OOO M

SN-og o>>o>» roh~'>o CM(M«- in>OKi >*>t>» >oh~oo r«i<Min v*o>ro o>oo ooco t^^^co KS-t*. ininin ^>0'>0 >*•>*•>» >*»*>*• ininin <Oin>0 >or^P^ in SOO ooo ooo ooo ooo ooo ooo ooo ooo ooo 00

^3 ^O ^0 ^O ^3 ^D ^3 "^ nO ^O ^3 ^D ^3 ^3 ^3 "O ^3 ^3 ^O ^O ^ ^O ^O >0 ^O ^O ^O ^O ^O ^v

>o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo (\J »x

t^ carvio roo>o vi-o-* o>>o>* >*«-^ roo>>*- in<0"* o^oo vt>oo^ incoeo o «-«-o ro>*fM iMi\jr\i ^^(Mo mooN- o>>orvi i<iO'>o in>oo in»oin rM«-«- ^OO OO^ ooo .-«-.- OO^ 0^«- CM«-«- .-T-T- oo^ ^OO I ooo ooo• ooo ooo ooo ooo ooo ooo OOO ooo * ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

h-t^O. Q>in>o O'Oh^ K>to<M >*eor>j corviO^ ineo>0 oinr^ ooo^O «-o^ ia v»hoiM o>ino> roiMin >oh^r\j r>>^(\j ooooo o»k>o o>o.in ojimm <r-^ooo fl> ooo CM>4'>«' (\J(M(M O-OO 'O 03 r- eOO>&' OOOOOO O^ 0< O' Kl->t>l' 00>9> "D -*>*>* OOO ooo ... 0^0.0 ... ... ... C300 oo>o> o o>oo ... t^r^r^ r^r^r^ o>o>o o C30C3 r- ^ T- ^- T- T- »-»- IMCNlrt rvJfVlfM (MCMIM hOfOM »-00

•->*«- o«-h^ oororo rviMvt vO^tiM ooo-*- >*-«-K ro^i-p^ >oino >i-N.oo j «-«-«- Ki>*(M rvirvirvj in»-rM inN-P«- ivjroo tomh- K-^o ininin rvj«-«- id ^O^ ooo ooo OOO ooo «-.-»- ooo «-^^ 1- r- (\l .-.-»- OOO OOO O ooo ooo ooo OOO OOO ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo C300 ooo 3

iMoro «-o>r^ ^'O^ -^ i^ ^ r>-oo> in'Oo v»r^>* toeoro ino>r>. ro«-»-

in>»-r'> O>vi-o i>r)«-in ^o^-f^J ^>0«- oeoo rsjinpo oo<o v»im>* «-^oo> 4-> ooo rj>i-in iMfvirj o>oo 'Soo»- 0>0<0 ooooo ooo> rONj-^* oo.o> «» >»>*>»• ooo ooo ... o>Oo ooo 0&.0 0) ooo ... r^N.oo t>^r<-r>~ ooo i- OOO ^r-«-T- .-.-^ ^^ (\IC\JKI fXJOJfVJ (MI\J(M »-«- MMM «-00 '-' OOO «-oo-* o<M«- OOO (Moooo >t^o Nj-MO oj^in >o-«to o>oeo

«-«-o roroiM «-f\jr>j rvioin «*^in ro«-i'i (\j>*-f<j <oroo ininm rj»-»- ooo ooo ooo ^^^ ooo ^^^ ^.-rj ^^^ ooo ooo OOC3 ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

'O'Oo in>*ro coino fMCMcvi oo>ooo ooino eo«-oo fvicoro k>m«- «-in<Nj

invi-vf oino >*f^J^o >ot^rM >OinK> oF-oo cm^oim oo-o inooo roeo«- ooo »*^>»-

<\j>»-vj- (\j(\j(M ooo •«eo«- eooo ooooo ooo k>nj->* ooo . . . ooo ... ooo ...

... ooo ooo ooo ooo ... r..(s.rw r«.(^r^ ooo ... ... ooo ^^»- T- X- T- •,- ^ (Mrsiro injimco roiMco «-»- rorom «-o«- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

oooo in^in oo>ooo ooo o«-«- ooo op^o (mk>(\i k><oo ooo ooo ^^^ ooo ininin ^^^ ininin ooo oooooo ooooco rororo ooc3 ^i-^in

«-»-»- CMCOINJ .-.-^fXIfVlfM «-•-«- in»-0 >OIO>0 «*fVJin «*v*<0 «->»-»0 OfMOJ 00>0 OOCJN- (\J>0<i- ooon- inoeo OM«- «-ogo ooin «-v»-eo ook»>* >»'00 in>oiM Ki>*in oo^o-^- «-«-o «-inf^ Oogo Kl^*!*! ^oo in>o>o >o>Oin roiOKi «-»-«- f\j»-<\j |s.N>N> ooo oooooo ... ... ... ... ... ... oooooo . . . . . . . . . oooooo ooo ooo ^oo ooooco ^^o ... roMd ininin ininin .-.-t^ »t.-«- lororo ror'ir'i «-«-.- .-«-«- ininin o«-fM in>o>o ororo ogoivi «-ro>«- o«-ro o«-f\j >oooo >s-t>-o «-ro>t

r^hwr«. s.N>N. oooooo oooo ooo ooo >o«o>o "O^or^ r^Kr^ oocooo

rs.r<.r^ i^r>.s> N-r~h^ r^N-r- r-r^rs. oooooo cmcvjim cocmim jmimpj (\i<Mru roKiro rowM fororo roMKi kikiki »ororo mkiki KirohO rororo Mforo

f^inr^ oo(M o-*>o cMin«- ruoooo oino o^M ^o*- o>o>i- orviro 0(M0 inoi- •.»o«- OOin N.o«- oF-O «-ru>* o«-l>«- «-<ooo inK>>o • hO« »*»->* ... ... ... orvioo inr^po ... ... ... O'O ... 0«-0 0«-0 "-(VJOJ ... ... 0C30 f\J«-«- oo»- OOO ininin C300 ooo >o>0>0 ooo ooo ooc3 vO<0>0 ooo o '0<o>o rororo •-»- ^•-^ in>oin in-oin ^ r- r- <r- t- ^ rororo % % % %%% «%% % % % % % 41: %%% <A M M tA iA ift MMM 4A M M

>»-in>o N-ooo o«-<M rovtin <or^oo oc3«- rsjio-* in^ot^ oooo «-rjM »-•-«- ^^»- ^»-»- «-rvi<M iMOjrvj roruiM rvjiMW roKifO

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oco«- <o>oro o>«-og »-N.o vtpjoo <o«-in oo^oo v»o>(m in«-«o eO'OS> mvs->* (Msi'Kf 6>>0>o «-o><\j 0>0><M ^i-O-v* rococo cococo F»r>-ro ^'2eo

©••ON- N-vO^O &>>*o5 ^Oroo> cofou^ >*ir>v»- o>oo r^^o> «-o>o »--om ^oo- ooo inin>* »MrM»- ^^o^o ininin «-rMf\j .-,-.- coco^ roroM ^r>-<0 ^0^0> ininin cococo minin mmm cococo iniAin ininin >4'-^n4' >»>*>*• «-«-«-tNJ<M(\J fNJP>J<M«-«-»-

MKifo «oN-N- r^r~.r^ >»••*>* o- o- o^ «^o»- h«.N.r«- oeoco >»-vt>4- s-r^N. ooo »-»-«- ^oo ooo Kiforo >*^>»- .-»-•- rororo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

^>»-* >*>*•<* r^r>-co r^<ocr> f\j<M(Nj mki>* t-po.- ^ki^s- >*-io>»- ^n-n. o^^ .-»-^ o^o C300 rofOKi Mforo i- f- w- (virMtM ooo o^o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

o«-o CO-*"- loifiu^ «-eoeo ro<oo 0>0>N- mir>ir> oo»- ii-t>fm o>o^^

N.r>-r>- o«-«- &>a>o> cor>-K (mcmm <m6jpj .-^»- rororo cococo o«oo> ooo ^»-^ ooo ooo ^ ^ ^ ^ ^ ^ ^ ^ ^ T- ^ w- ooo Q«-Q >0 ^ ^ ^ ^ ^ ^ ^G ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ "^O ^ ^ ^ ^ ^ ^ ^ ^ ^ MD ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

Kiwro 'ON-s- r>-N.r^ ^t-^*-^ o>^o> ^»-^ s-n-n. ococo «*>»>«• r^h-r^ ooo r- ^ T- ooo ooo rorofo *«»«* t-*-^ rororo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

•*^«* lAinin h^cOCO •<> -O in <0'>0>0 N-N-CO fNJfM»- ^m>0 inK>»* •>0^«-^^ ooo ^»-»- ooo ooo rororo roMro »-^«- (\jr\j(\j ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo> rMm>o -*rorj f>.co{>. «->oeo «-oo fM»-f\j >On»->o rortro N.ir>m

r-N-^o ooo o>o>o> K.r^f>. .-^»- (mcsicm ^»-^ (vjcmcu cocooo &.o>^ CDOC3 ^.-»- ooo ooo «-«-»- ^.-.- .-.-.- »-*-»- C3C50 OOO

OOO OOO OOO OOO OOO OOO ooo OOO OOO OOO

rorofo s-r-N- r^r^h- >j-n»^ o>o>o- «-«-»- r^r^r^ o>coco >»••*>* h-r«.N. r-, ooo ^^.- ooo ooo roMho -*>*>* »-.-.- roKifo ooo ooo m OOO ooo ooo ooo ooo ooo ooo ooo ooo ooo CO ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ^ ... ... ... ... ... ... ... ... ... . • . m ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o

-*>*>* »*>*^ ooN-eo in'O^* ininin >ON-r^ (Mf\j«- <om<0 into**- «ON-co 0> ooo «-^.- ooo ooo Mroro KirOKi ^^.- (virvjcvi ooo ooo o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo I ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo M

fMCOO- nOO>0> 0^>*•«- t^OON- <00>»- «-N.O «-OK» or^>0 >*IOM 'O'*-* h-^'O ooo coo>o> K-r^K. »-^tM fvi^cM ^r-^ r^^cjcM cococo ^*o> in ooo ^^^ ooo ooo ^ r- r- t- t- r- ^.-»- .r-»-^ OOO OOO CO ^ ^ ^ >0 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ *G ^ ^ ^ *G ^ ^ ^ ^ ^ 'O ^ ^O "^ ... ... ... ... ... ... ... ... ... . . . <o ooo ooo ooc} OOO c^oo ooo ooo ooo ooo OOO r\j to>o>* M»-o ru'Oog vOo>o o>o<o <ococo fvivi-oo N-mo o^eoin co«-<m o K-0>m PJCMfVI 10U-<>0 0>0<M ooo ooo 1\J(M«- ooo »->OCO «*<0'0 oo«- ooo ooo .-.-»- ooo ooo ooo ooo •-oo ooo I ooo 0C30 ooo ooo ooo ooo ooo ooo ooo ooo «: ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

m>»<\j ocoN «-op>j or>-iA o>foco vj-rocM incMO> ^Min ^^ooco ro'-r^ <a oor^ «-r^r<. idkico vj-mo. «->*-m o*mo cDto«- N»•^~^o ir>«-r>. roo>m v ooo* MfVlfVI inMO 000> 00>0> cococo (NJfNJfM ooo «-<MO- 0«-«- "Q ... ooo ooo ... vi-roK) rofOKi cjoo ^^<* ... ^,-«- o

cocor>- ooo> ooo> ... o (M(\ir\j ^^^ Ktroro «-»- ooo ooo ^^^ ooo «-«- t<M<t i<> oin'O ooco N-Ovf CM-j-in oo-N. '>oo>0' loioco 0>'^0> >4->*co ro«->* •m COKICO fMrM«- IA>0*0 >0<0>» «-00 ooo fVJ<M«- OOO fMino ^>o>o «

^- T~

O 0C30 ooo ^~ T- T- ooo ooo 0C30 OOO rO t- OOO

Q ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo OOC3 ooo ooo ooo ooo ooo 3

oe o»-«- r>.vo«- <or^fM ocoro inr^M >*>*•«- >o>*co o^o*- o-o*© >»og

o»-oo Kioo >oin«- "Oroo- K)inK- .-ro»- «-»i-(\j ^cor«- iacjco in«*co *-> 000> tOKlCM mM«- 000> 00>0' cococo CMfMCM OOO «-fVJO- OC\l«- CO ... ooo 0C30 ... -^ rrt ff) mroM ooo >s-^>* ... ^ ,- ,- o

cocor» ... ... ooo> ... ... ... ... ooc^ ... trvifvirvj »-^»- Kl^oro «-«- ooo ooo «-i-t- ooo •-«- Mhoro "- O'O'- o>N-co >orw<M ooeoi^ cmon. n.«\jo> (m»-n. eoroo^ o*o>h>- ki>Oj- (Moo T- T- T- <otn>o NtN.o> T-.-0 o«-o <\jf\j»- ooo MiTico >*inr>- »-«-«- ooo ooo «-»-o ooo ooo ooo ooo »-oo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

oN-m >*ro>* K)0>ro oo>o> o>kio> sfeo«- cor«-r^ rth-rvj o>oh- rvicoco

corvico {MO>co •-vtfM >Oro5> cjin^o «-ki«- «->*-j\j vj-N-r^ mrvico 'O^tfco 0•00^ rO<MC\J >OrO«- 000> 00>0> cococo fMfMPsI ooo •-(\JO> OfVjT- • •• ooo OOO ... ^a-roro roforo ooo >i->*^ •• «-«-«-

r>.ooh^ ... ... ooo. ... ... ... ... ooo> ...

<M<\j(M .-^-^ fororo »-«- ooo ooo «-.-«- ooo «-•- ft Kt fi ooo C300 ooo ooo ooo oo^ oo^ ooo ooo ooo

>*»*»* ^^^ h~(M»0 mrviin mmm >o>*'in o^^ 00^0. <ON->* P>J^$^ >0>o>o ooo coo^o. ooo irtmin ininm o^coo. •O'O^O o>o>0> N-r>-r>- fMfM(M ^^^ ^.-.- »-,-T- ^^.- .-^.- T- r- ^- T- w- ^- rO(M>» rovto ocoos *o«-co .-<Mr>. co«-co K>mt«i fio^O* eorofvi «-^in

invoro *or-M co(M^ ro«-iA r<^<oco ^o-ki «fl<o«- co>OfM ococo «->»-r'> ooo «-00 f\Jf\J»- COCOS- OIA^ ^N->0 00^0> <M>*^ OON- >»>*>* • •• IOK>rO PM^^ ooo CJtMfM rjPMCJ

tOKiro ... N^vt^^- minin ... ... ... ... >o>Oin *«*>» *>*»* COCOCO «-»-r- rsirvirvi minui mintn cococo inmin rgrvjCM »-»-»- mmin rvjrom o.o(\i <or«-o> «*mm co^»- r»-OKi mN.o >or«-co «-^>0 ooo ooo o«-«- »-^«- ^^^ ^t-cM o«-»- «-^(M (ViCNirsi roroKi

cococo cococo cococo cococo cococo cocooo KiKito tororo mroro Kttom

Kiroro roroM roroM roKiro roforo tOKiKi MKiro rororo roioro roroio

>*(Njin «4'inco >oo>co r^coin inN.^ o>cqo oo>0 copoo o^ inm >»«->*• «MO>co »-F->o fO(M>» h^>»^ como •-oO'O «\ijmk> <t o in co^t-rj ojm«- coinm ... ... cooo. ... ... ... ... inrvio ... . . . (M<-,- ooo ... cD.i-«\i .-«-.- oo>o o>«-«- ... ooo rNirsifM >o^*0 toroM o>oo> inmin inmin mcmki ro-*v*- o>oo lOrOKi >»«>* ^^^ r- f- n- <0r^*0 MMKI fOMKl rje\j«M KirofO <ON-r~ ^^^

%%% % % «: %%% ««% %%% «: % « MMM 4A <AM MMM MMM

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0.610

o

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o

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0.595

FE-3/4-8A

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o 01/28/87

01/29/87

* 01/30/87

§

i i

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1

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o

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e

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o 01/23/87

a 01/27/87

* 01/30/87

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I

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Pipe Reynolds Number

Figure 28A. Discharge Coefficient/Reynolds Number Plots, PE-4ABC

3 -Inch Meter Tube, 8 Orifice Plates, Final Data Base

•235-
Meter Tube PE-4ABC

0.610

0.595

10

FE-3/4-1A

Beta = 0.2032

„ 09/06/85

09/09/85

I i I i I I 10I r rT

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O

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0.595

FE-3/4-2A

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o 09/05/85

a 09/09/85

10'

1

1 1 1—TTT

10 " 10

Pipe Reynolds Number

Figure 28B. Discharge Coefficient/Reynolds Number Plots, PE-4ABC

3 -Inch Meter Tube, 8 Orifice Plates, Final Data Base

-236-
Meter Tube PE-4ABC

0.615

O

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0.605

O

0.600

io'

FE-3/4-3A

Beta = 0.4879

(P 7/26/85

^9/05/85

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r

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Co

1

07/26/85

09/05/85

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9

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1

1

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i

a

l/.Dl/U 1 r 1 1 1 1 1 1 1

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Pipe Reynolds Number

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3 -Inch Meter Tube, 8 Orifice Plates, Final Data Base

•237-
Meter Tube PE-4ABC

u.o/:u —

\

\ FE-3/4-5A

S \ Beta = 0.6507

\

S. o 07/26/85

07/29/85

* 09/05/85

o

Q) 0.615 - \ ° B

? ^\ * s \\

rfs \\ #B

o \X »

•5 \ \.

1^ \ \. «e

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r

0.610

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0.605

10'

FE-3/4-6A

Beta - 0.7315

o 07/25/85

D 09/05/85

I I I r

1 1 1—I—I I I I 10' 10

Pipe Reynolds Number

Figure 28D. Discharge Coefficient/Reynolds Number Plots, PE-4ABC

3 -Inch Meter Tube, 8 Orifice Plates, Final Data Base

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Ktrvjfo ooo »-»-»- .- ^»- CMrviro «- rjfviru roKito »-oo

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 3

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

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N-N-r^ r«.h-r^ minm h-r^r^ (mcmcj mkim rororo (mcjcm s-f^»o u^i/\>o ooo roiofo ^«-»- ooo ooo ooo ooo ooo ooo r- ^ r- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo OOC3 ooo ooo OOC3

ooo ooo ooo ooo ooo OOO ooo ooo ooo OOO

O>meo >o^'^ «-oo ir>in>* (Mrjfvi mrsjrvj mmm CM»-fM inmrvj o>r^r^ ooo pjrjfM .-T-^ ooo ooo ooo ooo ooo oo«- »-^^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o^o ooo ooo ooo ooo OOC3

ooo ooo ooo ooo ooo OOO ooo ooo ooo OOO

in>00 eom^- N-fvjeo ^oeoo> ©p>o ro«-^ (M<^JO^ c3»-<m >oe0'0 inKt>o oo»- ^«-»- >*>«•«* rjcjfvi ooo N-F-oo o-O^O- O>o>co eocoeo ooo MMfO r- ^ r- r- ^ r- 1- r- ^ OOO OOO OOO OOO r- r- O T- ^ ^ ^ >o ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ OOO OOO OOO OOO OOO ooo ooo OOO OOO ooo

N.rs.r^ r^r^r^ u^mu-i t^h.r^ (mcmcm mmki mmki (\jpj<m t«-f<-<o ^nm^o ooo Kiroro •-.-.- ooo ooo ooo oocs c3oo ooo <r-«-^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

S-N-co eo>OS- «-KiK( li^inin (M(\j<nj tntvirsj >»roro (\i«-f\i <o<00> eoeoco ooo f\jf\j<M ^^^ ooo ooo ooo ooo ooo ooo ^^^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

inN."* «-oo t^>oiA r^N->o >o>ON- (y ^ in >o>Ou^ >0'0>* romfsi ok>o> ooo >»'Nt>4' rvirvirvi ooo N.r^r>. eocoeo eoooco r^r^r^ ooo rsJiMCM

r- r- T- ,r- T- ^ ^- nr- r- r~ r- t- OOO OOO OOO C30^ «-«-0 ^- ^- ^- ^G ^3 ^9 ^3 ^3 ^3 ^3 ^D ^3 ^3 ^3 ^D ^3 ^3 ^3 ^O ^3 ^3 ^3 ^3 ^3 ^3 ^3 ^3 ^3 ^O ^3 ^3 ^3 ^3 OOO OOO ooo ooo ooo ooo ooo ooo ooo ooo

r^N.h.. r^r^r^ inmm ts-h-r- rvirvifvi mmm roKiro cjojpo ^.r^^o ir>in>o i-i ooo foroKi «-T-»- ooo ooo ooo ooo ooo ooo ^ r- r- in ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo CO ooo ooo ooo ooo ooo ooo 0C30 C300 ooo ooo >>. N- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo «- eoN-eo >t-*vj- N-coN- r^vor<- rjcviro vj-toro -^roro ojcvirj inino ino>*- o ooo >!•-*-* ^.-^ ooo ooo ooo ooo ooo ooo ^T-^ ^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo I ooo ooo ooo ooo C300 ooo 0C30 ooo C30C3 OOO M

«-eOO or^in rO'-o ln^O(^i N>*N h^eoin m^Ol/^ tnt^t'i 0vt>0 o '- t\J OOO roroio rvjcvipvj ooo Kr>-h>- eoeoco eocoeo KKK. ooo (vifvifM in r- ^ f- w- T- T- T- ^ ^ w- w- r- OOO OOO ooo OOO »-»-C^ ^- 1- T- CO

>0 ^ >0 ""O ^ ^ ""O ^ ^ ^ ^ ^ ^ ^ nO ^ ^ ^ ^ ^ ^ ^ ^ >o >o >o >o ^ ^ ^G ^^ ooo ooo ooo ooo ooo ooo OOO ooo ooo OOO <-

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r«-f\j>o «-oo (\)«-«- rOfOfM Oir>«- >*>om Or-r^ Klino M>*«- ininin ooo ooo ooo ooo o«-«- T-oo ooo «-oo oo»- ooo I ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo % ooo ooo ooo ooo ooo ooo ooo ooo ^oc3 ooo

vO^oo r\jco«o oinin "-ooo >om<o -*r^eo -*oo (m»»-j- <or>->o cocviin a> oN-o o>Oin >ocoeo >00>0 ^foo rom>» (Minin O'-o »-Oin pjvOO o ooo «-«-«- ooo «-«-fM ooo «-oo «-oo ooo O0(\jeo ooeo^f "5 «-«-0 >*•*>» «-»-»- r- r- 1- . . , ••. ..• •• 00«- ooo O

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 3

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KiMro ooo ^ r- ,- roroKi (mcjcj ^^^ ^ ^ ,- (\j(Mrsi cviroro t- w- ^ <-• inS->»- (\j>oeo 'O^O*- ro»0«- tvioin «-o^ >»Lr>0 oo<o f\j>*-<o Ktcoin

n1-«-ia «-oo o-rvirvi rorjM h^<Mfvj «-<o»* fviF^oo ocjo Ntroeo -j-mro ooo ooo ooo ooo o«-»- »-oo «-oo o«-«- o^o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ^oo ooo ooo ooo ooo

roMin -* O- t<i ojo-* 0(00 «-^>4- Ktinco ocOfO o^rvj go^^ f^Kirvj >*-inO oS-K ooo«- cofNjro t^-*Ki l^>^o^ >th-S- lOiriO oofoin eoo<4- ooo <M.-»- oo»- «-fMro ooo «-oo »-oo ooo eoK>eo eoom

sj>j>^ «—«—«— f— «— «— ••• ... ... ... oo«— ooo . .. ... ... ... eocoeo ooo ooo eoeoco ... ...

fOMto ooo .-T-T- rororo ojjmpj .-^^ »-^.- (\j(\jc\j (mmki »-«-«- ooo ooo ooo ooo ooo ocDO oo«- ooo o«-co ooo

v»[o»* (\j(\jra «-o>o ooo eocor^ orvio kikiki cq^^ 5S2 (mcminj ^-h^h^ ooo MKirj ooo cooaco >»>»•»*• ^-*>* cOeoco ooo rororo

>*-oo cor^M ooeo r^<oN- KlvJ^o incNjo okio -*oo qo'v' it^S foF-in rsjcoK coooo cviino fOfvifM >»Of»- ooN. rvifvifM cOnO^j- ^"-oo

eoeoco in>*vt fNj<Mf> ooo ... oN-K- oeor^ ... »->»(m o»-r^

tohOM (NjfNjcj ooo roMK) ooo »-oo ooo ^oo roKi«* ooo

MK»K> ^^^ (M(M(\j totoro ^^»- >o<o>o «<o>o ^«-^ tororo «\j(m«-

OfMK* COOJ^O »-tOin «-K1>* OCOCO vOCOO O^OOJ e0K>>O -ooo OfMlA

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r>.h.N. is.r>-r^ isTsirJ rJr>-N. r«.r^t^ r^r>.eo eoeoco ooo ooo ooo

(M<M<M r\jrNj(\j (\j(M(M rvicjcj cNjfvjfM cvirvjfM rvjfNJOj <\jfvi(\i fMcvirj (vjcvirvj N-'^i'ro (MOJin ir»«— vj' »— rjo (m>0>0 (m^->* ^-rvjcj pomo ocoin omia

eo«— <o nr- T- r- fifow m>oin cooo «— r^-ro ir>h>-h» ojroo s-N--* ocvjco ^Mif- ... (M<-r\j ... r^<\ir- ... ... (Meo<- ... ^,-(m • • utinin ... <— T-<- ... in^^ >*n»>j- ... rrrrrr »"..•.• mvtin ininin r^r^N. <o^«o >*in>* ooo ooo >j>*m >o^^ n-n.^.

ininiA «-«-»- ooo «-»-»- >0<0'0 »-»-«- «-.-«- >o>0>0 «-.-«- OOO

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4- Inch Meter Tube, 8 Orifice Plates, Final Data Base

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Pipe Reynolds Number

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4- Inch Meter Tube, 8 Orifice Plates, Final Data Base

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10/19/85

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4- Inch Meter Tube, 8 Orifice Plates, Final Data Base

258-
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4- Inch Meter Tube, 8 Orifice Plates, Final Data Base

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ro>*>* »-T-r- ooo ooo ooo ooo ooo ro>*ro ooo ^.-»- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ocDo C300 ooo ooo

r^r^r^ rorovi- ooooo oor^oo NONtm rvicvirsj o>o>oo •o^o^ (vjooo fMf\i«M

(NirjtVJ ^»-^ ooo ooo ooo ooo ooo (VJfVIfVJ «-o^ «-»-^ ooo 0C30 ooo C300 OOO ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

>»-<0-* ooo ro«OOJ >*(NJ(M (Njro>*- «-ror»j minin oeoo< orjcj o(\j<o «-ro-4- ooo ^-O^O* oooooo r^Kr^ (s-K-r^ <o>o>o oor>-.r>~ ooo r^r^i^ Q'O^Q^ On^^ ^0^0** {^^o* o^^^ ^o»o* O'C^^ ooo ^o^^ 0*0*0^ ^•O^O ininin ininin ininin ininin ininin minin >o>0^ ininm intnin ooo ooo ooo ooo ooo ooo ooo ooo" ooo o'oo

OnOO oooooo oocooo intntn ininin s^ni-nj- ooooco ooo ininin oooooo

ro-*-* »-«-«- CDC30 C300 ooo ooo ooo -*v*>* ooo ^»-»- OOO OOC3 ooo C300 C300 OOO OOO OOO OOO C300 ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

rororo ininin o>ooo> 0ON-O> >ON»-in cjrjfvi o>oo> »-«-.^ (\jo>(m >*-roro rororo t- t- t- ooo ooo ooo ooo o«-o rororo »-o«- t- t- ^ 0C30 ooo ooo ooo ooo ooo C30C3 OOO OOO OOO 0C30 ooo ooo OOO ooo ooo ooo C300 OOC3 OOO

ooo ooo ooo ooo ooo ooo ooo ooo ooo OOO

-*>*«- "-t-oro rorofM rOfON* .-to«- minin fv)«-«- ofvjro orvjin oro>i- ooo 2>2>0> oooooo K-Kr^ r«.K^t>>. vo>o>o ooooco ooo r>»rv-F- 9- 9- 9- o o o V* o^ ^ o^ o^ o* ^ ^ ^ ^ o^ ^ o* ^ ^ ^ ^ ^ o o o ^ o^ o* ^ ^ ^ sO>o<0 ininin ininin intnin intnin inintn ininin >o^<0 mtnin minin

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

O^oo oooooo oooooo inintn ininin >i->t'* oooooo o>oo ininin oooooo >- ro>t>i- .-«-»- ooo ooo ooo ooo ooo ro-*-* ooo «-^^ m ooo ooo ooo ooo ooo 0C30 ooo ooo ooo ooo 00 ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o

r-.r>~t^ rororo oor^t^ r^r^i^ in-*m (Mt\jf\j oooos- ooooo> ^r^^ rorofvi r- corjoj .-*-»- ooo ooo ooo ooo ooo rorviru «-o«- .r-^.- o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 0C30 ooo ooo I OOC3 ooo ooo ooo ooo 00<D C300 OOO OOO OOO M

oincvi <o-*«- roro«— ororo roino >*-*{m (\jp-oo t^^'O ooj>* «-(mo OOO ff-^-o^ oooooo r^r>»K. K-n-n. ^^>o<o ooP-r-- 9- 9- 9- r^h>-N- 5>?'?'

m ooo O^^^ ^O^O^ ^^^ O^O^^ ^O^^ O^^^ ^^^ O^^O^ ^^O^ 00 >0>0<0 ininin ininin ininm inmin mmin ininin ininin tninin ininm >v • • • • • • • . . • . . ... ... ... ... ... . . . >o ooo ooo 0C30 ooo ooo ooo ooo ooo ooo ooo (\J vO »-in<o -*roo^ ooo-o orooo ooo <oroPsi o>c3<o o-ca"- «-in-o >oi\j(\j o •-OC3 <Mf\jf\j r--or-- inca^ ooro>o oo>o«- r^oo»o o«-«- 00'>O(m <Nj(Mf\j ooo ooo ooo (\jf\jcj ^T-^ T- r- T- OOO OOO rocjro ooo i ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo % ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 3

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ooo «-oo ooo ooo ooo oo-o ooo ooo ooo ooo

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>o»*-»o eoo>r^ roroM oot^oo s.>ooo N-r>.r^ r-.-»- -j-%*^ •*>»»* ooo OOO OOO OOO CMfMfM r-.-.- (MCMCM i- ^- r- OOO CMCMCM »-»-.- OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO

OOO OOO <DOO OOO OOO OOO OOO OOO OOO OOO

to^-* -*Mm <or«->o o>cMt^ oin>o ooo> -*fMfM -j-roM foinin oo>oo OOO T-.-«- 0>0>0^ (Mroro rofMCM inin-* cmcmcm »-«-.- vt^>» mcmcm ooo OOO OvO>6> OOO OOO OOO OOO OOO OOO OOO >0 ^ ^ ^ ^ ^ m tr\ if\ ^ ^ ^o ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ >0 OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO

>*vi-Na- i>^r^t^ hororo ooeooo ^o^^^• ooeooo h-s-r^ r»N>r^ oooooo n-n-n. OOO OOO OOO MtOfO »-«!-^ MfOrO ^^»- OOO tOKItO »-»-^ OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO

OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO

>OinvO oooof^ MroKi O>^o oococo 0>^0> cmcmcm >*vtv*- '>o>0'>0 ^^^ OOO OOO OOO CMCMM ^^t- (MCMCsI ^ ^ t- OOO (MCMCM ^^^ OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO OOO

OOC3 C30C3 OOO OOO OOO OOO OOO OOO OOO OOO

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r..N.h. o^o>o> e>>o>o> c.. ... ... ... o<.o>o« ... ... «-«-«- CMCMCM forOK> tniniD rOMM lAinirt r^ioro ininin o»-ro N.o>«- Minl>^ '>oeoo «*invo ir>>*>o >ooooo o>r^S- inr^-S. oooooo »-«-«- «-«-CM v*-*«* -^-^in inmm >*•*.* ^-j-v* *>*»* rororo rororo

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>o>o>o t^eoeo vt>*-M roMK) ooo •.-.-.- r- ,- ^ ooo fororo toroM ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

vO>o>o i^r^r^ <o>o>o s.r^r^ Kiforo -*>*-* -*-*«* mkim r^r^r^ vo<o>o r-i «-«-*- KiMM ooo ooo ooo ooo OOO ooo ooo ooo in ooo ocDO ooo ooo ooo ooo ooo OOC3 ooo ooo 00 ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo oo

«-«-«- ininin inmin >»•>»•>» rofOM roforo KitOM KiroK> ^m>»- >*•«*«* cm «-«-»- <\i<\I(\J ooo ooo OOC3 0C30 OOO C30C} OOC3 OOO «- C300 0C30 OOO OOO OOC3 OOO OOO C30C3 ^OO OOO ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo I C300 0C30 ooo ooo OOO o^o ^oo OOO ^oo ooo «> 0(M«- ^irv>4- eoiNJin in«-M r^eor>- «-ineo rjinrvj >»«-o rooo 0>»-^

>0<o>0 N-eoeo Kivj-fo (viroKi ooo ^»-»- t-»-^ ooo rorvjfvi cmmm in ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo eo ^3 ^3 ^O ^3 ^O ^D ^3 ^3 ^3 ^3 ^3 ^ ^3 ^3 ^O ^O ^3 ^3 ^O ^3 ^O ^O ^O ^O ^O ^O ^O ^O ^3 ^O *^ . . . . . . ... ... ... ... ... ... ... ... in ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o^^

»\J o<oo -*>*>* «-o«- oeoo oo(\j oeoo f>o-* eoino o«-«- o^tfM «- «-oo ooo -j-roiM <\jT-.- «-vOfO -*toin >ooco Ofvi«* rorsjrj rjinrvj ooo ooo ooo ooo (MJMrj ooo ooo »-fvifM ooo ooo I ooo ooo ooo ooo ooo ooo 0C30 ooo ooo ooo » 0C30 ooo ooo ooo ooo ooo ooo ooo ooo ooo

>Oin«- ooinro cvjr^oo oo«-o oeoro MOO i>o-*in -*ino oroo eooN. (a inN-o oeoo «-eot^ rjt>^«- -j-mo K<o>» roro-o ^o^Oob oeorg rooN- tt) (\j»-f\j ooo >OinvO m-*in >o-Ot^ OOO ooo r^>»-<o in>i-in «-(m«- d ooo >*•%»>» ooo ooo ... ... ... ... ooo ooo O

r^r^h- ooo ooo t^r^-h. o •-«-«- ooo fOKItO MfOM C\i(\J(M ^^.- (M(\J(M rOfOtO KlrOKl

41 h-roo mKiv* ^0«- »-«-o inforvi oootn t«-»»o -^pj^* roroco »-«-^ *j o«-o ooo (M«-rM <M(\j«- »-coo <0>t'O K-'Oeo N.<oin fvj(M«- torjro «> ooo ooo ooo ooo (\jc\i«- ooo ooo «-c\jKi ooo ooo o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 3

<\i«-rvj eo^**- >oeoin eotnin ooo oioin OMin eoojo ^^J^oo «oegs- ^0<M «-oo ^^o inineo l^inw -Oin-* pjto^t eofviK) ooro K>^«- •w fvi«-f\j T-»-.- ininh- mv*v»- inin>o ooo ooo •o>»<0 >»-inin (M«-f\j in ooo N»>»vt o^o ooo ... ... ... ... ooo ooo 41 r>.h-r^ ooo ooo r^s-s. -

«-«-- ooo KlfOrO MMtO (MfMfM ^- r- i- (M(M(NJ flKIIO rOMKl '-' <\j«-«- -*M>»- eo»-»^ eo>Oh~ eOv*l^ (vih-t^ oeoo inv*-in okipj mfir"-

»-«-»- ooo roKtro rocjcj (mcjo eoS-eo eor^o 0«->0 ruroro rocsirj ooo ooo ooo ooo <\j<\j»- ooo ooo «-(\jrsj ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

eorjrsj >*r^m >Otno rvi>±in OOK «-<Oin oeo»- o-*in ininro «-KifM >»OCM (MOO »-eoro rooorsj N.mf\j eoinro «-«-in N-rvi^ eo»-in in«-ro

CM»— <M »—»—«— ^inh- <Ov»in inm>0 OOO ooo 'O**^ >*inin (vj(\jfM OOO >4'>4'>l' ooo O^^ ... ... ... ... ooo OOO i^s-i^ OOO OOO t^N-r*.

T- T~ T- ooo rororo t'lMro CMPvipg «-«-t- rvjrsjrM toroKi rororo OOO ooo ooo ooo ooo ooo ooo ooo 00«- CDOO

oo<o eoeoeo >»roro »-oo ooo <mcvi«- >ON*f\i .-oo «-«-o >*Kiro

rororo ooo eoeoeo ^o^o^O >0>o>o >0^0>0 '43>o>0 >0«>0 >0>0>0 eoooeo

«-inv» >r-eo>o inS-o inoo oeoro 0>0-* minin (Mvi-jnj <\j«-r«- in>oo »->Om ^Q5JK> rgrM>*- ooo <M«-in •-oo in<oeo ^ooro OOO >»%»>» (NJOO 000000 ... ... ... ••• ... ... ... ... ... ... ininin in>^in •*»*»» OOeo OOO ^rO"* >*»*>* v»>*>*- »-o«- eoeoeo ooo ooo »-«-»- eoeoeo eoeoeo «-«-«- -O o o ooo >0>0>0 fOrOM <!-«-«- ^^«- rororo .-^«- r- r- t- lororo .-•-«- .-^^

C3-4-0 o-OCM eoeoo (M«or'i oo«-eo >j-o<m >*-oo won. roO'O o«-ro

i^r>.r<. eooo oo«- CNirvjro >tinin ^'ON- ooo r-rsirvi kim**- tnmin

ooeooo eoeoo OOO OOO OOO OOO OOO ooo ooo ooo

(\j(M(M rvjpvjrvj <\i(M(\j (MCNjrsi ojrsjrvi (MNrvi (M(\if\j mroro KiKim MtOfO

<4'>oo ineoin ooo eoKo roroK* o«o«- N.inin r-Ov* rjinh^ >*r>.»* o^o F-oeo «-^.^o «-S-o OOO r^om {mooS- >»ooo eo'0>* r^'Oo oroK) inrooo ooo ooo ... oh-h- inin-'^' in«*>* inmin inin>4- OON- ... ooo «- ininin

.-ir-»- ooo \Oinin oeoeo »-«-.- ooo OOO «-•-«- ooeoeo OOO toror'* .-•-«- ^^.- »-^»- .-.-.- roKiro inmtn

%%« %«% %%% % % « %«% % % % MMM MMM MMM

MM V» •r-tviro >*in>o h~eoo o»-«\i ro>*in <or^eo oo«- c\jr'>>i- in«ON- eooo «-»-«- «-^»- «-ir-^ «-(MCM INICMfM (MfVICM fNJ<MIO

-290-
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291-
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L. (M O" >0 >*• SJN. to f^ (NJ in On nO

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>. 3 Of z , >o >o ^ On 0> On ,_ «- o O. On On

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CO

w

g o o o o o o CJ CM CM ^» «- o CNJ CM CNJ ^~ ^~ ^~ o o o o o o X o o o o o o o O O o o o O O O o o o o o o o o o o o <D o o o o o o o O <3 C5 o o O O O o o o o o o o o o —

Of • • • • • • • • • • c> o o d o o o d d d d o o o o o o o o o o o o o o 1 O fM M fM NO in O tv. ^ O On 00 !o55 to CM O to to to to in «-

II 1 o <M (\J 0> O O On

in in NO to to to >* ^ vt fM fM fM 1 u o o o o o o o o o ^5 ^D ^3 o o o o o o o o o o 1 ^ >o >o nO <0 in nO NO NO nO nO nO NO >o >o NO NO NO nO nO nO vO NO nO

4-' odd o o <s o o o o o o o o o o o o o o o o o o

oe (0 , \0 >o >o 0> £^ On ^ ^_ ^_ On On On o o o On On On On On On >o >o nO

<D c 1 •M o o o o o o -* vj- s* ^- »— N* •.* >* o o o o o o 4-» « 1 (» o o o o o o o o o o o o o o o o o o o o o o o o « 1 > C3 O O o o o o o o o o o o o o o o o o o o o o o

CDu 1 v> • • • • • • • • • • • • • o o o o o o o o o o o o o o o o o o o o o o o o

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01 01 ^? o o o o o o <\j C\J CM ^ o o CM CM CM o o o o o o f o o o o o o o o o o o o o O O O o o o o o o o o o u u (0 o o o o o o o o o o o o o o o o o o o o o o o o c 3 oc

0>

1. o o o o o o o o o o o o odd

ddd o dd o dd ^»

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in to -* >»

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a. (M f 1 o o o o o o o o o o o o o O

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tJ 1 >.

OO C3 o o o <3 C3 <3 C3O <3O C3 o O o o 13 C3O C3O C3 >^

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CO o o o o o o o o o o o o o o o o o o o o o o o o «0 I «- <M >* rj in in 00 vf CO ,_ t"^ to O- in CM O t"^ On CM CM %* >* N* CM 1 1 O ^~ v~ r" fVJ C\J On O O On

>» in in to to to in in no vS- to to CM fM fM r~ r~~ ^~ in

tJ lU 1 u o o o o o o o o o o o o o o o o o o o o o 00 su

u. ' ^ <o >o nO nO in nO nO nO nO NO nO NO nO nO nO nO nO >o >0 NO nO NO NO N^mo 4-> o od o o o d o o d o o d d d d d d d d d o o o

M-

(D »- ro hw nO t^ On to CM

O CM in -4- ^ CM «- nO >* to OO -* NO * o r^

fM H- a. in iM o C\J ^ ^ o O CM CM o o o o o o o o o o o On CO t-^ 0) Q o o «- o o o o o o o o o o o o o o o o o o o «- o 1 o a> I/> o o o o o o o o o o o o o o o o o o o o o o o o u o % c- o o o o o o o o o o d d o o o o o o o o o o o o 0) H- ^s a> O) •a 3 N- in ^ in ro »* in CNJ On to 00 o CM nO to m in «- f^ 00 fM ^- to 1^ CA c 1- O C ro >0 »- in (Nj >* (M 8:S

N* in >» fN. in >* to «- fM o to ^ o o 0>

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O On

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(A ' 0)

1-

ro ro ro

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<A

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fM •.* ^. o o 4.1 CM (D 3 iP »- o o OO N- O o On O o o o o o o O On O On

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0)

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(- 0> tr\K\0 PO ^ «- o o »- o o o o o *-

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«- to 00 nO On nO On ^ On o r^ in o 3 c in [O ^ oo K- o

CO 8:S to 00 no >» -* CM CM fM CM fM ^ o o oe (D «- o o o o o o o o o O On O On

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r^1 I- oT

O 00 »- o »- in o to o On

O

O On CM nO o to o o ^ o o fM

O UJ

a.

V Of »- >» »- g . S. ^^ in nQ O nO

oS On On

On TO CJn 0> On

O OnO On OO o o to On SS 1 3 S5 sO >o ^ >* in in >! >* N* in >* m «* >! in o o o nO ^ o

'"'"'" ^— »— »— *"" *~ CM CNJ ^

^'N CO r^ <o NO On vj- 00 On C> NO 00 00 00 «- NO CM

O

O sN. nO

(- 3 v CA o>

O <\J >* »- ro r- in On CM tifo CM »- o s ^t ?JS8f2 in to

a>O •w •^ t^ >o <o N- t^ f^ h- CM CNJ CNJ On On On in nO in

M ^ (0 ^ o o o nO nO nO 3 5 5 On On On nO nO nO On On On nO nO nO o O o «> u. oe

x: %^ fO K) fO T- «- «- o o o o o o d ddd

d

d »- »- «- to to to . O ^ (\J CJ to «- On CO N- o cNj NO OO O ^ On to ^ in

00 o6 00 N. to in to N- in

J

g- ^

in in in •* >* lO CM »- »- o o o OO OO fN- OO On On o CD (D i o-^ &^ o^ <><>(>• On" <>On' (y <y <> d d d o o o o o o ^ ^ ^ 11. H- Q <M CM ro CNJ CnI t\J CNJ CM CM CM CM CM to to to to to to to to to to to to X ^ in >*

On o •«

>* to nO ,- «- >* >o «-

O

^^^.

NO Nf CM CM fM 00 in > i u o »-; >* o «-; >» <3 CM to CD to On m On to ^ ^^ o> oJ doJ o o o o o »- d O O d d ^ o o «-

fc

tN^

dd On On

a t- CA ^ rj ^ 0> On On o o o o O

O o o o o o o fN. On fM ^— ^—

to to to to to to to to to to to to «- «- % % % % % % % * «: % % % <A m m M M M 4A M M M M M c . «- rj ro >» in <0 N. COOn o «- CNJ to Nt in NO f- 00 On o «- fM to >* 3 o ^ V »— fM CM fM fM rj

oe z

292-
Meter Tube PE-7ABC

U.O 1 V —

\

\ FE-7/8-8B

§ - O

w 0.605 - \ -

to

^ 0.600 -

' 8

\ i

\ %

\ o

\

\

\

\ O

i

Beta = 0.1018

o 12/05/85

D 12/06/85

Orifici 1

1

1 \

\

- \

n ^TQ^T

^> U.OaO 1 III! III] 1 1 1 1 1 1 1 1 10 10' 10

Stolz Buckingham

0.605

o

•g 0.600

.5

0.595

-

a

^, " ...

FE-7/8-1C

Beta = 0.2041

o 12/05/85

12/06/85

n "~ ~- -~ _

1 1 1 1 1 1 1 1

1

1 1 1 1 1 1 1 1

1 10' 10'

Pipe Reynolds Number

10

Figure 31A. Discharge Coefficient/Reynolds Number Plots, PE-7ABC

6 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

293-
Meter Tube PE-7ABC

5» 0.608

0.598

Stolz Buckingham

"t^ 0.613 - § : \ \ \ \ \ \ \ \

X^

^^^^^ oe ^

FE-7/8-3C

Beta = 0.4898

12/04/85

12/06/85

h 0.608 -

o

~-X_^

?» 0.603 - ~~^^^'~^^^~^=~^=--=~=r-^ 1 =

U.oira 1 1 1 1 1 1 1 1 1

1 1 I 1 1 1 1 1 10' 10'

Pipe Reynolds Number

10

Figure 31B. Discharge Coefficient/Reynolds Number Plots, PE-7ABC

6 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

294-
Meter Tube PE-7ABC

U.O lU —

\ \ FE-7/B-4B

s

\ \ Beta = 0.5715

"K \ \

Q>O

Co o 12/04/85

a 12/05/85

Q) 0.610 -

^b^ "v^

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12/05/85

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Pipe Reynolds Number

Figure 31C. Discharge Coefficient/Reynolds Number Plots, PE-7ABC

6 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

295
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Figure 31D. Discharge Coefficient/Reynolds Number Plots, PE-7ABC

6 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ^oo ooo oo^ ooo ooo ^oo ooo

tr\ ooot\i CM fMPvirj ooo >t-4-ro ooo ininin ooo <\j(mpj ^v*^* .-.-.- >o<o<0 «-^>* hororo ooo ooo ooo ooo ^»-»- ooo T-.-«- ooo rorOKi ooo cMcofNj ooo ^^.- ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

r^eoeo r\jin>o ooeooo oinin o>eoo o-n-s. mroeo oo^^eo eoo>o> eo>o<o roKiK) N»->»>j- ^>i->* in>o^ N-N-oo S-N-K- eoeoeo 0>0>0> s-s-n- >*'>4'>4- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ^O ^ ^ ^G >0 >0 ^ ^O ^ >0 ^ ^ ^ ^ ^ ^ ^O ^O ^G ^G ^G "O ^G ^ ^ ^ ^G nO ^G *G ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

rorofo ooo t«ihO>«- ooo tororo ooo <o>o>o ooo >o>o<o '0>0'0 eoeoeo eoeoeo >0'0'0 rowro ^«-T- ^.-.- roroKi forofo ^- ^ t- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

rorvjcM ooo CMCMCM ooo ho^m ooo iri ooo>t ir\ r-.-»- rvirorvi eoeoeo eoeoeo fviroro fomfi t~ ^ ^ »-«-»- (virviCM cMC^MCO ^»-.- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

firocM eo>oeo ocmcm ino>eo cdo«- o>-oco ooin o(m«- «-eoro >0>00> >»>»>* vj-v»->i- ininin -G ^ ^ eoeoeo r^h-r*. <>o>eo 0>0>0> eor«-eo >»•>«»* ooo >0 «0 ooo ooo ooo ooo ooo ooo ooo ooo ooo ^ ^*0 ^ ^ ^ >0 ^ ^ ^ ^G >0 ^ ^G ^ ^ ^ ^ ^G ^G ^ ^ ^ ^ ^G ^ ^ ^ ^ OOO OOO ooo ooo ooo ooo ooo ooo ooo ooo

i<^K)ro rOfOsf Kiroro >0>0<0 ^0^0^0 '0'0>o eoeoeo eoeoeo >0>0>0 roMM r-i ooo ooo ooo ooo ^^.- «-r-.- rOMM MfOKI «-«-«- OOO in ooo ooo OOO ooo OOO OOO OOC3 0C30 C300 OOO OOO OOO OOO eo OOO OOO ooo ooo ooo ooo OOO >N ooo ooo• o- ooo ooo ooo ooo ooo ooo ooo ooo pg roropo CMCMCM ro^tin ininin cmpocm (M>i-fO ooo> ooo Kiroin mkim eo ooo ooo ooo ooo ^«-<r- t-»-«- roMCM toMM «-»-»- ooo o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo I ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo «A forocM eo>oeo o«-cm ineooo cM«-fM «-eoo> <oino r~t^o> o>h-o r^>oO' >»si-^ >*>»•>» ininin >o^>0 eoeoeo cor«-r>- 0>0>0> eoeoeo N-K-eo »»•>*>*• in ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo eo ^D ^O ^3 ^O ^3 ^3 ^O ^D ^D ^D ^3 ^D ^3 ^3 ^3 ^3 ^3 ^G ^O ^3 ^3 ^O ^3 ^3 ^3 ^O ^3 ^G ^3 ^O ^^ • • = . . vO OOO ooo ooo ooo ooo ooo ooo ooo ooo ooo (M>v

eo vOt^O^ »-o>«- oh-CM eotno oooeo r^«-ro >Oinr^ r^«oin eOMO> CMinro o eomo inin>* oovr^ cmcmm o«-o «-fMfM ooo ooo o«-fM r>.eooo «-«-»- ooo »-oo ooo ooo ooo ooo ooo ooo ooo I ooo ooo ooo ooo ooo ooo ooo OOC3 ooo ooo * ooo ooo ooo ooo ooo ooo oo^ ooo ooo ooo

oom o>l>^«- roeo<0 N.«-o >oorM inNiro N-N-in r>j>0'0 rM>»-in incMeo co oot>-0« Oseoh- inoso >»eocM «-ct>0> incMO> M^tr') r^-vO'O eo>»-<M «-^n. 41 inS-N- &>o>o< oo>o «-eor>. rocMCM mmcm ooo o>o>a> «-«-«- ooo> "5 oo>o^ 000 000 -*vt>* roforo ooo ... 5 Mroto a-o-o. oo>o oo9> o (MrVICM ^ »- tOCMCM r-»-»- ^ r- r- OOO OOO r-^»- »-»- -4-o«- r^inin vtroin eoo>>0 eO'O*- •-eOfO •ON-^ in>*in ^th-O' hOO>K *-• O^CMvO to»*in eoo>4' cM«-fM oor- t-.-.- 000 000 r-^.- a<N.N- CO «-«-«- 000 o«-«- 000 000 000 000 000 000 000 a 000 000 000 000 000 000 000 000 000 000

000 000 000 000 000 000 000 000 000 000 3

MCMeo oinro «o>o>» eoo>o fM«-co «*eoo oooeo CMMin •-N.o or-oo

fihOvO ooeo^o ^oo&. oo>*o> «-eo« incMO. roforo eoK-P«. n.**^ (m«-<o

m

inl^N- o>0>0> oo>6> oeovo mcmcm wkicm ooo 0>0>0> .-.-.- ooo> co •• oo-O" 000 000 >»•>»>* KirOfO 000 ... « MKIfl ^o>^ oo>o> ... ... ... ... ... ... 000> I— CMCMCM »- fOCMfM r- r- ^ »-.-.- OOO OOO »-^^ r-^ -< »»CMin invto M'O-* «-«-in r>-ino> o»-h~ N-h^in >Oinm inineo >O^M l^o>» ro«*in o>«-M CMCMCM 000 «-CM«- 000 000 «-«-CM eON-K-

«-«-«- 000 o«-«- 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000

000 000 000 000 000 000 000 000 000 000

fO»*-N- oinin <o^Oln ^^^o«- inf>-in 00'->o fOO«- ino>eo o>oo eo«-Nfifo^o coeo>o ^eoo^ eomo oN-eo v*fMeo cmmm eoN-r>- s.tncM r- r- ^ inKr^ o>OvO> oo>o> oeor«- mcmcm fowcvi 000 o.o>o> ^ t- t- oo^ oo>0> 000 000 >*>*>* roforo 000 ... toroho o>o>o> c50>o- ... ... ... ... ... ... ooo> CMCMCM »- MCMCM ^ t- r- t- ^- t- OOO OOO r- ^ x- »-«- CMOO 000 000 0«-0 r- ^ O 000 000 0»-0 000 000

000 ooo> oo>o N.^>* ^00 o«-cM CM>ON- h-r^N- »-r>.»- eooo 000 iniAvi- oof^eo >*-in«* eoeoeo r^r>-N. ^.-t- t-«-^ r«.'ON- N-eooo oocM cMO^o CMMO o>>*-in o>CM«- in>»->0 o<Oin eo>OCM ino^ -*N->» MCMto hocMCM eo^l-in ino>N. roh>-0> cm»»-n. o>«-0^ «-o>o ro«o«- in>»-CM

CMO>r«- focMCM >*rocM ro^i-ro fM«-CM o o^ &• ...

invo>o

«-<-<- 000 C300 ... ... ... ... ... ... ^00 -^vd-vf >»sr-* ^-^o^O ininir> ininin eoeooo eoeoeo in-*>* >*^>*

CMCMCM ^.-.- ^ X- T- S-S-N. >J'>4'>4' >4''>4'>4' CMCMCM CMCMCM •*N4->t ^»-.-

o»-hn >OCMin ooocM sj-eo«- inoro ocM>t eoocM «-^eo CMro>* o«-(m

rs.N.K. h^ooos o>oo oo«- «-CMCM roMM ro^*"* 4->*>» minin o>o>o

»-«-«- r-»-»- «-CMCM CMCMCM CMCMCM CMCMCM CMCMCM CMCMCM CMCMCM CMCMCM

rororo roioro lOforo rororo mmm KirOfO lororo fororo roMro roroK*

cMr~>* >ooooo >ocosf ino>oo mo»- o>»cm -*cm«- inr«.ro o>-or^ «-ro^

CM«*CM 'Or>-o -*•*<> <QcM^ ineoo «-^o^- ro>*«- N.ineo >*o>'- ^^eb ... ... eocMN- eoN-in ... rooo^ oo>-4- m>oin 0>n1-o> (moo^ oeg^ '-00 m>t^ >oeoeo 000 »*>*>* >t«*'4 «*'*•* ^^o m'^in inmin o*^©' >»'^>*

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6 -Inch Meter Tube, 8 Orifice Plates, Final Data Base

-309-
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310-
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6 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

311-
Meter Tube PE-8ABC

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o 08/16/85

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Figure 33A. Discharge Coefficient/Reynolds Number Plots, PE-9ABC

10 -Inch Meter Tube, 8 Orifice Plates, Final Data Base

-327-
Meter Tube PE-9ABC

\ FE-9/0-2B

V 0.608 -J \

Beta = 0.3718

o s \ / 1/07/85 o \ \

\ \

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\ \

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_ 11/07/85

I 11/12/85

T

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Pipe Reynolds Number

Figure 33B. Discharge Coefficient/Reynolds Number Plots, PE-9ABC

10 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

-328-
Meter Tube PE-9ABC

0.610

FE-9/0-4B

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/ 1/12/85

0.600

0.610

oro

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FE'9/0-5B

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1 1/07/85

1 1/12/85

1—I—I I I I

I T \—I I I 10'

Pipe Reynolds Number

10'

Figure 33C. Discharge Coefficient/Reynolds Number Plots, PE-9ABC

10- Inch Meter Tube, 7 Orifice Plates, Final Data Base

-329-
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S* 0.603

o

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a 1 1/08/85

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1 1 1 1 1 1 1 1

1 I 1 1 1 1 I 1 1 10 10 ' Reynolds N%imher

Stolz Buckinghani

10

Figure 33D. Discharge Coefficient/Reynolds Number Plots, PE-9ABC

10- Inch Meter Tube, 7 Orifice Plates, Final Data Base

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(A

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CO lo o> o in to

to fM fM o o o

fM in fM o o o oo

fM <0 O «- in vi- to fM fM o o o

fM -d- fM

C5 O C3 o o o o

>» o- «-

«- in N» fl fM fM o o o

CO in to

in in >» o o o

nJ- >* CO «- fM to o o« o>

fM >0 vt

fM t- ^

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in fM in

in fM «- ^ fM «- o o o

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fM vO in o e5 o

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«- fM to o a. o- ^ S- >*• in in in o o o

CO to «- 0> 0> N- o o o «* »* ^

SIin ^ in o> o »- «- o o o

fM «- «- o o o o

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in in ^ »- «- o o o

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«» o w >v

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>

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»- «- o m in in w fM fM fM

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>o >t o> fM fM «- OO CO 00

00 (> o

M 5 O fM «- fM

to o> to o >o to >* >* >*• m m m

CO CO CO m in m

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fM fM fM r- r- rtO CO to

o> 3 >o

>«• fM h-

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u.

01 o o o

to to to ro to to to to to fM fM fM

to to to

fM fM fM to to to fM fM fM to to to

> 1

t— (A

150.21 150.14 150.06 245.27 245.79 245.34 199.80 200.14 200.76 150.02 149.93 149.81 230.20 230.37 230.22 84.871 84.893 84.959 % % % * * « % % % M <A M M M M M M M

o

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•- CM to to to to>*• in <0

to to to

t>~ CO f>

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346-
Meter Tube PE-OABC

FE-9/0-7A

Beta = 0.09977

o 11/15/85

D 11/18/85

* 1 1/2 1/85

Stolz Buckingham

0.606

o

r

0,600

0.595 T—I—I I I I

I

1 r 10'

Pipe Reynolds Numher

Figure 34A. Discharge Coefficient/Reynolds Number Plots, PE-OABC

10 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

347-
Meter Tube PE-OABC

^

0.608

o

<^

o

•5 0.603

«^U

r

0.598

\

\

\ \

FE-9/0-2A

Beta - 0.3739

11/14/85

D 11/19/85

— \ \

o

1 1 1 i 1 ! 1 1 1 1 1 1 1 1 1 1 1 10' 10 10

Stolz Buckingham

0.610

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1 1

1—1—I I I I 10' 10'

Pipe Reynolds Number

Figure 34B. Discharge Coefficient/Reynolds Number Plots, PE-OABC

10- Inch Meter Tube, 7 Orifice Plates, Final Data Base

-348
Meter Tube PE-OABC

oro

r

o

O

0,608 -

0.603

10'

Stolz Buckingham

0.610

10'

Pipe Reynolds Number

Figure 34C . Discharge Coefficient/Reynolds Number Plots, PE-OABC

10 -Inch Meter Tube, 7 Orifice Plates, Final Data Base

349-
Meter Tube PE-OABC

0.605

O

'^

I

-g 0.600

0.595

FE-9/0-6A

Beta - 0.74815

o 11/14/85

a 11/15/85

I I I 1 r T—=7—I I I I 10 10 10

Figure 34D. Discharge Coefficient/Reynolds Number Plots, PE-OABC

10- Inch Meter Tube, 7 Orifice Plates, Final Data Base

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•-»-«- IMM«- 0«-0 IVlrOKI OCMOO OOMO *-> ooo ooo ooo ooo «-«-o «-ro<\j ia OOO ooo ooo ooo ooo 0C30 o . • • • . ... ... ... ... 1— ooo ooo ooo ooo ooo ooo •- >or\ieo O^ooN- rM>o>o vttoin rvi^tN- inooco OMM ojvoo Minoo ^o«- «-ro>» h-«-Ti\j«-«- >ooro ^ T- rf\ o- <:> r- ooo ooooeo

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ooo ooo ooo ooo ooo ooo

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ooo ooo ooo ooo ooo ooo

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N-^ON- »*<Mr^ ^o«-^0 toeoeo or^«- p>eoo^

S-0>o> N.v*ro oo>oo >oro>* rooo«- S-torvJ O>oooo ttKp> oo>«- ir\ o O oo»- rvjivjpj 0C30 K-S-S- N-vO^- oo>o> rororo cooooo

«-«-»- r- r- ^ ^- w- ^ cjivjrvj minin ooeoeo romoo N-oro tol^K» \r\ <y t<\ moi^ »-oo> ooo »-rM«\i K)ro^ if>in>o S-oooo t-cmim

rJsIrJ rJrJrJ rJhJs! hJrJtsT rJt>^rJ eoodoo

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irtu-iiii Mroro .-.-«- .— .-«- eooooo >*>*>l- %%% %%% %«% %«% % % =«: %%%

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ooo ooo ooo ooo ooo ooo ooo ooo ooo OOC3

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ooo ooo ooo ooo ooo ooo ooo ooo OOC3 C30C>

roio-* in>OfM o>p.o o-o«- <OK»in vO^oo fM«-ro »-o«- t>-eQfM fMcoo

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>OfM<0 OfMO" h-fMf\J ^OOOin r0-*0 N1>0^ fVlfM^»• OfMO OvOO N.in«—

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»*«*in ooo >*inin ... ooo ooo •r'z'^J ^'-T-J' ooo »*inin

«-•-«- «-«-«- »-T-«- oo>o Ooo «-*-«- ^o<0^0 o>OCT> «-«-»- «-•-•-

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

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o^ o^ V* o^ o^ o^ ooo o^oo o^ o^ o^ ^o^o^ o«os^ ^cK^ ooo ooo ininin ininin >o>o<0 in>o<0 ininin inmin mtnin ininin sO^OsO <OsO>0 ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

000000 ^>s->j- o>o>o> COOOOO COOOOO ininin inmin ^a-^vt o>oo o^oooo

«-»-«- ooo fotoio »-»-»- ooo ooo ooo ooo to>*N»- tototo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

tOCVItO fVJ<VI(\J -*>*vl- 0C30 Nj-sl-vJ- tototo "-mt- «-.-»- >oooo r->0^ T-^^ ooo (M(M<M r- r- r- OOO OOO OOO OOO fVJtOPO tOfMCJ ooo OOO OOO OOO OOO ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

O^^-O «-tOfM inin«- p>o«- f*-<oog >Oinp>. >*into N-h-s- oo«-in inrocM

eoo-co so^oso oo«- 6>oo eoooeo t«.F»p. n-kK- >osO>o pj»*to ^v»«* r-» o^^Qk. ch o*- cy ooo ^OQ o^o^o* ^o*o* ^^o» ^^^ ooo ooo in mmm ininm sO^^O m>0<0 mmm mmm mmm mmm >o^>0 ^OsOsO oo ... ... ... ... ... ... ... ... ... ... ««» ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo >o

CNJ COOOOO ^•«>4' o-coo h-coco COOOOO minin ininin va-^^ o>o>o oooooo O "-•r-^ ooo tototo »-T-^ ooo ooo OOO OOO toto^ tototo o ooo ooo ooo OOC3 ooo ooo ooo C900 ooo o^o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo I ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo (3 >*^Nt fvirjiM t>»pjr~- vt->j-^ COOOOO -o<o>o >ot^>o tototo o>fvio «-n.o>

«-«-«- ooo tototo inmm «-»-*- ooo ooo ooo fMtoto tofsifvi in ooo ooo ^.-^ ooo ooo ooo ooo ooo ooo ooo oo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 'N. . . . . . . . . . ... ... ... ... ... ... • • • m ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo (M <\ito»- orofvj f».<orvj coOnO- inmN- <Omoo r^co^O tororvj rvjcoo^ to«-(\J 0> 0>0>0> ^O'-O'O 0-*>r- 0>$'0> oooooo N-S-f^ >0>OsO ^O'O^O r\JfM«- tototo o

K^ ^ cy< ^ ^ ^ ocso ch ^ o^ o^^o^ o^^^ ^ ^ o^ ^^^ ooo ooo mtnin mmm >om>o inmm mmm mmm mmm minin >o>0>0 ^^^ • ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo vt

oo>orvj t^cvjio toiMPO toto>* >ooom »*-(\jco oot^in totoin to»-to >*toom «-«-Pvi co^tin ooo ooo oo«- rvi*-^ fMm«- mroro «-ro«- fM«-fM oo ooo r-t-»- ooo ooo OOO OOO o«-o ooo ooo ooo "*, ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo >4' ... ... ... ... ... ... ... ... ... ... »- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ^CO O.f^co >0>*-4- m<\JO« oto<o >otn<o ooN.«- moj«- >OfMvt toino toooco o inOvO. mr^f\j toinrj •-'O^ ^OP0^^ Nj-vi->o toh-co n-ojo^ ^o*-^ tos-r>- o6>On o>coo> ooo (m.-^ pjrM«- ooo oo^o "Oh-'O ooo> i-^^- i oo>o> ...

... ^>j--* ooo ooo vi->»to ^Nt>*

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t^t^N. ... ... ... ooo 00>0 ooo ... ... ;|t: «-00 (MfNJtM OOO t-^^ tototo •-^.- r- »- (\J(\t(\J OOO OOO

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•-«-«- fNJIMCM ooo ^T-^ tototo «-•-»- »- •- rvJfMfVI OOO ooo 3

t^N»0> tOinO tON-(M tOrvl^ t«-tv.O O«-00 OfNJ>» (MI>~>0 «*fM0O to«-co «-«-«- •^fvi>s- o«-o ooo oo«- (Mcjm >»fNj«- m>*-* ^<m^ fvj^«-

w ooo .-.— «- ooo ooo ooo o^o o«-o ooo ooo ooo (/> ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo V . . . ... ... ... ... ... ... ... ... , , w t- ooo ooo ooo ooo ooo ooo C300 ooo ooo ooo •-• >*>0«M vtp>co inr>-o >»o»- tom«- «->*to in>oto inpjoo -d-msO ^t^'O >ooo <oS-(M tototo T— N-m oo>*'0 in>»sO in»o oinro int-v* rviKr^ ooo o>oo^ o»-o (\j.-«- r\j(\j(\j ooo oo>«- N.F-r«. c^oo^ .-.-.- ooo ... «4'v^v4' ooo ooo ... ^l-vl-tO >*>*>*• . .. t>.t^t^ ... ... ... ooo oo^o oo^ ... ... •-«-.t- (M(\j(M ooo -^ r- T- tototo «-«-«- «- «- ojpjrvj ooo ooo

ooo ooo o«-(M fMfvjto ooin oto«- oo<M oeoin toorsi ooo

>o<o>0 ooo •.*>*«* <OsO>o (M(\jo «-mrvj o>0>0> (M(\j(\j >*>tNt ooo vO<o<o ^»-«- ooo mmm >0<0>0 vO>0>0 oooooo vt>t»t oooooo minm ooo (VI(M(Ni «-if-^ ^^^ ^^^ ^^,_ ^^^ ^,_^ rvi(M(\i v»ot\i mto«- tooom t>>.t^rj mrMO> covot^ intoo> >*.-t«. o>too •.»»-o >*o>co coKflO orvio <M0ON- to«-p> GOmva- «->i-^ mino> >OfMO oN-t>- 00>0 ^©•0> r- r- ^ (Vj^^ ooo> oo«- ooo«- o«-o «-«-o tototo

O>oooo ... rvifMCM a>0-0> totorvj ooo oo-o >0'>0>0 (Mtvjrvi rvirvicM ... o^^o> ... ... ... ... ... ... ... ... »-«r-^ r- r- ^ ,- ^ ^ tOtOtO <0>OsO vOm<0 COOOOO r- ^ w- ^- w- ^

to-j-<0 <ocoo fON«->j- •.*>*m o>co>o «-o.o o.^«- mv*>* oo<0(M cocooo

>*>»•>* >0'0>0 0>0-0> 0>o>0> o>0>^ oo^o o^oo «-«-«- msO^O mmm

oooooo oooooo «>oo> OsO>o> o»o^o^ do>o o^ocj ooo rjcMrj cMCurvi tototo tototo CVI(Mr\J (MfVjrvl <M(MC\J tOfMtO CMtOtO tototo fMCMCVJ (M(MrO

«*>»>Q

mt>-oo t«.>ON- oov*«* o«-f>~ vOm-* tO'^v* mv*to o>t^r<- vj-t*-fM ootoN- a.»-o ^^^ m<om tocMo s»oo«- ofMto nj->o^ invtfM >o>i'00 »->«.- ... ooo «-»-»- ooo ooo mmm ... ooo ooo ooo «-«-«- ooo "O^O^O «-*-»- ooo T-^^ ^OO C300 (M(M<\I .-^«- >o>o<o (M<M(M ^^»- tototo njcMCj r- r- T- m>0>0 tototo rjjNjfv) tototo «-«-«- %%«: %%% MMM MMM MMM MMM MMM MMM C3C30 (3(3(3

o>o*- jMto-1- sOt^co o>o»- (Mto^ m^o^^ oo(>o "-rvito -*m>o t«-co^

vot^t>- r^K-N- f^f^r^ S.0O0O oooooo oooooo ooooo> o-o>o> o>oo> o>o-o>

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eocooo ininin ooooco >*'>tNt cooooo ininin eoooco v^^vt v^vi-^i- ininin •-•-«- ooo ooo ooo ooo ooo OOO ooo r-ooor- w- oo^ ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

o«-o lOfOro >*>»--* »-«-r- oo«- roroto «*-*>»• <m»-t- (virvirM (m>o>o

»—ooor-«— ooo ooo ooo ooo ooo ooo «—«—•— ooo ooo ooo ooo ooo ^oo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

r-^vf ooo >0>0>o P^h; N.0QN- ©.roPM LniONO cqoo> ocqoo oot^^ tororo ooo N-N-s- o^coeo <o^>o o>oo F^hwN- ooooco r^5555 ^S^oOS K-K-K- 0>0-0> 0>0'0> 0>0>0> 0>00 O^^'On o>o>o> o^o^o^ o^o^o^ o^o^o^ >0«o>0 minin tnmin ininin in>o<0 ininin ininin ininin ininin ininm

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

eoooco ininin ooooco vtvtvt ooooco intnin cooooo >4'>4'-^ ^d-^^t intnm »-•-«- ooo ooo ooo ooo ooo ooo ooo «-»-«- ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

Ot-o lororo ^>t«* t- r- t- (virvjcvj rotOfO >*--4-^ ro«-«- rororo (Min<o »-«-»- ooo ooo ooo ooo ooo ooo ooo t-^.- ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

Q»T-f\j NO-Oin 0>0>cQ CQCQCQ ino>N- Lnin>o r>-o>l^ ooooo oof>->0 roro>»- o-oo r^hwK ooooco >o>o^ 9>2'9>' F-s-r>- cooooo r>^9^ ^ 'O Z K>K-r>- i-i o^ o o o^ o^ o^ ^ 0^ o^ ^ o^ o^ v^ ^ iy< ^ ^ ^ o^ o^ ^ ^ ^ ^ o* o^ o^ 0^ o^ o* m in<o>0 ininin ininm inmm mmm minin tninin ininin minm ininin 00 • • • . . . . • • . . ... ... ... ... ... ... >^ 000 000 000 000 000 000 000 000 000 000 nOo

coeoco ininin cooooo ^«*>» cooooo ininin cooooo -*-*•* vj-^vj- ininin •- «-«-«- 000 000 000 ^T-»- 000 000 000 000 000 «- 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 I 000 000 000 000 000 000 000 000 00^ 000 (B «-fM«- hororo -4-sj-v* ^^^ toroio rofoto ininm fM«-«- fviPOCM in>or^ 000 000 000 ^^^ 000 000 000 000 OOC3 in 000 000 000 000 000 000 000 000 000 000 CO 000 000 000 000 000 000 000 000 000 000 V, ... ... ... ... ... ... ... ... ... . . . rvj 000 0C30 ^00 000 000 000 000 000 000 000 (M ^-0>N. >0«4-tn r^r>.in r»oocQ ros-m ^tinvO cooof^ oh-co 0>oo<0 ro-.*^ o 9>o>o> r«.N-N. cooooo >0>0^ ?'5>5> ^^^^^- cooooo t>.<o>o ininin >OnO>o »-

v^ O^ ^ O^ ^ O^ ^ ^ O^ O^ O^ O* ^ O^ v^ ^ O^ ^ ^ ^ ^ ^ ^ o^ o^ ^ ^ o^ o* ^ ininm mmm mmm mmm mmm mmm mmm mmm mmm mmm

000 000 000 000 000 000 000 000 000 000M

inN-m mcoo t\jv*-o> roh^>0 >*»*<0 co«-t^ t^ojo. N.«-o> r>.«-<o o>og>* in o«-o roioro «-«-o torofvi 000 »-m»- o«-o o>rjfvi <omto >oooco co 000 000 000 000 000 000 000 000 T-T-«- o«-«- >» 000 000 000 000 000 000 000 000 000 000 vO

f\j 000 000 000 000 000 000 000 000 000 ^00 v^ •*ooo> vOm>o fO'Ofvi rjino. forvjfM <oco(m o^Oin mo>fvj ooN- <>-(mo> o

roh«-«* Mfvirj >o«-m (y <y r- <-ooca roN-m pjoo-«i- >omh~ coroo> cj^om

o^ & o 000 mmm mm>o O'.coco oo>o> m^ro to^-* 0>0>oo oo>0> > 5s6»o ...000... 000 ... C300 ... o^o>o> ...

... 000 ... ^••' ••• «^ oo>o> ... 000 r^r^N- oo>o> %

oo«- 1- T- ,- rororo porvjcvj 000 «- toroto popjru pjcjcm «- m-o«* ro>»o «-rooo «--4-io M>*m «-Mro r>jr«j>o t\imco cO"— «- <OKO </) o»-o pjMfo »-»-o roroto 000 lomro »-t-o ocoto >*>o>j- >oS.o> «j 000 000 000 000 000 000 000 000 «-«-«- o«-«- "5 000 000 000 000 000 000 000 000 000 000 oo 000 000 000 000 000 000 000 000 000 000 01 OvON- -0>0N- K»«-0> ^<ON- <0^00> N-OOfM OOrO«- «0«-0 mOf^ »-^o> M

^ooin ro<M(M K»-vf o>^«- (\joo> pjh^m too-^o >o^t^ F~ro^ fvj<om «o 9' O' o 000 mmm inm<o ^coco oo>^ m>*to ro**^!' o>^oo oo>^ o

5^ &> o ... 000 ... 6> Ch

O • 000 • • • ,,• ,^" ,^* ^ ^ ^ .- • • 000 ... 000 ... oo>o> ... 000 ^~^.^«. oo>o> c oo«- ^.-^ rororo (\i<\j<\i 000 «- roroto <\jfvi(M PvipgfM «- 3

>*>»ro >0«-<0 cO(mS- >ONOm >«->*->o <\i«\jro oa>co oroo <M»-f\j mm>o

o«-o "-rjro o«-o ro^j-ro 000 romro •-oo >oro^ «-cjro O'toco

m 000 000 000 000 000 000 000 000 «-»-»- o«-i- l/> 000 000 000 000 000 000 000 000 000 000 0) ... ... ... ... ... ... ... ... ... ... t- 000 0^0 000 000 000 00^ 000 000 000 000 •—

0>roro >»^rs. co^ro pj<oo> roros- o>o>pu mcoo >tcoro o-mOj -*5P»- >»-0<S- rofocvj ooroK. o>o>«- tooo por^-m toor*. •o•>o^^ lOTrSP 'D 9" ^ o>o>o 000 mmm mm>0 0sO.o. 00^ mmro ro^*** 00^ oo>Ch O-Ono ... 000 ... (So^o^ ... 000 ... ... ... ... 000 ... 000 ... oo>>o> ... 000 COOON- o^^

oo«- »-«-.- rororo (\ipo(m ooo «- rororo fvjtvjrj rvifvjfvj «- «-oro o«-c\j 000 ro«-ro o>r-m <m«— cm omo »--»>* oor- 000

m<a^ m^-s- N->oco mm^ >om»o f>jro«— co>om (\irvjfM 000 ^ <y (> sO^^ S>K«S- ^>^^ ^>o>o ^^>o OOOOCO mmm oocooo 000 >^>^n^

«— *— T— «—«—*— «— «— ^- *—«—«— «—«—«— «—«—«— CMfVJCVJ V— r— V—

v»-N*ro >*roro N-<oo> o«-o> «-N*-t\j »-i\j«- cofviro ooom >omco tncorj

r^<MO> infvipvj «-oo&. orom mroro toc>><\! o>ooo oosrls rroj*. J^ittt o>^o 000 fM«-«- o^o^o^ o>o>o> ooooo »-<i-T- •j->o<o ooo- 9'opcp ooo>0> 000 rororo mmm ooooco 00-0> rororo mmm _•• O' O^ O^ ... ... ... ... ... ... ... ... 00^ ... •-.-.- >o^<0 rororo ooooco »-«-«- <omm rororo ooooco «-«- inmm

rofvjcvj ocoi^ (\j>*>* rov±«* 000 eoN-^ «— «— ro ro(vj<M roS-cvi S^^o^• ^.0>0 N-^^ ^^>c ooooco *o^^ ^^>o ^>0>0 coeoco nOON- rococo

eocooo cooooo coeoco coeoco >0^>0 ^'O'O ^o^-o ^o^o^o -o^^o ^^<o rvjcvjcM (virvjctj p>j<\j«nj fvjf\ifM <\j(v«m fvjojrvj (M(M(\i rsjrjcj ojcsjcm (M(M(\j

>*m>* ^>oo voom S.COO nO<0«— »— N-ro NOro^ rOJViN- NO>Oro m'OvO

'-N-oo mrooo t>-fM>i- «-oON. O>h>-eo n-i-^ ooo>«- mroin meooj «-m<Nj • •• eo«-«- ... ... ... vororo .... ... ... ... 000 ... ^i-inin oo^o oo>o ... s*-^m 000 (m«-<\j ooo 000 o>oo »-«-«- oo>o oO'O o>oo «-»-«- (M(Nj(\j >o>o<o 000 fMfMJM m<0-0 «-«-«- fM«-fM «M«-f\i m^o^O «-«-T- (vi(M(M »-»-«- rorOfO « * % »%» %** *%% MMM MMM MMM MMM (3 O C3 CB (3 (3 o«-fNj fo>*m <or^eo o«-Pvi >oh^oo fMro>* m>ON- ooo>o «-f\iro >»mvO ooo C300 ooo «-«-«- »-«—«- rgrvjcM (virviro ojfviro rororo rororo

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ooo ooo ooo ooo ooo ooo ooo

OnO«o< ininin vj-vj-v* ininin cocoeo h-h^s. N.N.0O

fOfOfO ooo ooo ooo ooo T-»-.- rororo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo

in>*?* roinro (\j(m<\j ool^h- oo-oo lOfNJrt f>-0>>0 (VfMfM ooo ooo ooo «-00 ^^r- (NJrOCM ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo

fMO«- M>»!\J vOr^^O invO»0 ^Oln^O >O^Oin «*»-oo

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ooo ooo ooo ooo ooo ooo ooo

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ooo ooo ooo ooo ooo ooo oooM

«->Oin MMCM >oinin f^ooo> N.»*N. oOfOI^ oc>'>*

fvjrjro KS-N- >o>ovO Kr^r^ ooooco 2>2'5' •«*to>* in ooo ^^o^ o^o^o^ ^^o^ o^o^o^ ^ ^ o* ooo co v0>0>0 ininin ininin ininin ininin ininin ^^O^ ^ . . • . . • . • • • I . • • • • . • . . . nO OOO ooo ooo ooo ooo ooo ooo o

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ooo ooo ooo ooo ooo ooo ooo

oo>in oN-o roroo ficMN- Mor^ o>oOM oeoro cfl v»-o><0 "-vOeo oroo f^>i-r^ ointvj i-cnjoo -j-inro o> ooo »-oo ooo O'O^O' ocMro kikicvj Kiro«- "O ^>*-N* oo>oo ooo -*-*>«• o • •• ooo OOCOOO o>o>o> .•• .•• ... u ooo ^- r- w- (Njojco Mcvirvj »-.-»- ooo 4> 0>N-in vj-foo- inoovi- invoro ro«-o cO'-o oo»*r^ ••-• ooo o>Keo invflrvj >»c^«- o>ooh^ ojcviro «->»o (o ooo o«-o ^^^ {\j«-(\j ooo ooo ooo a ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo 3

Of pj^O> «-^ooo >Oi^ro «-(\Jin N->o>>- ino>ro <\jki<\j «*&.in •->or»- o>c\JO N-vj-K o>horvj fMroo> >*->0>* ••-• ooo «-00 0>00 0'0>0> 6><MM rOIOCM i'>to«- </> •4 ^ ^ 5>O>00 ooo >*>*>* 01 • •• ooo r^oooo o>.o«o> t- OOO r- T- ^ <NJ(M(>>J (M(M(\J r- r- t- OOO '-' ^h-»* ioo>fM »*ro^O «-eoro N-ino invOI>^ -j-^-t^ ooo to>0«- «M-^^ oor^co mN-in <\jfvi(\i <i->*o ooo ^^^ »-^^ (Mr-T- ooo ooo OOO ooo ooo OOO ooo ooo ooo OOO

OOO OOO OOO OOO ooo ooo OOO

N.N.T- o<'Cooo r«-o«* tninvo n*>o.- r«.oo«Q o><ooo in«-co O'Oh- Ov-4-«- ^oro^ eo-*»- »->»eo >*>0«* o«-o «-oo O'oo o>0'0' o><viN5 roMtvi mm«- «*>*•«* ... ^••' ... $.(>>«} ooo ^«*>*- ooo . .. ooo N-eooo o>o«o> ^«-«- rM(M(M (M<M(M ^.-.i- OOO

sroin o«-o «-oo ooo ooo ooo oo»-

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r»>otn ^o>o> ooo ooo ooo ooo <-^do> «-«-»- <M(MCNJ tororo (OMM MfOPO MIOM «-«-

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ooo ooo ooo ooo oo^ oo^ ooo ooo ooo ooo ooo ^oo

ooo ooo ooo ooo ooo ooo oo^ ocjo ooo ooo

ininN- »»in>* ^»l/^^o >*«*ro ^0>*>0 inpjm ininin ro«— «— com^ r>-M-«*

»\J<M<\J ooo «-«-«- OOO OOO ooo ooo ooo ooo ooo »—»-«- (MrUlM r-»-T- OOO OOO

OOO OOO OOO ooo ooo ooo ooo OOO ooo OOO OOO OOO ooo OOO OOO

ooo ooo ooo OOO ooo OOO ooo OOO OOO OOO

r- T- o o.o>o >*>»in <oh-m «-(\Jro ^^f^ eoo>f^ in>3-o> Mvt-* >oir><o >*>*«* ooo (MOJM ooo r-ooor- r- O- 9' O' ooo fvjfvifM Mforo cjfvjfvj ooo «-o>o^

<>>&•&> ooo ooo ooo ooo ooo oo»o> >0^0^ >0>0^ ^>0^ lAi/^in >0>0*0 ^^>0 >0^>0 >0^>C *0>0>0 *^ if\ if\ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooeoeo rs-N-N- r>.ts.s. roroto >*^>»- N-r^-h- eoeoeo r^r^<o -*-4->»- f^roM

ooo roMfO T-»-.- ooo ooo ooo ooo ooo ooo ooo »-.-«- rorOM »-«-«- ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ^oo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

N-N-N- inmin N->o>0 >*>*« ^0•*>0 P>-to^ o«-o inwoj ooinm oorOM

(\i(M(\i ooo r-ooor- w- ^oo ooo ooo ooo ooo ooo .-^^ fjforo ^.-.- ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooeoN- '0>0>0 m^Oln inN-S- «\j»-tM s.(m»- (mk)(\j o>eorvi -*>*-^ oo<0>0

(MfvjfM ooo (MfvicM ooo »-.-»- ooo a'9'^ ooo (\JK>K» N*vi->t <M(\JM OOO «-a-a>

o^ o^ O' OOO ooo ooo ooo ooo oo^o> >0^^ >0^>0 >0 >0 ^ ininin ^>0>0 >0 ^ ^ •'O ^ ^ ^^>0 ^^^ ^iAii% ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooeoo r-r^t"- r^N-r^ KiroM >*•*>» N-t^h- ooeoeo r^t^>o -*^«* t^KiM >-. KirofO ooo «-«-.- ooo ooo ooo ^^.- roroM »-«-«- ooo ooo in ooo ooo ooo ooo ooo ooo ooo ooo ooo oo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo >»

eo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o

N-oooo >tro-* <o>0<0 -*>*K) insj-in vS-cm-o ooh-r^ vttorvj <oift>* oororo S. JMOJCM ^^»- ooo ooo ooo ^ ^ r- fMCVJIM r- r- ^ OOO OOO O ooo C300 ooo ooo ooo ooo ooo OOO OOO OOO ooo OOO ooo ooo ooo ooo ooo OOO OOO OOO 1 ooo ooo OOO ooo ooo OOO C300 ooo ooo OC3^ M

r>-mir> eON*->j- \0 in in ^000<0 M«-~* f^»-0> >O>4-e0 f>.«-l^ fivtro fMf^in K)MK> rjojfvi r- ,- r- <> o- O' ooo cMhotM roKifO tvirofvi ooo "-O-^ •* OOC3 ooo ooo o>&>o> ooo ooo Qoo ooo ooo 0&>0> 00 vO-^^O >C^>0 ^^>0 U^1/>IA ^0>0^ >0^^ >O>0^ ^^^ >C>0^ ^i/%ii^ ^^ ooo O^O ^OO ooo ooo O^O ^OO ooo ooo ooo CM

"»» o>oo>* ror>-Nj- r>-»-(\j t'><Ovt ^<Mr- r^oN- «-(mo oo>>o otn»- i/^>oro o oo«- KiMM lAvi-in >o>»0> 0>«-0> rofMM «-r-»- ro«-«- ^ou^^o m m t\i ooo ooo ooo (>jrj«- ^»-^ ooo ooo ooo rM«-»- o»-(m i ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo % ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

S.oo<0 «-M<o in-j-o- eooooo oo>r\j «-fviM 0>-*m ococm ^«-o> ojca*- co oo-oo vj-r-T- o>KiiA oo<om •>o6'0O r'i>oK oooo f^Ntv* >o>*>«- «->o>* o» o<>>o> ooo oooooo cooOoo o^ooeo ^ t- o »-oo »-«-c\j «-o>o oooo -a v»roM ooo o^O-^ ... ... 0C30 -*•-»>* ooo ... (y . . 6 . • ... ... h.|^.^^ o^o^o^ ... ... ... ooo -0000 tj ooo »-»-T- (Mfvirvj fvjfMfvi »-.-«- ooo «-»->- «- «- r\j(\j(\j

0) oo-fM -*>*>t o>t^>o 0>0^'- <oo>^ rvj»-oo rjinrj oeo>0 Kivnin -Ofvio *j •i-O'T- rotoro ir»>*>» s-oo ooeoeo srcuvi- ^.-^ m«-»- K<ONt voroeo <o ooo ooo ooo (MfVJIM t- r- r- OOO OOO OOO (M.-»- 0«-«- Q ^oo ooo ooo ooo ooo ooo ooo oocD ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo 3

Of inin>* (\jf>j«- roooeo -.i-ofM oooho «-ofM foot^ r^roo >jO>o OMhO fvi»-o tncMM oo«-in o>f^«* inoeo (Min<o oN-oo inrofvi <) rn m oia>* ij OOO ooo oooooo oooooo 0^0>« «-«-0 T-OO «-«-(\J «-0>0 oooo CO >4->»'>* ooo 0>00> ... ... ooo Nj-vtvJ- ooo ... 0>.. 4) .«. ... ... r>.r^h. o^oo ... ... ... oo>o -oooo i— ooo »-^.- (Mrorj CMrjrvj ^- ,- t- ooo »-»-«- «- •- rvirjpj •-' r>-o>o t^NOo- r- o T- r- m ^ r^o<o ooos- ro«-o oroo rvir^o o>*^o

oo«- ro(\jK> «*•*>» .-«-vo >o<M»* (\i»-ro «-«-o i>ocm«- o-om r^oro ooo ooo ooo KJOJx- ^.-.- ooo OOO ooo fM«-«- 0»-«- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

to^oro N.»-r^ h-ini^ ooo>o n*oo r'i>*eo «-«-fi mor^ intviro >o«-eo «-oo. ^roM r^(M>o m >o <t mooo pom^ «-o^O> <Oin-4- >o>*-m iq-4-v»- ooo ooo oooooo eooooo oooo »-«— o «— oo «— «— cm «— oo oooo

>*>»ro ooo ooo ooo -sj-Ni-vt ooo ••• ^ ' ' ... ... ... r^h.r^ ooo ... ... ... ooo -eoeo O^O «—.-.- (M(M(\J (MCstCM .-.-»- ooo «-.-«— «- «- CMfMfVJ ooo ooo ooo ooo ocMO ooo ooo ooo ooo ooo

oot>~o »-c\jcM ooo in-jin r^cooo Mvj->i- f^>oo ^^^ t^m»- rriPin

>*»i->a- OOO ooo oooooo N»Nt>t ooo •O'O^o ^o^o>o ln^o^o oooo .-.-»- f\jrj(M ^^«- ^»-^ .-^r- ^ T- T- »-T-^ r-

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>o in

m >o>o>o ... ... ... r«>r>>NO >0^0<0 h-f^t^ •»'.• _"_"_• . . . ... ooo ooo N-N.h~ ... ... ... OON-S- OOO roMM lAinin pjpvicM ^^»- i/^miA rorofO iAir>m ^- ^- t- pjcj ^toir> »-rON» Ovi-vo «-fviN» >oh~o N»in>o t^O»- oroin -^nOoo oooeo MroKi >*>»>» utiniA '>o>o^ >o>o»o ^«.^-^«• s-n-oo oooo o^o tviKiro ooo oo^ oo^ ooo ooo fviojfvj cMCjrvj pjfMfvj rotoro fororo

fOKiro Kiroro mmm roioro Kiroro tn to to kimk* mmki kimm Ktroro

f^J^^o f\jf\j>o eoro«- o«-ir> N-oro >omoo fMh-»— «-oo>o «— ^o^^ >oo^ oeo>0 pjoooo oow »»-*o infvjpj ororo 0«-»m o>»-o »->a^ KiMro ... vorvifM ... >a'00>4' ... r>.KiK) ... _•• ... • r- m

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vtin>o t^ooo o«-(M ro>»in >ON-oo «-<\jk> N*m<o h~ooo o«-(m Ktr^oo

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O^ o^ o^ v»«*N*- rororo >o>o>o »*>*•>* eoeow o>o>o> o>oo 2525r«. ^»-^

lOKiKi >*Na-vj- tororo r^r^s. >*»*>» cvjcjcvj >*>** >*•»*>* ooeooo o>0'0 «-«-«- (\J<\J(NJ (MCMfM

^>*«* ooo N-N-r^ KiKtro t«.s.N. soN-^o ooeoeo s-r^h- i>^N.r^ r^r^r^ roioro ooo »-.-«- ooo ooo ooo ooo ooo ^•-.- ooo rofoo «-»-«- «-.-«- ooo ooo

ooo ooo ooo ooo ooo ooo ooo oo^ ooo ooo ooo ooo ooo C300 ooo

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h->0>0 ooo o«-«- Nj-roro <0>0S- M>»>4- Nj-inin r^>0'0 to^j-fi oooO'O roK)f)

ooo .-^^ ooo ooo ooo ooo ooo »-^^ ooo ooo rvirMCM »-«-^ w- ^ w- ooo ooo

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ooo ooo ooo ooo ooo ooo o^o ooo ooo ooo

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PsIPJPsI .-.-.- ooo .-.-.- ^ r- T- PJPOPO KlMKl .- OOO OOO OOO ooo OOO ooo ooo ooo

ropjpj vj->*-in poo-N- oo.- »-.-«- foro>* oeoo- >o^-r>- eOeoeo «*>*>* n»>i->» o>o>0> <0>o>0 eoeoeo oeoeo >»•*>*•

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N-eoeo 0>0-^ POPOPU coeoo- oo>o coF^N. eoeoeo ooeoin ... ... >o^^ N.N-S- eOS-eo ... ... ... 0»^0> N.N.N. ... ... ... 0>0>0> ^^0> N-N-eO

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ooo ooo ooo ooo oo^ ooo oo^ ^oo ooo o^^

inN.>o ooo <M«-Ki >or^r^ sf>0>0 mmm »-»-.- mmm S-eovO -*v»>* rvirvjtM «-«-^ rvjCMCV ooo ooo ooo ooo ooo fMCvlCM »-»-.- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ^oo ooo ooo o^^

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

Ovto M^-4- eop>f- >oooo> NO»Oin N-eoo> eoeoi^ o«-o» »-vi-cM inwfo ininin ooo >o>o>o ooo h-s-S- ooo mmm ooo mmm ooo fM«\j(M ooo mmm ooo inin%* ooo h^r^r^ >o>o>o >0>0^ >0^^ >0^^ Qoo ooo ^^^ >0^>0 >0^^ ^^^ >0^^ ^^^ "O^^O

ooo ooo ooo ooo ooo ooo ooo ooo OC3C3 ooo

s^-^^ ooo N-h-r.. eoooeo mmm mmm <Mf\ifM mmm r>.h~r^ eooooo >o>o>o .-T-.- MMM ooo ooo OOO OOO OOO MMM «-«-»- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo OOO ooo ooo ooo ooo ooo ooo ooo ooo ooo

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

POfMCM rjrvjrj rofvirvj minin »m(M(m »-»-«- vi'^ro roKivj- rtrom inm'O ooo ooo ooo ooo ooo roroio «-«-»- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

oo«-»- «\io^«- oo>o> >»-«-K> cM>*in N-^o io«->»- ino>r«- <\jcm»- ^o^>4' in^o^O in>*ir> >i-roKi s-n-K- minirt (viNro ooo •*>*>*• roforo <0'>0^ ooo >0 ooo ooo ooo ooo T- w- X- t- T- ^ ooo ooo ooo "O ^ ^ ^ ^ ^ ^ ^G ^ ^ ^ ^ ^ ^ ^ >o ^ ^ >o ^ >o ^ ^ ^ ^G ^ >o ^ *o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

>»>*-* -*v»>» KiKiio f^N-rs. vtvt^ o>o>o> r«.r>.s. vi->f>*- rororo r«.N.i>«. ooo ooo ooo ooo ooo foroKi »-T-^ ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

CNIOJfO (VJCMCM (\JCMC\J ininiD PJCMCM CNJtMrO »n>*>0 MMK» fMJMtO ITIIA^O ooo ooo ooo ooo ooo fororo ^»-«- ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo C300 ooo ooo ooo ooo ooo 0C30 ooo ooo

ooo ooo ^oo ooo ooo ooo ooo ooo ooo ooo

»-»-»- oo«-o .-.-o> <\j«-fo c\iKi»- ».roin roov* o>o«- mm>o oo^o ininin invO«0 forocvj >0^>0 ^>*>t o»-«- o>0'&> vj-min roroto ^O'Oh^ r-. ooo ooo ooo ooo OOQ «-»-»- ooo ooo ooo OQO in

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•j-^^vt -^vj--* MMro r^r^r^ •j-n*^*- o>0'0' t^r^s. >*-^^ roMKt r^s-r^ oo ooo ooo ooo ooo ooo fOfOfO ^.-^ ooo ooo ooo o ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo I OOC3 Ood OOC3 <3C3C3 0<3C3 OOO OC3C3 dc=>d dc>C3 OOO O

cMCMfo cvjrooj CMfVJM tninin rocMfi ^«-«- inroin (virocsj rvJCMCM ininvO ooo ooo ooo OOO ooo rototo ^.-»- cjoo oocs ooo

m ooo ooo ooo ooo ooo ooo ooo C300 ooo 0C30 00 <30o ooo 0C30 ooo ooo ooo ooo OOC3 ooo ooo >x ooo ooo ooo ooo ooo C300 OOC3 ooo ooo ooo ro kiOnO o>«-<\i fvioo (\j«-m »->ocM N-too oc\JO> &.»-«- ininin ooi^O> t^ in«*in in-o-O rorocM <o<o>o >«--4-^ «-«-c\j oo-co Nj-inin roroKi ^>o>0 o C300 ooo ooo ooo ooo .-^^ ooo 0C30 ooo ooo ^ ^O >0 ^ ^ ^ *0 ^ >0 ^ ^ >0 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^G ^G ^ ^ ^ ^ ^ ^ ooo OOC9 ooo ooo C300 O^O ^OO OOO ooo ^OO M

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o>o>o ooo t>^r«-oo ... ooo o.o>o r^N-K ... c

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a; ooooro ro'-oro mro^o »-ino roc\j>o ooooo> ^o^-^o «-o>o> ooh-o k>«-'« m^r~ >*>oin (\j>»«- cjcmm oo-j-t^ ooo c\i«-f\j inr^m oo>*ki rofivj- +j ^OO ooo .-.-CM ooo ooo ooo ooo ooo 0>r-.- OOO CO ooo ooo ooo OOC3 ooo ooo OOO ooo ooo ooo 0) ... ... ... ... ... ... ... ... ... ... (- C300 OO^ OOC3 ooo OOO OOO OOO ooo 0C30 OOO -• «*rM.- >*<\jo 0>0>0> ooo- OM^- tnooin oOvj-oo cmo>o roineo o>*-<o

eoooro inooN- >j-cmoo kiO-st mcmki ininin «\j.-o ooo^i- ^>to ooo^O^ o>o>o ooo o<o>o .•• K-mvj- ooo <y (>• o^ ooo ^o>o oooooo o^ o^ o ooo ... lororo ooo ... .••• oo»-

o>o>o ooo f^t^oo ... ooo ... ... o.o>o N-h-N- ... «i- .-.-.- cMCMCvi IT, tr,tf\ .-r-<- ooo »-.-.- »- (MCMCvi roroM

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ininin in-o^O >*>»>» f~-h»h~ ininin r>-N.N. N-h^h^ ininin >»%»>» N-h~N.

oooooo oooooo .-.-.- %*>j-N» oooooo .-.-.- rsic\j(\j oooooo .-.-.- >*>*»*

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ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o^o ooo ooo

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fvjfvifM o>roo ^'Om ^p^^ -o ^\r\ «-o«- o>cvjo Ktwin rorONi- t'ttMOj S-r^r^ ooo «-jM<\j T-T-»- o>o>o> ooo co9>oo ooo >o^o^ OOQ ininin ooo ooo>9> »-«-«- ^>4'>«' mmm

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r«-s.r>. ooo rowfo oooooo <o^>o «-«-.-N.N.r«. ooo »*<*>* ooo roroM r^Kh^ >o<0'0 o>o«o> mmm

ooo ooo ooo ooo ooo ooo ooo .-^.- roroho ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo

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N.&.r^ ooo «-oo <*>*M ^A^O-* (\j(MK) MMfM >ooooo <i-«-(M r^N-N- rororsi ooo foroho ooo r-oooT- <r- OOO OOO OOO ooo «-.-«- rvjfvirvj ooo

ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo o^o o^o ooo

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>* CM CM CM o ro

«- CM ro o o o in m m

>i- in >o ro ro ro 1^ CO o ro ro ro

>o r>- 00

403-
r^ h- o rvj lO ^0

in •* >»

fvj rvi <\j

00 o tn T- ^ O >* v»- ror>- ^ O >o 1^ 'O

ID in in CO 00 00 ^ %o ^ O IS —I Of o o o o o o d

>* * <M O PO (M o o oo

f^ o o> o> o> OO

sO >o >o o o o

h^ tv «o o o ooo

-*O 00

M ro fVl

(\l fVJ fVJ >o >o <o

Nt vt in

•* •* o o o

•4- vj- in «M (M (\i o o o o

r^ ro ro

o> o o>

(\J

M CM

vO >o «o

in in in

(M <M <M O O O

\0 <0 >6 oj CM rvj >o ^ ^

ca c

4-> (U GO U

U) < — 41O) >o (- I N- <0 I O

(M

U I • tA O •-

>* Nj- vO o rj fvi o o

IS. o> vj- 0> 00 o> ^ ^ <o o o o

>j- rO in O (M CM o o oo

«o o r^

o> o> OO

>o >o >o o o o

vO ^ ^ o o o oo o o

>0 N- <) o o o o o o o

•-

M 00

ro ro po

«M «\j r«j >o >o ^o o o o

%o ^ ^o o o o o

fVJ

O >0

ro fO (M

ro rvi (M ^ "O <o

>* >* in ^ >* <* o o oo

v»- >* in PO CM <\j o o o

in ro «-

F- CO 00

f\J f\J fVJ <0 >o >0

>* sj- in o o o o

vO o 1^

PJ PvJ f\) o o oo

<Q ro pu

eo On

O CM pj r>j >0 'O -o

in in in

pj <\i pj o o o o o

»- o «-

<0 ^ >0 PO PO PJ >o <o ^

inm in

(\J (M PJ o o O o o o o o

(\J PJ PO r-i «-«-«- in o o o «-

>o *o >o

PJ OJ Pvl no >o <o

41ou

(0

O (A

U I %^

<n I .- 4) O M t4) 3

4) x: (A U U (A

••-

C 4J

>«- - «_

;: fC o o o o o o

Pvl o O in fC

00 ro <o • fO ro o O 0>

<o fo r^

«- PvJ 00

.- 1^ N- o o o o On ro

00 TOm

lOM On • • o o> m o« hpj t^ in ^ vO F- o o o o o o

sim 00 o in Nt

oo ro N- ro ro

o> . . o> o«

PJ

O ro

in in V* o o oo

>0 »- in

oo >} PJ

PJ <0 On o o> 00

00 •- N-

>* in ro o o o

s* r^ sj- «- «- rvj ro nO 0> o o> oo

fN- >o ro o o o

r^ 00 PJ o ro >*

lo >o On O On 00

r^ nO o o o «-o

1^ vO vO

in f^m in in >*

Nj- -* «* O O O r- r- Tno fs. On (\J s» «- o o o ^ T- ^ o o o o o o o o o o o o

oo o t^

in nO s* >* -J- vt

rvi o hh- On in

in in >*

>«• -J- -*

CO ro «- o «- «- o o o

no in o in no ro ^ »* -* o o o

(A

41

T- \Q

O ts- nO >*

-* ~* s* o o o O O O ^ T- ^

in On «- PJ •* rsi O O «- r- ^ r- o o o o o o o o o o o o o o o m >o On

«0 NO ro o o o

00 >o h^

C- 3 4> (A

4)O •-> "v. •->—» (0 ^ 41 u. OC —

o in ro

ro o 1-

On 00 oo

>* s» sf ^ o o o

r- no PJ o ro r^

oo 00 nO o o o

oo l>- in

(NJ PJ PJ

nO nO nO * yj

—' S 41

•^ .^ 4) O >— (A

r>- 00

nO nO NO o o o OJ PJ PJNO no no o o o fVI PnJ fM % % %

•- PJ ro * * %

«* in no % % %

r^ 00 On % % % o «- r\j

-404- I
Meter Tube DAN-4SS

u.ouu — FE-5/6-8A

^

1

o

Co 0.595 -

#

*

« 1

Beta - 0.06232

* 1985 Data

Oj *l d

& : * «

-g 0.590 -

« •5 :

* §

«

* o

.$^ 0.585 - * «

«>o

nU.OtJU Kon 1 III 1 1 1

1

1

1 1 1 1 i 1 1 1 10 10 10'

Stolz Buckingham

u.oou — FE-5/6-8B

^

- \ #

\ * Beta - 0.06143

O * 1985 Data

l^ \ *

Q» 0.625 - \ P5 \ ^

\

\ ^

o

1 •5 \

c^ \

0.620 -

\ * «*(<> \ «

\

\

u.oio — 1 1 1

1 1 T 1 1 1 I 1 1 10 10' 10'

Pipe Reynolds Number

Figure 35A. Discharge Coefficient/Reynolds Number Plots, DAN-4SS

4- Inch, Stainless Steel Meter Tube, 8 Orifice Plates

Final Data Base

405-
Meter Tube nAN-4SS

0.610

O

05 0.605 -^

o

S

0.600

0.595

0.610

0.595

10

Stolz Buckingham

FE-5/6-1C

Beta - 0.2170

All 1985

"TT n r 10' 10'

Pipe Reynolds Number

Figure 35B. Discharge Coefficient/Reynolds Number Plots, DAN-4SS

4-Inch, Stainless Steel Meter Tube, 8 Orifice Plates

Final Data Base

•406-
Meter Tube DAN-4SS

2 0.607

CO

o

0.597

10

* t *y

FE-5/G-2C

Beta = 0.3725

* 1985 Data

^** ^

*$

"1 1—1—

10 10

Stolz Buckingham

U.O 1 u —

4^t FE-5/6-3C

O

to ». **«

*« **,.

Beta = 0.4963

* 1985 Data

1 -

-g 0.605 -

CO

o

1 - O

nu.ouu finn

1 1 1 1 1 1 1 1

I

1 1 1 1 1 1 1 1 1 10 10 ' Pipe Reynolds Number

10

Figure 35C. Discharge Coefficient/Reynolds Number Plots, DAN-4SS

4-Inch, Stainless Steel Meter Tube, 8 Orifice Plates,

Final Data Base

407-
Meter Tube DAN-4SS

0.615

2 0.610

-g 0.605

CO

.^ 0.600

0.595

10

t

* **

t* *»

I n

FE-5/6-4C

Beta = 0.5583

* 1985 Data

^%

t#

10

%

*%«n

10

Stolz Buckingham

U.O/CU

- FE-5/6-5C

s

~ Beta = 0.6512

"K -^ Q>o « ^.^ t

* 1985 Data

Co 0.615 ~- * * ? t*** f

f^ 0.610

* t*%

# ^

CO H%

.^ 0.605

s

i:

0.600 1 1 i 1 1 1 1 1

1

1 I 1 1 1 1 1 1 10 10'

Pipe Reynolds Nximber

10

Figure 35D. Discharge Coefficient/Reynolds Number Plots, DAN-4SS

4- Inch, Stainless Steel Meter Tube, 8 Orifice Plates,

Final Data Base

408-
Meter Tube DAN-4SS

l/.OfO —

1. FE-5/6-6C

§ - 1* Beta = 0.7443

Q»O • 41 1985 Data

«J «•

« w 0.610 - h'*%

^1 •1

•5 t

0.605 - <I.1*-

* 11 t

U.OUU 1 1 1 1 1 1 1 1

1

1 1 1 1 1 1 1 1 10' 10 10'

Figure 35E. Discharge Coefficient/Reynolds Number Plots, DAN-4SS

4- Inch, Stainless Steel Meter Tube, 8 Orifice Plates,

Final Data Base

409.
D. Statistical Analysis of the Final Data Base

Statistical Analysis of Data Collected in 1985 and 1986

A statistical analysis of the results obtained from the test run data

has been performed to develop the statement of uncertainty in the

measurements and to document and review the procedures leading to this

statement. In the course of the analysis, the data base relating the

dimensionless quantity, discharge coefficient, to pipe Reynolds number

for the final data base is examined for abnormal flow conditions and

outliers. Plate and pipe designations are shown in table 50 in two

groupings by type of pump used. Since the effects of piamp type (capacity) were evident in the results for specific condition ranges, an analysis of the results taken from the final data base was made. Table

50 segregates the orifice plates run in each meter tube into two general

groups. The large pump column contains plates which were run using the

1000- and/or 3000-gpm pumps, either singly or in combination.

Similarly, the small pump column lists plots for which the 20- and 100-

gpm pumps were used. The following designations are used.

Pump A - 20-gpm capacity pump

Pump B - 100 -gpm capacity pump

Pump C - 1000- or 3000-gpm capacity pump

Table 50. Meti

Pipe Steel Pipe

ID type diameter

PE-1 Plated 2"

PE-2 Plated 2"

PE-3 Plated 3"

PE-4 Plated 3"

PE-5 Plated 4"

PE-6 Plated 4"

PE-7 Plated 6"

PE-8 Plated 6"

PE-9 Plated 10"

PE-0 Plated 10"

DAN Stainless 4"

Meter Tube and Plate Configurations

Plates

8B

Small Pumps

lA, 2A, 7A

IB, 2B, 7B

IB 2B, 7B, 8B

lA, 2A, 7A, 8A

IB, 2B, 2C, 7B,

IC, 2C, 7C, 8A

IC, 2B, 8B

2A, 7A, 8A

IB, 2B, 7B

lA, 2A, 7A

IC, 2C, 7C, 8A, 8B

Large Pumps

3A, 4A, 5A, 6A

3B, 4B, 5B, 6B

3B, 4B, 5B, 6B

3A, 4A, 5A, 6A

3B, 4B, 5B, 6B

3C, 4C, 5C, 6C

3C, 4B, 5B, 6B

3A, 4A, 5C, 6A

3B, 4B, 5B, 6B

3A, 4A, 5A, 6A

3C, 4C, 5C, 6C

The following notation describes the data base for a single orifice

plate/meter tube combination.

y. ., - discharge coefficient from the upper Paros transducer

z.., - discharge coefficient from the lower Paros transducer

-410-
ijk natural logarithm of the pipe Reynolds number

where the index j (j=l,...,3) refers to run number,

the index i (i=l,...,n) refers to repetition, and

the index k (k=l,...,5) refers to nominal differential

pressures of 0.4, 1, 3, 10, and 27 psid respectively.

The data bas

differential

These values

measurement

coefficients

indicative o the 4 - inch

,

established

e was subjected to an initial screening based on the mean

pressure values for the top and bottom orifice meter taps. are expected to agree within the random error of the

system. Thus, a large difference between the two discharge

computed from upper and lower transducer mean values is

f abnormal flow conditions. In preliminary experiments on stainless steel meter tube, control limits of + 0.002 were

for differences of that type. Differences

d. ., = y. -1 - z. ., ijk -^ijk ijk

i = 1, . . . ,n

j = 1,....3

k = 1,...,5

were computed for all data from the API experiment, and the control

limits of + 0.002 were verified for data taken with the large pump. For

the two smaller pumps, tighter control limits of + 0.0015 proved to be

more appropriate. Consequently, the following statistical control

procedure was implemented. Where

d. ., < -0.0020 or d. ., > 0.0020 for pump C ijk ijk ^ ^ or

d.., < -0.0015 or d. ., > 0.0015 for pumps A & B ijk ijk ^

the run was flagged as being out-of -control and subsequently was excluded in any further analysis of the data base. In most cases where

all three runs at a single flow rate were out-of -control , reruns at a later date completed the data base. Data taken on August 1, 1985 for

plate 6A on meter tube PE-lABC were considered to be outlying because

9 of the 15 runs for that day were out-of -control based on the criterion

cited above and because the other 6 runs were very close to being outof -control .

Based on analyses of the test run results from the orifice plate set

used with the 4 -inch, stainless steel meter tube, it is assumed that the

discharge coefficients are influenced by random errors of two types:

i.e., short-term random errors which account for differences among runs and long term random errors which account for differences among

repetitions. Where the same pipe Reynolds number can be achieved from run to run for each nominal differential pressure or equivalently for

each nominal flow rate, the resulting discharge coefficients can be

compared directly using an analysis of variance technique. This

-411-
technique allows estimation of the components of variance of the

measurement process at each nominal differential pressure from the model

y... = n. +7-1 +e.., "^ ij k '^k ' ik 1

J k

i=l,..

k=l,..

,n

,3

.5

(47)

where for a particular differential pressure, /z, is a constant to be

determined; the e.-^. are short-term random errors; and the 7., are longterm random errors. It is assumed that the e.-i^ are independent and

identically^ distributed with mean zero and standard deviation s that w

depends on the differential pressure; that the 7., are independent and

identically distributed with mean zero and standard deviation s, that

depends on differential pressure and that e.-i^ and 7., are mutually

independent. Examples of the standard deviations from a one-way

analysis of variance are shown in table 51 for two cases utilizing

differing pump sources. The number of degrees of freedom, 1/ , associated

with the within- group standard deviation for a given nominal flow rate

are also shown. (All analyses are performed on upper quartz oscillatortype transducer data with the lower quartz oscillator- type data being

used for control purposes. Quartz bourdon tube -type transducer data are not analyzed.

)

Table 51. Within and Between Standard Deviations from One-Way

Analysis of Variance

PUMP C in OPERATION

Pipe Plate Nominal Within SD DF

ID ID Diff. Press. sw

1/

PE-0 4A 0.4 0.000264 13

1.0 0.000278 8

3.0 0.000286 14

10.0 0.000076 6

27.0 0.000077 6

Between SD Repetitions

,000758

,000413

,000225

,000103

,000110

n

4

4

4

3

3

PUMP B in OPERATION

PE-2 IB 0.4 0.001120 7 0.000782 2 1.0 0.000548 7 0.000391 2 3.0 0.000159 6 0.000307 2 10.0 0.000055 4 0.000074 2 27.0 0.000065 4 0.000086 2

•412-
In general, it is not possible to obtain estimates of the variance

components in this manner because even at the same nominal flow rate,

the pipe Reynolds number is not always repeated from repetition to

repetition because of fluctuations in water temperature or other system

changes. Typically, the pipe Reynolds numbers, r.., , are spread across

a regime as shown in the previous figures of discharge coefficient vs. Reynolds number. Thus, the discharge coefficients cannot be compared

from repetition to repetition without imposing a model which describes

the functional relationship between discharge coefficient and pipe

Reynolds number. The following quadratic model is used to describe the

data on a single meter tube/plate configuration:

i=l, . .

. ,n

yijk = ^ -^ ^ ^ijk + ^ ^ijk^ + ^ik + ^ijk j=i' • • • '3 (^«)

k=l,...,5

where A, B, and C are unknown parameters to be determined, and the other

quantities are as previously defined.

The data will not satisfy the statistical requirement for independence

in the measurements if the long-term random errors 7,, are large

compared to the short-term random errors e.., . Therefore, we compute

averages of the three runs for the discharge coefficients and Reynolds

nvimbers , thereby reducing the model to

^i.k = ^ -^ ^ ^i.k + ^ ^i.k^ -^ ^ik -^ ^i.k i=l' • • • '^ ^^5>

k=l,...,5

where the dot (.) in the subscript signifies an average over three runs

at a given flow rate. Then the random error term, 7., + e. ., , which is

associated with an average discharge coefficient can be assumed to come from a distribution with mean zero and standard deviation s . The

quantity s depends on the differential pressure and is functionally of

the form

, 2^1 2,1/2 ..^,

^t = ^% -^ 3 %^ - ^^°^

The assertion that the random errors do not come from a single

distribution but, rather, from distributions whose standard deviations

depend upon differential pressure can be verified from the data. For

example, see figure 25A, where the spread in the discharge coefficients

is much larger at low Reynolds numbers than at high Reynolds numbers

In the presence of heterogeneous variance, as in this case, a weighted

least- squares analysis can be used in conjunction with the model of eq

(49). The most successful analysis, from the point of view of

-413-
simplicity and effectiveness, assumes that the variation among discharge

coefficients, for a given differential pressure, is inversely related to

differential pressure. Specifically, we impose weights in such a way

that the residual standard deviation from the least-squares fit is the

proper estimate of s for discharge coefficients at a differential

pressure of 27 psi.

Then the standard deviation s „ at a specific differential pressure, AP, can be computed by

s^p = s^ (27/AP)^/2 (51)

where s is the residual standard deviation from the weighted leastsquares fit. The quantity s.p correctly estimates the standard deviation of an average discharge coefficient at AP and is functionally of

form (50).

Weighted least-squares analyses were performed for all plate/meter tube

combinations, and the standardized residuals were examined graphically

for randomness and independence in order to judge model appropriateness.

The standardized residual is a normalized difference between a discharge

coefficient and its corresponding value from the fitted curve [26] . The

examples in figures 36A-D show standardized residuals plotted versus the

pipe Reynolds number for all plates run in the DAN-4SS meter tube except

plate 8B which had observations at only four flow rate settings.

In the analysis of the discharge coefficient/pipe Reynolds number data,

any single point which was obviously not consonant with the other data

was considered an outlier. Any average discharge coefficient which was

far removed from the fitted curve was identified via its standardized

residual. The standardized residual is distributed approximately as a Student's t statistic. Therefore,

a standardized residual < -3 or a standardized residual > 3

is indicative of an outlier. Whenever an outlying discharge coefficient

was discovered, it was deleted from the data base and the analysis was repeated to obtain a more representative estimate of the standard

deviation.

Table 52 lists the test runs deleted from the data base either because

of abnormal flow conditions recorded at the upper and lower taps on the

orifice plate or because of outlying discharge coefficients as discussed

in the previous paragraph or in graphical analysis of the results.

-414-
Meter Tube I)AN-4SS

FE-5/6-1C

a^ -2.0 -

a; 1.0 - «

*

**

•a * *

** w 0.0 —

•a **

-a -1.0-

1 - ^ -2.0 -

— 1 n

»

*

*

*

—if.U 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 10^ 10' 10

3.00

3 2.00

"aXQ> a; 1.00

•a

Q) 0.00

-aa

-a -1.00

?ia

•wto -2.00

-3.00 -[ 1—I—I I I I 10" 10'

Pipe Reynolds Number

Figure 36A. Standardized Residuals vs. Pipe Reynolds Number for

DAN-4SS, 8 Orifice Plates

-415-
Meter Tube DAN-4SS

3.0

3.00

%

a; i.oo

•n

.2 0.00

•§ -1.00

I

^ -2.00

-3.00

10'

FE-5/6-4C

• * »

^f» * *

~[

1 1 1—I I I I 1 1 1—I I I I 10 10

Pipe Reynolds Number

Figure 36B. Standardized Residuals vs. Pipe Reynolds Number for

DAN-4SS, 8 Orifice Plates

-416-
Meter Tube DAN-4SS

3.0

3.00

-3.00 1 1

1—I—

10' W

Pipe Reynolds Number

Figure 36C. Standardized Residuals vs. Pipe Reynolds Number for

DAN-4SS, 8 Orifice Plates

417-
Meter Tube DAN-4SS

0.1/

•«> —

%

0; 1.0 -

M n n

* *

« #

* * K *

FE-5/6-7C

.2 *'•'' •a

•§ -1.0-

1 ^

Co -2.0 -

*

*

«

»

It

9 nn

1'

1 1 1 1 1 1 1 1 1 10'

1 1 1 1 1 1 1 1 10'

o.UU

^ 2.00 - %

Q; 1.00 - 5

«

FE-5/6-aA

«

,w 0.00

4 -1.00-

1

Co -2.00 -

9 />/)

« «

*

*

—o.UU

n)'

1 1 1 1 1 1 1 1

1 10'

Pipe Reynolds

1 1 1 1 1 1 1 1 H

Number

)'

Figure 36D. Standardized Residuals vs. Pipe Reynolds Number for

DAN-4SS, 8 Orifice Plates

-418-
Table 52. Tabulation of Test Runs Marked as Outliers

Outlier Identification Criteria

2 -- Absolute value of the standardized residuals to the

model eq (49) greater than 3,

3 - - Abnormal flow conditions

,

and

4 -- Entire day(s) out- of -control

5 - - Obvious outlier from graphical analysis

.

Meter Orifice Date -- Test Runs! -- Criterion

Tube Plate Begin End Total

PE-IABC FE-1/2-1A 09/03/85 32 32 1 3

FE-1/2-5A 01/07/86 47 47 1 3

FE-1/2-5A 01/07/86 53 55 3 3

FE-1/2-6A 07/29/85 13 13 1 3

FE-1/2-6A 07/29/85 15 15 1 3

FE-1/2-6A 08/07/85 16 30 15 4

FE-1/2-7A 09/04/85 60 60 1 3

Total Outliers 23

PE-2ABC FE-1/2-6B 08/09/85 19 21 3 Total Outliers 3

PE-3ABC FE-3/4-2B 09/11/85 39 39 1

Total Outliers 1

PE-4ABC FE-3/4-6A 09/05/85 31 32 2 Total Outliers 2

PE-5ABC FE-5/6-1B 10/15/85 20 20 1

FE-5/6-4B 10/16/85 34 34 1

FE-5/6-5B 10/17/85 21 21 1

FE-5/6-6B 10/10/85 29 31 3 Total Outliers 6

PE-6ABC FE-5/6-3C

FE-5/6-6C

06/26/85 6 6 1

06/26/85 19 21 3 Total Outliers 4

419-
Table 52 Tabulation of Test Runs Marked as Outliers Continued

Outlier Identification Criteria

2 -- Absolute value of the standardized residuals to the

model eq (49) greater than 3,

3 -- Abnormal flow conditions, and

4 -- Entire day(s) out-of -control

5 -- Obvious outlier from graphical analysis.

Meter Orifice Date -- Test Runs -- Criterion

Tube Plate Begin End Total

PE-7ABC FE-7/8-1C 12/06/85 30 30 1 2

FE-7/8-4B 12/04/85 16 16 1 3

FE-7/8-6B 12/05/85 10 10 1 3

Total Outliers 3

PE-8ABC FE-7/8-3A 08/26/85 2 2 1 3

FE-7/8-7A 08/30/85 13 30 18 4

Total Outliers 19

PE-9ABC FE-9/0-1B 11/12/85 10 12 3 5

FE-9/0-1B 11/12/85 20 20 1 3

FE-9/0-2B 11/07/85 34 34 1 3

FE-9/0-3B 11/07/85 13 13 1 3

FE-9/0-5B 11/12/85 20 20 1 3

Total Outliers 7

PE-OABC FE-9/0-4A 11/18/85 23 23 1 2

FE-9/0-5A 11/21/85 58 58 1 3

FE-9/0-7A 11/15/85 16 16 1 2

FE-9/0-7A 11/18/85 28 28 1 2

FE-9/0-7A 11/21/85 49 49 1 3

Total Outliers 5

DAN-4SS FE-5/6-1C 09/26/85 112 112 1 2

FE-5/6-3C 12/10/85 120 122 3 2

FE-5/6-4C 07/05/85 31 33 3 3

FE-5/6-4C 07/05/85 37 39 3 3

FE-5/6-4C 12/10/85 64 66 3 2

FE-5/6-5C 09/24/85 37 38 2 3

FE-5/6-5C 12/10/85 77 79 3 2

FE-5/6-6C 06/20/85 22 24 3 2

FE-5/6-6C 10/23/85 86 88 3 3

FE-5/6-6C 10/23/85 92 94 3 3

FE-5/6-7C 09/26/85 50 50 1 3

FE-5/6-7C 10/22/85 63 63 1 3

FE-5/6-8A 09/26/85 17 17 1 3

FE-5/6-8A 12/10/85 25 27 3 3

FE-5/6-8B 11/13/85 7 7 1 3

Total Outliers 34

-420-
Statistical Analysis of Data Collected in Early 1987

The major part of the experiment on orifice meters was conducted during

the latter half of 1985 and January 1986. A much smaller experiment

covering selected pipes and plates was conducted during the first 2 months of 1987. Because of the time lag and change in operational

procedures between the two experiments, we attempt to identify

pipe/plate configurations for which results of the first experiment are not corroborated by the results of the second. We test for a significant change in the relationship between discharge coefficients

and Reynolds numbers by comparing the empirical curve derived from the

first experiment with the empirical curve from the second experiment.

The quantities needed for this test include a residual standard

deviation, s^, for the full model

y. 1 = A, + A^x ., + B,r. . + B„r, , x ,, +

''i.k 1 2ik li.k 2i.k ik

2 2 *

C,r. , + C^r. 1 X ., (52)

1 1 . k 2 1 . k ik

which allows for a change in the empirical curve in 1987 where x ., is an indicator variable such that

{1 for 1987 data

X ., =

ik

{0 for all other data

and a residual standard deviation, s , for the reduced model

r

y. ,= A + B r. , + C r. , ^ (53)

•'i.k o o i.k o i.k

which assumes the same empirical curve for the two time periods.

The coefficients Aooo , B , C and A,iZiZlZ , A„ , B, , B„ , C^ , C„ are estimated in

the usual way by weighted least- squares for the combined data from the

two experiments as are the residual standard deviations, s and s^. The

experiments are said to give comparable results if

F < F (n-6, 3) a

where the F statistic is computed as

421-
F =

2 2 (n-3)s^ - (n-6)s^

3s^

(54)

for n, the total number of repetitions for the two experiments, and

F(n-6,3) is the upper a percent point of the F distribution with (n-6)

and 3 degrees of freedom in the numerator and denominator respectively.

Results are shown in table 53.

Table 53. Statistics for Testing for a Difference Between

the 1987 Experiment and 1985 Experiment

Meter Orifice

Tube Plate

PE-IABC 6A

PE-3ABC 7B

PE-4ABC 7A

8A

PE-5ABC 7B

PE-6ABC 2C

8A

DAN-4SS 4C

DAN-4SS 7C

F Statistic

24.,8

7,,7

10,.8 145,.2^

0,.6

8,.8

4,.2

Degrees of Freedom

"1

15

14

6

25

6

21

13

Insufficient 1987 data

0.6 26

Indicates significance at the 99% probability level.

Plate 8A for meter tube PE-4ABC is the only configuration for which the

1987 results are significantly different from the 1985 results at the

99% probability level. Therefore, the 1985 results are treated as outliers. The 1987 results and 1985 results for the other plate/pipe

configurations are consistent. Thus, there is no basis for preferring

one data set over the other, and the data are combined for the

statistical analyses.

-422-
Comparison of Discharge Coefficients for Unplated and Plated Pipes

The original experimental design called for three runs at five flow

rates on each meter tube using the #2 (Beta = 0.375) and #6

(Beta = 0.75) plates before the meter tube was plated. These results were to be compared with runs made on the plated tubes at a later time.

Because operational procedures for small Beta ratio plates were changed

at NBS on August 23, 1985, i.e., the 100 gallon/minute pump was operational after that date, unplated and plated meter tubes are not

comparable for data taken on the #2 plates prior to that date.

Graphical comparison of the discharge coefficients for the unplated

versus plated tubes (see figs. 37A through J) and statistical analyses

similar to those outlined in the last section indicate no differences

between unplated and plated tubes for the majority of meter tubes.

However, large differences for the #6 plates in the 10- inch- diameter

tubes at high flow rates are apparent. The appropriate F statistics are shown in table 54.

Table 54. F Statistics for Testing for Differences Between Unplated and

Plated Meter Tubes

Meter Tubes Tube F Statistic

Plate F

2A 0.08

6A 4.24

6B 0.54

6B 14.21

6A 63.29*

2B 33.08*

6B 46.97*

6C 10.90

6B 4.62

2B 7.33

2A 4.67

6A 8.61

2B 4.72

6B 169.11*

2A 5.52

6A 94.38*

Indicates a significant difference between unplated and plated pipes

at the 99% probability level

FEl vs

.

PEl

FEl vs

.

PEl

FE2 vs

.

PE2

FE3 vs. PE3

FE4 vs

.

PE4

FE5 vs PE5

FE5 vs

.

PE5

FE6 vs

.

PE6

FE7 vs PE7

FE7 vs PE7

FE8 vs PES

FE8 vs. PES

FE9 vs

.

PE9

FE9 vs PE9

FEO vs PEG

FEO vs PEG

Tube

Diameter

2"

2"

2"

3"

3"

4"

4"

4"

6"

6"

6"

6"

10"

10"

10"

10"

Degrees of

Freedom

^1 ""2

3 9

3 20

3 10

3 11

3 9

3 12

3 16

3 IS

3 12

3 12

3 S

3 11

3 12

3 12

3 12

3 11

-423-
Tvuo-Inch Meter Tube 1

0.610

0.600

10'

0.625

O

« 0.620 - r

o

•2 0.615

0.610

10'

Stolz Buckingham

FE-1/2-6A

Beta = 0.7239

, Plated

Not Plated

• 9

T 1 1

I I I I

I

1 1 1 1—I I I I 10' 10'

Pipe Reynolds Number i

Figure 37A. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

424-
Two-Inch Meter Tube 2

u.oiu — FE- 1/2-2B ^ « Beta = 0.36Z1

Q>O

*

* Plated

Not Plated

\ % * h ^ \ # e \\

•^ 0.605 -

•2 N B

*

Q)

\

S. \v 1 «

•5? N \^ «a

^ - D

N. ^ ^\^

o D ~-- c^"t::^-*^^^^^ n cnn ' ^ -^_ — — __ _

I 1 1 1 1 1 1

1 1 1

1 1 1 1 1 11 10'

10'

10'

Stolz Buckingham

10

U.OlCiO —

\ \ FE-1/2-6B

"^ \ \ Beta = 0.7243

«» \ \

a :

<» 0.620 - \\ 1

• Plated

D Not Plated

\ * r - \\«l

o

•2 \\ 1*

Q \ \

« 0.6/5 - ^»

s

\ \

\ e«

n c 1 n \ «]»

U.biU 1 1 1 1 1 1 1 1

1

1 1 1 1 1 1 1 1 10'

Pipe Reynolds Number

10

Figure 37B. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

-425-
Three-Inch Meter Tube 3

^ 0.609 -

o

FE-3/4-2B

Beta = 0.3661

» Plated

Not Plated

J

0.604 -

O

f\ IZQQ

^ ^ *

U.oHif 1 III 1 1 1

1

1 1 1 1 1 1 1 1 10' 10 10

Stolz

0.620

o

Jo« 0.615 - r

0.6/0 H

O

0.605

10'

Buckingham

FE-3/4-6B

Beta = 0.7320

, Plated

A'^o* Plated

"1 I I I I

I n I r I I I I Pipe Reynolds Number

Figure 37C. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

-426-
Three—Inch Meter Tube 4

0.598

FE-3/4-2A

Beta = 0.3655

* Plated

a Not Plated

10'

"T

1

\—I

\—

r

ri| I I I 1 I I TT 10' 10

Stolz

10'

Buckingham

U.OtiV

V\ FE-3/4-6A

§ H \\ Beta = 0.7307

0) \\ a

O "1 Ci J

* Plated

^ \ P

u Not Plated w 0.615 -

\ \

S \ \ a

rfJ \ V *

CJ \ *

•2 \ \

0.610 - \ X f.

CJ \ \s^^

•! - ^"^-^^^

u.ouo 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 10'

Pipe Reynolds Number

10

Figure 37D. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

427-
Foul—Inch Meter Tube 5

o

(J

0.609 -

I

0.604 -

C5

0.599

FE-5/6-2B

Beta = 0.3706

it Plated

a Not Plated

10'

T

1

I I I I

I

1 1 1 1I I I I 10' 10

Stolz Buckingham

0.600

FE-5/6-6B

Beta = 0.7411

* Plated

Not Plated

I

10'

Pipe Reynolds Number

Figure 37E. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

-428-
Foul—Inch Meter Tube 6

^0.

o

I

6f3 -

608 -^

0.603

Stolz Buckingham

Figure 37F. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

429-
Six-Inch Meter Tube 7

0.598

Stolz Buckingham

O

I

o

o

608

603 -

0.598

FE-7/8-6B

Beta = 0.7352

* Plated

o Not Plated

10

~\

1

1—I

Jill T—I I I I 10'

Pipe Reynolds Number

10'

Figure 37G. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

-430-
Six—Inch Meter Tube 8

0.610

o

r

•^ 0.605

o

0.600

\

\

FE-7/B-2A

Beta = 0.3698

* Plated

D Not Plated

^~~~~-^

1 1 1 1 1 1 1 1

1

1 I 1 1 1 1 1 1 10' 10"

Stolz Buckingham

10

0.610

FE-7/8-6A

Beta = 0.7395

» Plated

D Not Plated

Pipe Reynolds Number

10'

Figure 37H. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

431-
Ten-Inch Meter Tube 9

0.598

O

I

u

«>oO

0.604 -

0.599

0.594

10

10'

Stolz Buckingham

FE-9/0-6A

Beta = 0.7438

* Plated

Not Plated

T 1 1 1—I I i I T 1 1—I—I I I I 10'

Pipe Reynolds Number

10'

Figure 371. Discharge Coefficient/Reynolds Number Plots, Plated and

and Unplated Results for 2 and 6 Plates

-432-
Ten—Inch Meter Tube

O

Co

•5

O

0.609 - \

\

FE-9/0-2A

Beta = 0.3739

-

\ \ \ \ \ \ \

* Plated

a Not Plated

-

- 0.604 -

n ?ao

\^ * 4^ *

U.oHH 1 1 1 I 1 1 1 1

1

1 1 1 1 1 1 1 1 10'

0.605

to

10'

Stolz Buckingham

10

FE-9/0-6A

Beta = 0.74803

, Plated

Not Plated

1—I I I I

I T-^—I I t I 10 * Pipe Reynolds Number

10'

Figure 37J. Discharge Coefficient/Reynolds Number Plots, Plated and

Unplated Results for 2 and 6 Plates

•433-
Analysis of the Combined Final Data Base

We have examined the data for each plate/pipe configuration in detail in

order to identify anomalous individual points or groups of points and

assess the effect of system changes between 1985 and 1987. Now we examine the data across all plates for pipes of the same nominal

diameter in order to identify anomalous plates. For this purpose we make use of the Stolz equation derived in [23] which is of the form

y.ijk = 0.5959 + 0.0312 ^ -^ - 0.184 ^ + 0.039 ^

l-)9^

0.0337

^^

+ 0.0029 yg^-^loVpij^)

0.75

(55)

where ^ refers to beta ratio, D refers to pipe diameter, and IL. is the

pipe Reynolds number.

Differences, identified by plate number, between observed discharge

coefficients and discharge coefficient calculated from the Stolz

correlation are shown in figures 38A through E plotted versus pipe

Reynolds number. The plots show egregious departure from the Stolz

equation for small Beta ratio plates as follows:

Beta Ratio Plates

0.12 7A & 7B

0.12 7B & 7A

0.06 8A & 8A

0.06 8A & 8B

Pipe Diameter Pipes

2" PE-1 & PE-2

3" PE-3 & PE-4

4" PE-5 & PE-6

4" DAN-4SS

The plots also confirm the disagreement between the 1985 and 1987 data

on plate 8A with meter tube PE-4ABC and support the exclusion of the

1985 data for this plate/pipe configuration.

Analysis of Process Performance

Table 55 contains the residual standard deviations for discharge

coefficients at differential pressures of 27 psi as computed by weighted

least- squares from the DAN-4SS data and from the other plate/meter tube

configurations. The most useful information should reside in the the 4-

inch stainless steel check standard data where the repetitions sample

the measurement process over several months time and, therefore, cover a larger range of laboratory conditions than smaller numbers of

repetitions on a single meter tube. The latter were frequently, of

necessity, done only a day or two apart. Data on the stainless steel

meter tube corroborate the data on the plated meter tubes.

-434-
Standard deviations are pooled by beta ratio at the bottom of table 55.

From the aggregate data it is fairly obvious that process precision is a function of beta ratio and that, as expected, process variability is

greatest for very low beta ratio plates. In this case, process is

defined for a single repetition where each repetition is the average of

three successive test runs at the same flow rate. These standard

deviations, based on hundreds of degrees of freedom, represent the best

estimate that we have for the NBS calibration process of orifice meters.

They reflect the ability of the entire system, consisting of a variety

of pumping arrangements, water collection and weighing operations,

transducer reactions and flow characteristics to repeat themselves over many month's time.

Standard deviations for nominal differential pressures of 0.40, 1, 3,

10, and 27 are computed from the pooled standard deviations according to

eq (51) . Limits to random error for the NBS flow facility are computed

as three times these standard deviations. For simplicity, we use the same limits to error for all beta ratios greater than or equal to 0.10

based on the largest pooled standard deviation in that range.

-435-
03

03O

c^

(^ o

CO

«p

, CNVJ

>.»

•d — C

^

- CO $ _ n

"fiQ) tJ

(»

"<J

(tt ^%> H<^ __ ti ti d ».> inO XO

11. lO<^N

a, a. *^% 4-1

4-1 O X -{x 1-

0)O

u

U ^ Q> (U 0) ^^ ^^ r

"*>» •J SJ -tJ d b b b % -S.^ o

>0 xO P>0 >«^ w c 0,0,0,0,

o n < + :1c : ^

•r-l O

^2

JSf^ o

0) V-i 03 O

O ^

't 5"

0) o atP c^ 0) u

«5)<©o

c^ 4-) *

DIQJ^Xl U

CO

(O OCTO (1) 4-1 #c -ti-it 0) -o

4-1 0) O^ O CD

-

of

Dif

Comput a *

-

- CO 9) U CO «t •«« -

O O

*» -tt-Cx •M>t«i CO

1

1 1 11 1 1 1 11 1 1 — "vJ 0)

'

1 ' 1 ' 1 ' 1

I 1 1 >* ^ to O lO c) lO o iJ3 a

CO CV| cv^ >» >« o cs S

^ •H O C) O cs c:> o o c^ [S4 CJ c> cj cj c:I CJ ci ci ^l^lS — pdrtxasqQ

436-
CO

0) 0) (^ •J fj -^ d d s p>0 f"^ ^-o a, a, a, o X -ii

x^

D

P

a

1

a

-

Plate Plate Plate Plate

1^^^

i

1 -

o a < + *

cHii m

I -

*

-

• m

-

* ^ / r

-

1

1

1 1 1 1

1 1 '1

1

1

CO

•o

00

CNJ

C5 o

o

o C5

•dC

cdn

4JC

a) ^ o

U-l JO (1) X. O ^ U

3 (U ^ cd ,c

C/3 o ^p«o 4J o (U .-1 ^ t^

?5i <D U

CO O

c^ 5 ^

c^ O

N

0) O

c^ 0) 4-) g.

•u

(1> (U •(7^ CQ 4:: Q. 4J

CO

(1) e

c 5-1 <U (4-4

S-i <u t3 (M 0) (w +J •H 3 Q O-£

tw u

en <u V cfl ^ x:

CL, H

OQ00

CO

0)V43

bO z^o^j.^ — pdnj.3sqo EE4

-437-
I

o

Q) 0} 0) to to -W b d b •ioO lOJ no

O X -it

di di di cs to to -|o -to b e e 53

»*0 ^«.d P<0 x-J

*^ cvj Co rj. O D < +

>o

©"

EO

llf*

<«<I

«» ***

I

I

I

I lO c> »o

CO 00 cvj Ci OS o

T"

c5

)•• * **

z2o:^S p3aj.3sqQ

438-
COo

03

cc

Co

-

(tt (U Q) -

to to -W e d e

p>«>.d i*^ f^ ^^^ -

iO<toN.

*>«<»: X -(t rf«S>

asx — ^*%. -

Q) (U ^ Q)

•+^ fj -tj -K) *

-

VMitd seed »«0 t*^ f-O ^^

-

».CVJC0'<^ JT- - < +

>

+ ~

^< "^^b - ^BB^ -

(@|)

-

^offito *o

0^ =

HKK — S>o

—

-* ~ 00 <J^ -

{r-Wtt -

1

1 ' 1 '

1

N

o

»o

-o

PD

I

X)

COc

0)

(4-1

(Uou

(1> hO

V4

cdo

CO C

o

•U •0 CO

o

0) o

^ CO

4-1

<u C4-1 u

4-1 <S) 4-1 4J

, s

cw O o u

CO 0) •U CO o o

r-l Xi

Q

00CO

<u

^l^^S — p^(^^^sqQ

439-
CO

en [-'^ S

to

S'

C5o

^ (U Q>

"(^ "ij -M 6 ti d >«i> KO xO

•+j> tJ •<«» -M 6 b b e no r-O l>0 laO 0,0,0,0,

>• cvj Co ^jO D <J +

•WKt^

Xj -o

-o

CO

lOo

o

I

(0c

0)

0)o

0)bOU

c«O

M C

•H O Q T^

0) r-l

o

N

C r-l

0) o

a> ^

& CO u

0) (V u

COo o

c ^^

(V (M

Q a

, E

(4-1 O

o o

0) 0) o o

CO

COo

bO ^l^^S — v^^^^^w

-440-
Pipe

PE-1

PE-2

PE-3

PE-4

Table 55. Standard Deviations for Average Discharge

Coefficients at 27 psi Differential Pressure

Beta Degrees

late Ratio Pump Standard Deviation of Freedom

^t

7A 0.12 B 0.0001164 6

lA 0.24 B 0.0000551 6

2A 0.36 B 0.0000410 6

3A 0.48 C 0.0000667 11

4A 0.54 C 0.0001269 9

5A 0.66 C 0.0001102 14

6A 0.72 C 0.0001245 18

7B 0.12 C 0.0000797 6

IB 0.24 B 0.0001115 9

2B 0.36 B 0.0001170 7

3B 0.48 C 0.0000516 12

4B 0.54 C 0.0000799 9

5B 0.66 C 0.0000306 9

6B 0.73 C 0.0001072 8

8B 0.08 A,B 0.0001176 8

7B 0.12 A,B 0.0001268 17

IB 0.20 B.C 0.0000893 7

2B 0.37 B 0.0000414 3

SB 0.49 C 0.0000485 8

4B 0.57 C 0.0000963 10

5B 0.65 C 0.0000931 8

6B 0.73 C 0.0000605 9

8A 0.08 A.B 0.0000563 11

7A 0.12 A.B 0.0001023 15

lA 0.20 B,C 0.0000345 6

2A 0.37 B,C 0.0000911 4

3A 0.49 C 0.0000783 9

4A 0.57 C 0.0000490 7

5A 0.65 C 0.0000929 9

6A 0.73 C 0.0000746 6

•441-
Table 55. Standard Deviations for Average Discharge Coefficients

at 27 psi Differential Pressure -- Continued

Pipe

PE-5

PE-6

PE-7

PE-8

Beta Degrees

late Ratio Pump Standard Deviation of Freedom

"t

V

8A 0.06 A 0.0000749 4

7B 0.09 A, B 0.0003338 9

2C 0.12 B, C 0.0000484 11

IB 0.22 B, C 0.0000969 10

2B 0.37 C 0.0000457 9

3B 0.49 C 0.0000919 8

4B 0.56 C 0.0000559 10

5B 0.65 C 0.0000710 11

6B 0.74 C 0.0001913 13

8A 0.06 A, B 0.0002483 16

7C 0.09 A, B 0.0001989 14

2C 0.37 B, C 0.0000712 24

3C 0.50 C 0.0001195 10

4C 0.56 C 0.0000984 20

5C 0.65 c 0.0001030 9

6C 0.74 C 0.0000949 14

SB 0.10 B 0.0001454 5 IC 0.20 B, C 0.0000546 6

2B 0.37 B, C 0.0000708 9 3C 0.49 C 0.0001015 7 4B 0.57 C 0.0000630 8

SD 0.65 C 0.0000492 8

6B 0.73 C 0.0001318 9

7A 0.10 B 0.0000997 9

8A 0.21 B 0.0000346 12

2A 0.37 C 0.0000573 6

3A 0.49 C 0.0001015 7 4A 0.58 C 0.0000948 14

5C 0.66 C 0.0001114 9

6A 0.74 C 0.0001004 8

-442-
Table 55. Standard Deviations for Average Discharge Coefficients

at 27 psi Differential Pressure -- Continued

Pipe

PE-9

PE-0

DAN

Plate

7B

IB

2B

3B

4B

5B

6B

7A

lA

2A

3A

4A

5A

6A

8A

70

IC

2C

3C

4C

5C

60

Beta

Ratio

0.10

0.20

0.37

0.50

0.57

0.66

0.74

0.10

0.20

0.37

0.50

0.57

0.66

0.75

0.06

0.09

0.22

0.37

0.50

0.56

0.65

0.74

Degrees

ump Standard Deviation of Freedom

^t V

0.0001223 8

0.0000930 9

0.0000707 8

0.0000876 9

0.0000687 9

0.0000917 8

0.0000728 9

0.0000965 10

0.0000780 10

0.0000647 10

0.0000887 11

0.0001044 19

0.0000632 18

0.0000779 8

0.0003853 11

0.0002255 26

0.0001047 21

0.0001058 7 0.0000689 35

0.0001080 46

0.0001166 33

0.0001145 32

Beta Ratio

0.06 -0.09

0.10 -0.12

0.20 -0.24

0.36 - 0.38

0.48 -0.50

0.54 - 0.58

0.64 - 0.66

0.72 - 0.75

Pooled Standard Deviation DF

0.10 - 0.75

0.0002387 99

0.0001063 87

0.0000863 90

0.0000758 87

0.0000788 129

0.0000958 161

0.0000938 136

0.0001212 122

0.0000956 812

443-
VII. Acknowledgments

Many people have lent their assistance to this project in one way or another. The authors would like to express their gratitude to those who

have done so. Specific persons have worked closely with the authors on various aspects of the project, both NBS staff and various individuals

associated with the American Petroleum Institute through its Committee

on Petroleum Measurement.

In particular the principal investigator wishes to thank Nancy Skinner,

Carol Kimmel, and Monica Mock for their excellent work in preparing the

various manuscripts Involved in finally completing this report. Messrs.

J. F. Houser, J. D. Melvin, and K. R. Benson contributed materially to

the development or modification of various pieces of equipment used in

the measurement systems. The efforts of Mr. G. Scace in operating the

water flow measurement facility consistently for one of the three shifts

during the 24 hour/day running schedule in 1985 are much appreciated.

Many useful discussions with Mr. F. E. Jones contributed to the

development of various data reduction algorithms used with the

measurement system. Dr. T. Vorburger and Mr. C. Giaugue graciously

provided measurements of the the surface topography of rusted meter tube

specimens described in Appendix A. Dr. G .E. Mattingly supervised the

data collection procedures on orifice meters and velocity profiling

measurements which occurred in early 1987. He and Dr. J. J. Ulbrecht

wrote Appendix F. Mr. Stefan Leigh and Dr. J. Rosenblatt of the NBS

Statistical Engineering Division provided many useful discussions. Mr.

J. Hord, Dr. M. M. Hessel, Dr. J. J. Ulbrecht, and Dr. J. W. Lyons were instrumental in various phases of the project's management and

coordination with the API. The principal investigator would like to

thank Dr. H. G. Semerjian for his encouragement and many suggestions

during the latter phases of the work and Mr. B. R. Bateman for his

invaluable assistance in archiving the data base and for his suggestions

of various computational techniques in completing the data analysis and

presentation.

Several individuals outside NBS contributed their time, effort and

thought. The membership of the API Orifice Data Base Steering Committee

(OSC) , with little exception, remained the same throughout the project,

and contributed suggestions, observations and opinions to the work. In

particular Mr. W. A. Fling, as the API Project Manager, maintained close

contact with the work and closely scrutinized the test run results as they were developed. As a result, he consulted with the NBS principal

investigator frequently and was instrumental in the solution of several

difficulties. Mr. E. L. Upp and Dr. R. Teysanndier of Daniels

Industries, Houston, Texas, provided invaluable assistance in the

reconditioning of the meter tubes in a timely manner. Mr. D. Goodson,

also of Daniels Industries, performed most of the orifice plate edge

sharpness measurements. The principal investigator would like to thank

Mr. Fling, Mr. Upp and Mr. T. L. Hilburn for many useful technical

insights, discussions and suggestions. The members of the OSC

maintained a high level of interest throughout the project and were very

instrumental in its direction and progress.

444-
VIII. References

[I] Beitler, S. R. , "The Flow of Water Through Orifices," The Ohio

State University, Engineering Experiment Station Bulletin 89,

73 pp. , May 1935.

[2] Ku, H. H. , "Notes on the Use of Propagation of Error Formulas,"

Journal of Research of the National Bureau of Standards - C,

Engineering and Instrumentation, Vol. 70C, No. 4, October-December

1966.

[3] Certain commercial equipment and instruments are identified in this

paper in order to describe the experimental procedures and results

adequately. In no case does such identification imply

recommendation or endorsement by the National Bureau of Standards nor does it imply the material or equipment is necessarily the best

available for the purpose.

[4] Kinghorn, F. C, MacKay, A., and Harrison, P., "The New United

Kingdom Primary Standards for Water Flowrate Measurement." In

Flow: Its Measurement and Control in Science and Industry . Vol. 2, p. 761, Instrument Society of America, Research Triangle

Park, NC, 1981.

[ 5 ] Ha3rward , A . T . J . , Flowmeters. A Basic Guide and Source-Book for

Users, John Wiley & Sons, New York, NY, pp. 144-147, 1979.

[6] Jones, F. E., "Estimating Diverter Valve Corrections," Int. J. Heat

and Fluid Flow, Vol. 5, No. 4, pp. 247-250, 1984.

[7] Pontius, P. E., Mass and Mass Values . NBS Monograph 133, 1974.

[8] Jones, F. E. , "The Air Density Equation and the Transfer of

the Mass Unit," J. Res. of NBS, Vol. 83, No . 5 , pp. 419-428,

1978.

[9] Kell, G. S., "Density, Thermal Expansivity, and Compressibility of

Liquid Water from to 150 °C: Correlation and Tables for

Atmospheric Pressure and Saturation Reviewed and Expressed on 1968

Temperature Scale," J. Chem. and Eng. Data, Vol. 20, No. 1, 1975.

[10] Heydemann, P. L. M. , and Welch, B. E., "Part III. Piston Gages,"

Experimental Thermodynamics, Vol. II, pp. 147-202, 1975.

[II] American National Standard, "Metric Practice," E380-76, ASTM,

345 East 47th St., New York, NY 10017.

[12] Tate, D. R. , Acceleration Due to Gravity at the National Bureau of

Standards, NBS Monograph 107, 1968.

[13] Touloukian, Y. S., Kirby, R. K. , Taylor, R. E. , and Desai, P. D.

,

Thermal Expansion. Metallic Elements and Alloys . Thermophysical

Prop, of Matter, Vol. 12, 1975.

-445-
References (Contd.)

[14] Heldelberger, P., and Welch, P. D. , "A Spectral Method for

Confidence Interval Generation and Run Length Control in

Simulations," Conun. of the ACM, Vol. 24, No. 4,

pp. 233-245, 1981.

[15] Sprenkle, R. E. , and Courtright, N. S., "Straightening Vanes for

Flow Measurement," Mechanical Engineering, 80, 71-73, 1958.

[16] "Electroless Nickel Plating," Metals Handbook, Vol. 5, pp. 219-243,

1982.

[17] American Gas Association Report No. 3., Amer. Gas Assoc, Catalog

No. XQ0178, Arlington, VA; also American National Standard

Institute/American Petroleum Institute 2530.

[18] Kestin, J., Sokolov, M. , and Wakeham, W. A., "Viscosity of Liquid

Water in the Range -8 "C to 150 °C," J. Phys . Chem. Ref. Data,

Vol. 7, No. 3, p. 941, 1978.

[19] Swindells, J. R. , Coe , J. R. Jr., and Godfrey, T. B., "Absolute

Viscosity of Water at 20°C," J. Res. of NBS , Vol. 48, No. 1,

p. 1, 1952.

[20] Fluid Meters . 6th Edition, ASME, New York, 1971.

[21] Miller, R. W. , Flow Measurement Engineering Handbook . McGraw-Hill,

New York, 1983.

[22] Bean, H. S., and Murdock, J. W. , "Effect of Pipe Roughness on Orifice Meter Accuracy," Rept. on AGA Research Proj . NW-20,

Amer. Gas. Assoc, Arlington, VA, 1960.

[23] Stolz, J., "A Universal Equation for the Calculation of Discharge

Coefficients of Orifice Plates," ISO 5167, FLOMEKO 1978, IMEKO

Conference on Flow Measurement of Fluids, Groningen, North-Holland,

Amsterdam, 1978.

[24] Britton, C. L. , Caldwell, S., Seidl, W. , and Snowdon, T.

,

"Research Program to Develop an Archival Data Base of Low

Reynolds Number Discharge Coefficients and Related

Parameters for Sharp-Edged, Flange-Tapped Orifice Meters,"

prepared for the American Petroleum Institute, Measurement

Coordination Dept., Sept. 1986.

[25] Gorter, J., "Deformation of Orifice Plate; Theory and Practice,"

FLOMEKO 1978, IMEKO Conference on Flow Measurement of Fluids,

Groningen, North-Holland, Amsterdam, 1978.

[26] Draper, N. R. , and Smith, H. Applied Regression Analysis. Second

Edition, John Wiley & Sons, New York, 1966. See p. 144 for a specific definition of standardized residual.

446-
APPENDIX A

Operational History of the Project

Introduction

This appendix gives a rather detailed chronological account of the

major events which occurred during this project. It is written as a record of the difficulties encountered and overcome before the successful completion of the data base. Hopefully, future workers may benefit

from the insights gained in it. Significant portions of this appendix

were taken from the monthly progress reports prepared for the API by

the NBS Principal Investigator (J. Whetstone). These have been edited

for clarity in the context of this document and for proper language

usage. Verbatim excerpts are usually indented for clarity.

A strong advisory role was played by the API Program Manager and the API

Orifice Meter Database Steering Committee composed of the following:

R. Beatty - Chairman, AMOCO Production Co.

! D. W. Kemp ~ Cities Service Co.,

Occidental Petroleiom Corp.

& W. A. Fling - Cities Service Co.,

Occidental Petroleum Corp.

- Daniel Industries

- Daniel Industries

- El Paso Natural Gas Co., Retired

- Phillips Petroleum

- Natural Gas Pipeline Co. of America

- API Staff representation

- API Staff representation

! Ex officio membership on the committee as Chairman,

API Committee on Petroleum Measurement

* R. Teyssandier replaced E. L. Upp at approximately

the mid-point of the work.

& API Program Manager

Although there was periodic participation by other members of the API's

Committees on Petroleum Measurement, Dynamic Measurement and staff, the

membership of the Orifice Steering Committee stayed essentially the same throughout the course of the project. Frequent meetings of this comm- ittee occurred and, at times, strongly influenced the course of the

planning and execution of the project's technical work. On several

occasions task groups of the steering committee performed specific

tasks. As an example, a facilities task group headed by Mr. Hilburn

inspected the measurement facilities at NBS during their development and

witnessed the commissioning of the completed system and various additions to it which evolved after the initial commissioning.

* E. L. Upp

* R. Teyssandie

H. L. Bean

T. L. Hilburn

G. Less

J. K. Walters

R. L. Schreibeis

447-
As in the main body of the report, reference is made in the remainder

of this appendix to the correlations of Buckingham [Al] and Stolz [A2].

These correlations were either completely or substantially based on the

discharge coefficient data base of Professor S. R. Beitler developed in

the late 1920 's and early 1930 's [A3] at Ohio State University. This

experimental work, which is often referred to as the OSU work or re- port, provides a comparison base for the work reported here because of

its wide use in flow measurement for commercial purposes. The Buckingham correlation is incorporated in AGA Report No. 3 (API 2530) which is a widely used, standard measurement practice in the United States. The

Stolz correlation is used in a similar manner in the European Economic

Community and is incorporated in the International Standards Organization's R91 document. Because Beitler did not test identical sizes of

orifice plates and meter tubes as those involved in this work, the

Buckingham and Stolz correlations are used only for convenience of

comparison.

II. Development and Commissioning of the Measurement Systems and

Initial Results

The project initiation date was early 1982. The initial phase involved

the development of the data acquisition, storage, and control systems

which were obtained and made functional in the latter portion of 1982.

Modifications to the NBS water flow measurement facilities in the form

of electronic weigh scales (to minimize the occurrence of data entry

errors by the operators and speed data acquisition procedures) and automatic controls for the diverter valves became operational in the early

portion of 1983, with orifice flow meter testing beginning in the late

spring and early summer of 1983. Total system shakedown testing began

in early 1983 using one of the 4- inch meter tubes, FE-6ABC. From June

to August 1983 preliminary data were collected using FE-6ABC with

orifice plates ranging in nominal beta ratio from 0.2 to 0.75. Data for

a 6-inch meter tube were taken during September and November 1983.

A considerable number of test run repetitions over the beta ratio range

were performed. The results obtained from these observations in the low

Reynolds range of each plate, corresponding to the low differential

pressure values, consistently and significantly differed from both the

Buckingham and Stolz correlations. However, the discharge coefficient

values computed for the higher differential pressure values for each

plate showed the expected level of agreement with the correlations.

As a result of this inconsistency between the discharge coefficient

values obtained from the test run data and the Stolz and Buckingham

correlations at low Reynolds numbers, a thorough analysis of the performance of the entire measurement system was made. This was done to

determine whether artifacts of the measurement system were unduly influencing the results, and if so, to eliminate or reduce their effect.

Considerable effort was focused on the differential pressure measurement

system, particularly the transducers, but these were found to show no systematic effects due to tap connection, physical location, or to any

-448-
other change. It was noted, however, that the transducers showed a tendency to increase their indication slightly in the initial step of

the transducer calibration procedures when a slightly negative differential pressure was applied. Additionally, all of the transducer calibration models required the addition of a constant coefficient to minimize the residual standard deviations of the fit of their response to

the calculated differential pressure developed by the two working press- ure standards. Investigation of the working pressure standards revealed

that the mass values assigned to three of the weights of one of the

working pressure standards and to one weight of the second working

pressure standard were incorrectly assigned. The weights affected were

those comprising the constant load part of the weight stack, which made

identification of the problem difficult: Because the weights with

incorrectly assigned mass values were always part of the load on the

deadweight testers, no indication was produced during the calibrations.

These mass value assignment errors were traced to transposition errors

in the recording of the weighing data. Subsequently, mass assignment

procedures were repeated on all of the weights used in the calibration

procedures for the differential pressure transducers. The results from

this second set of data agreed with the previously assigned values within 1 part per million except for the four weights mentioned above.

Several additional observations were made on these four items to ensure

that the correct mass values were assigned.

Use of the correct working pressure standards mass values resulted in

much better agreement with the Buckingham and Stolz correlations in the

low differential pressure range of each plate. Regeneration of the data

for all orifice plates produced discharge coefficient values which were

in much better agreement than had previously been the case. The new

values showed similar levels of offset from the Buckingham and Stolz

correlations over the full range of differential pressure for each

orifice plate. However, this level of agreement was not realized for

the largest beta ratio orifice plates, particularly at the highest flow

rates. These divergences were relatively small on a day-to-day basis,

but, near the upper limit of the range of expected reproducibility.

Although this behavior in the data was unresolved, a decision was made

at the urging of the API Orifice Meter Database Steering Committee to

proceed with a full test schedule of all orifice meters beginning in

late June 1984.

III. Full Database Production Runs - 1984

A schedule of data base generation test runs was agreed upon and begun

in the last week of June. This testing was to be done on a relatively

tight schedule. Peculiarities in the observations were to be noted.

Orifice meters showing unexpected behavior would be investigated for

operational/analytical errors, and, rerun after completing the testing

schedule. Internal consistency checking of the measurement systems was routine and gave frequent indications of their level of reproducibility.

-449-
Data collection activities for the full set of test runs - five flow

rates for each plate, five observations per flow rate, fully replicated

at least once on another day - for the various meter tubes were completed in early December of 1984. During this series of tests the data were collected on a single meter tube for all orifice plates to be run with

it, i.e., seven orifice plates for the 2-, 6- and 10-inch diameter meter

tubes, and eight for the 3- and 4-inch diameter tubes. (An eighth ser- ies of orifice plates had been added at the steering committee's request

to cover very low beta ratios which were coming into use in the industry

at that time. These were nominally 0.25 inch orifices for both meter

sizes.) The data collection activities for a single meter tube required

between 2 and 3 weeks to complete using a daily schedule of testing with

five repetitions taken at each flow rate setting. The meter tubes were generally left filled with water when testing procedures were not in

progress, in an effort to reduce rusting of the meter tube interiors.

In a review of the results calculated from these data there were significant differences between results obtained for the large beta ratio

orifice plates on the first day and on successive replications, for the

majority of the meters. Figures A1-A3 show an example of the characteristics of the discharge coefficient values obtained for the full set

of plates for the FE-6ABC meter tube. (This meter tube was run more

often than others and serves as a check standard for the data base production.) The discharge coefficients computed from the observations for

each test run are plotted. The FE-5/6-1A (nominal beta ratio = 0.21)

orifice plate and the FE-5/6-2A (nominal beta ratio = 0.375) given in

figure Al shows the expected capabilities of the measurement systems. The

results obtained from all observations for each day are shown for one of

the transducers. (The Paros Transducer connected to the upper set of

taps are plotted here exclusively.) This is done to illustrate the

level of performance of the measurement system/orifice meter com- bination. Replication of discharge coefficient values at similar differential pressure and Reynolds number values on different days are quite

good. These replications include removal and insertion of the orifice

plate in the meter flanges. Typically the reproducibility of the re- sults within a group of observations at a single flow rate and between

days at nominally the same Reynolds number were below 1 part in 600 at

the higher differential pressure values. The scatter in the discharge

coefficient values increased somewhat at the lower differential pressure

values as is expected due to the larger uncertainty at those pressures.

Figure A2 gives the results of test runs performed on the FE-5/6-3A

(nominal beta ratio = 0.5) and the FE-5/6-4A (nominal beta ratio = 0.56)

orifice plates. Five days of observations are plotted for the 3A plate,

while 2 days of observations were taken on the 4A plate. The magnitude

of variation in the results are similar and reflect the level expected

from the propagation-of -errors analysis. However, for most of the flow

rate settings, the scatter between the results taken on different days

has become noticeably larger. For the 3A plate this is accentuated by

the large number of observation days. The 4A plate has only a single

replicate showing a small day-to-day variation in the results.

•450-
Metp^r Tube FE-6ABC

v.ouu —

o

FE-5/6- 1A

All 1984

*

*

*

* h 1 -

-g 0.600 - *

n CQC

*

U.Oi/ii 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 10 10 10

o

I

O

*

1

FE-5/6 -2A

All 1984

0.603 -

J

n KQQ

•

^

1

U.oUa 1 1 1 1 1 1 1 1

1

1 1 1 1 1 1 1 1 10* 10 ' Pipe Reyixolds Number

10

Figure Al. Discharge Coefficient/Reynolds Number Plots, 4- Inch

Meter Tube, Beta Ratio 0.2 and 0.375 Orifice Plate,

1984 Observations

• 451-
Meter Tube FE-6ABC

V 0,609

o

O

r

0.604

10

t

FE-5/6-3A

All 1984

1 1

1—I—I—

r

10

T

1 1—I—1—r—rr

10

U.O 1 o —

'^ FE-5/6-4A

CM All 1984

o

JoV •

os * s

e

-g 0.610 -

1

*«1 •c» C|

Vtw 9 •: :p* * ^

e

U.OUu — 1 i 1 1 1 1 1

>

1 1 1 1 1 1 1 1 1 10' 10'

Pipe Reynolds Number

10

Figure A2 . Discharge Coefficient/Reynolds Number Plots, 4- Inch

Meter Tube, Beta Ratio 0.5 and 0.56 Orifice Plate,

1984 Observations

-452-
Meter Tube FE-6ABC

^0.618

o

•5 0.613

CO

0.608

10

t

f

FE-5/6-5A

1984 Data

I i r 10

1 1

VT

10

U.O/CU —

2 0.615 ~

t

*

t"

1

• * t

FE-5/6-6A

All 1984

-g 0.610 -

•5 :

1

t X

%

Q) «

•^ 0.605 - ^ : t

U.oUU 1 1 1 1 1 1 1 '

1 '

1 1 1 1 1 1 1 10 10' 10'

Pipe Reynolds Number

Figure A3. Discharge Coefficient/Reynolds Number Plots, 4-Inch

Meter Tube, Beta Ratio 0.62 and 0.75 Orifice Plate,

1984 Observations

453-
Figure A3 shows plots of the results of test runs performed on the

FE-5/6-5A (nominal beta ratio = 0.62) and the FE-5/6-6A (nominal beta

ratio = 0.75) orifice plates. The initial observations were taken July

25, 1984 with the 6A plate installed. The following day data were taken

on the 5A plate. Three additional days of observations were taken between July 25 and August 9, 1984. The variation in the results taken at

a single flow setting on one day are most clearly shown in this figure

and is greatest at the higher Reynolds number values, where the discharge coefficients calculated from five successive observations do not

overlap another day's results but differ from one another 1 to 2 parts

in 600. The 6A plate's results shown in the figure were taken from 5 days observations taken from July 25 to August 9, 1984. As with the

results from the previous orifice plates the scatter within a group of

five observations at a single flow rate is quite small. However,

day to day difference is much larger, and increases substantially with

increasing Reynolds number. In both cases this effect is sufficiently

strong to substantially remove the dependence on Reynolds number of the

discharge coefficient after several weeks of daily running of the meter

tubes. Due to the lack of reproducibility in the results on these

plates, test run groups were taken on the FE-6ABC meter tube for a con- siderably larger number of days than with the other meter tube.

However, the characteristics of these results were not limited to the

FE-6ABC meter tube. Similar characteristics of varying magnitude were observed for other meter tubes in the set. Since the testing schedule

was based on single replications for all orifice plates of a set in a single meter tube, most of the orifice meters had data collected on them

for only 2 days. Generally most, if not all, of the meter tubes showed similar behavior in their results. Reproducibility of discharge

coefficient values obtained on one day was within that expected for the

measurement systems for the low beta ratio plates, but deteriorated

steadily as the beta ratio increased.

This characteristic was not observed uniformly throughout the data base,

but appeared to affect only certain of the meter tubes. Two sets of

examples are shown in figures A4 and A5 . Figure A4 shows discharge

coefficient plots for the 2 -inch meter tube, FE-2ABC, orifice plates FE1/2-2A (nominal beta ratio - 0.375), and FE-1/2-6A (nominal beta ratio - 0.75). Replication of results over 2 day periods for the smaller beta

ratio plate is consistent with the measurement- system' s estimated uncer- tainty limits. (Observations on this plate were taken on successive

days with the plate remaining between the orifice meter flanges

overnight.) However, the replication of the results for the 6A orifice

plate shows a between day variation approximately an order of magnitude

larger than the variation in five successive observations taken at the

highest Reynolds numbers. The increased separation between successive

day's observation results with increasing Reynolds number is obvious.

The discharge coefficient vs. Reynolds number plots for the two largest

beta ratio plates of one of the 10- inch meter tubes, FE-OABC are shown

in figure A5 . The discharge coefficients calculated for the observations taken on the FE-9/0-5A orifice plate have a small between-day

454-
Meter Tube FE-2ABC

0.610

O

Co

-g 0.605

03

0.600

10'

»

i

1—

r

10

FE-1/Z-2B

o 10/08/84

10/09/84

1 1—I—I

m

10

U.OiCU —

_

c2 0.620 - 1

FE-1/2-6A

05/31/84

06/05/84

-g 0.615 -

1

D

.5 D

B

W

.^ 0.610 - ^ :

U.OUO 1 1 1 1 1 1 1

1

1 I 1 1 1 1 1 1 1 10 10'

Pipe Reynolds Number

10

Figure A4. Discharge Coefficient/Reynolds Number Plots, 2 -Inch

Meter Tube, Beta Ratio 0.375 and 0.75 Orifice Plate,

1984 Observations

-455-
Meter Tube FE-OABC

0.610

o

r

-g 0.605

0.600

-

D

i

D a

FE-9/0-5A

05/18/84

D 05/29/84

A 05/30/84

—

D

I 1 1 1 1 1 1 1

1

1 1 I 1 I 1 1 1 10 10 10'

U.Q 1 U — FE-9/0-6A

45

O

^ 05/31/84

* 06/04/84

Q) 0.605 - >

I 06/06/84

> b > is , o

•2

0.600 - 4 1

* 1

O f s*

•Hs

t

U.olfo 1 I II ' 1 1 1 1 1

1 1 1 1 1 1 1 1

1 10 10 ' Pipe Reynolds Nvimber

10

Figure A5 . Discharge Coefficient/Reynolds Number Plots, 10 -Inch

Meter Tube, Beta Ratio 0,62 and 0.75 Orifice Plate,

1984 Observations

-456-
variation. The results obtained for the FE-9/0-6A orifice plate have a somewhat larger scatter, but do not exhibit a pronounced day-to-day

difference as do the 2 -inch meter tube results.

Generally the scatter in the results from the data gathered on the

larger beta ratio plates was not absolutely consistent in showing this

effect. As a result a considerable level of confusion was encountered

since a clearly defined cause and effect relationship was not evident.

However, the data base had been substantially completed. The anomalies seen in the results were initially seen as a relatively minor factor

which could be eliminated by rerunning those plates having results with

unacceptably large day-to-day differences.

IV. Selection of Orifice Meters Requiring Reruns

With the substantial completion of the data base production schedule,

the orifice meters to be rerun were to be selected. The selection criteria were based primarily upon the level of internal consistency in the

data base, i.e., the level of reproducibility of the results for an orifice meter between observation days. Between-day variation in the

results greater than that predicted by the propagation of errors and

analysis were considered to be adversely affected by an uncontrolled and

undefined source of variability in the system.

As discussed above, a significant number of the large beta ratio plates

showed a disturbing degree of non-reproducibility . The degree of variation in the results appeared to decrease with decreasing beta ratio.

Unlike the previous occasions in which results were not as expected, the

measurement systems were not considered to be at fault. Replication of

the results on the small beta ratio plates, coupled with the internal

consistency checks in the observation procedures and the small withingroup variation, indicated that the measurement systems were performing

as expected.

Extensive discussions were held in November and December, 1984 between

the NBS Principal Investigator and the Orifice Steering Committee to

determine the list of orifice meter tube/plate candidates to be rerun. The dominant concern was the as yet unknown source of the large day- today variation in the results on a significant fraction of the total

number of orifice plates tested.

With the completion of the testing schedule, all of the meter runs ex- hibited some visible degree of corrosion. Those which had been involved

in the early testing conducted during the initial phase of the project,

particularly the FE-5ABC meter tube, showed considerable levels of

corrosion throughout each tube section. Although no quantitative sur- face roughness measurements had been made, it was the feeling of some members of the Orifice Steering Committee and NBS personnel that the

roughness level was probably outside the allowable limit of 300 microinches given in AGA Report No. 3 and considered as the acceptable limit

for commercial practice.

457-
Strong consideration was given to the possibility that increased surface

roughness due to corrosion was affecting the results. Several corrosion

experts were consulted to determine whether

(1) treatment of the water used in the NBS flow facility could be

effective in reducing the level of corrosion in the mild steel

meter tubes, or

(2) application of a metallic coating to the meter tubes would

inhibit corrosion, i.e., a 0.0005 to 0.001 inch thickness of

electroless nickel.

The first course of action was strongly urged by the Orifice Steering

Committee which was extremely reluctant to depart from its requirement

and concept of the use of "commercial quality" meter tubes for development of the data base. The nickel plating option was suggested by NBS

as the most effective and expeditious method. After some investigation

and consultation with various corrosion experts, it became clear that

the possibilities for water treatment at low concentrations were limited

to a small number of chemicals. It was decided to attempt the use of a sodium silicate-based inhibitor for initial testing. If this was not

satisfactory then zinc chromate would be considered, although its disposal presented a substantial problem. In treating the water the effect

of chemical additives on the density and viscosity of the water was considered to be small since the concentration of the additive chemicals were at the few hundred part per million level or less, and neither

were known as strong rheological modifiers in water. A series of tests

were planned to investigate rust/corrosion inhibiting effects in an attempt to resolve the discrepancies in the observation data base.

V. Investigations of the Effects of Corrosion Induced Surface

Roughness Variations in the Observations.

The FE-5ABC meter tube assembly was shipped to the manufacturer to be

refurbished. It was returned to the NBS-Gaithersburg site in late

December, 1984. As a result of refurbishment, its diameter had been

increased by approximately 0.020 inches. The surface finish of the

meter tube in the flange regions appeared to be a newly machined/ground

finish and consisted of a bright metallic finish with no visible indications of corrosion. This type of finish extended three to four pipe

diameters inside the three meter tube sections. The interior lengths of

each tube section were substantially rust free and of a moderate brown

color.

A controlled, short set of test runs were planned as an experiment to

determine if corrosion was the cause of the previously observed behavior

of the discharge coefficient values. These were to use the FE-5ABC

meter tube with orifice plates from both 4- inch sets of nominal beta

ratios of 0.5, 0.62, and 0.75. Exposure of the meter tube to water was

to be minimized to reduce the amount of rust formed in the meter tube

assembly. The meter tube sections were to be wiped with ethanol soaked

458-
rags and air dried quickly after removal from the test section of the

flow facility to remove the remaining water from the tube. The test

plan incorporated the 0.5 beta ratio plate as a control plate, since

previous results had shown it to be affected less than the larger beta

ratio plates. The tests were run January 9, 1985. A synopsis of the

results is given below.

V-1. Initial Meter Tube Rust Test Plan Execution and Results

The following report of test results was developed shortly after the

test plan was executed.

During the first day, three of the four possible combinations of weighing/diverter systems were used at three differential pressure values (1,

10 and 28 psi) with the 3A plate (0.5 beta), FE-5ABC meter tube. This

procedure tested the consistency of the diverter corrections applied for

each diverter and was a check of the weighing systems. The collection

times were selected to minimize the effect of possible scale errors

(5,000 indication units or more were taken). The results are tabulated

below.

Diff. Press. Weighing System Capacity

(psi) 50,000 lb 10,000 lb 2,000 lb

1 .60699 .60715

10 .6044 .6048 .6049

28 .60515 .60422

These data were taken with one pump configuration (1000-gpm pump only)

Immediately after taking the above data one of the 3000 -gpm pumps was used to repeat the 28 psi point. The discharge coefficient value obtained was 0.60532. It appeared that pump disturbances, if present,

could be detected within the performance of the system at that time.

During this phase of the tests the density of the water was measured for

a sample taken during the tests. The samples from previous fills of the

flow facility's sump were measured during late December. All of the

measured density values were slightly greater than the corresponding

distilled water density by 80 to 150 parts per million (0.015% or less).

Further Analysis of the Data

During the running of the tests, Messrs. Fling, Upp, and Whetstone had

extensive discussions of the results (as they were developed) and looked

for the existence of correlations between the day-to-day coefficient

increase and other system operating parameters. These other parameters

included temperature, plate condition (all 4- inch plates on hand were inspected by Messrs. Upp and Fling), and transducer calibration. The

following list of possible interfering effects and checks on the performance of various of the measured parameters was compiled.

•459-
1. Mass

2. Diverter Time/Crossover

3. Weighing System/Crossover

4. Plate condition

5. Tube condition

6. Transducer Calibration

7. System pressure

8

.

Temperature

9

.

Operator quirks

10. Computer analysis

11

.

Computer programming

12. Pump combinations

13. Results evaluation

checked

clean

No variation over time

See below

No correlating pattern could be

found

.

None were found.

No logical errors in the analysis

have been found by several

different observers

.

Same comment as no . 10

.

None found in these tests or in

those carried out by Southwest

Research during their

investigation of the frequency

spectrum seen around the meter

taps and in the transducer

connection lines.

No effects evident.

Plate condition varied, particularly orifice edge sharpness, but all

plates inspected (4- inch sets) by Messrs. Upp and Fling were within

acceptable limits. These ranged from as sharp as when made to "not

quite as sharp .

Having run the FE-5ABC meter tube for 2 days of testing, the results

calculated from the observations showed scatter which was at the level

expected from the measurement system performance, i.e., below the 1 part

in 600 level at the higher Reynolds number values . Only a very small

degree of rusting in the meter tube had occurred and the meter tube was dried and sealed after the tests were completed.

Tests Conducted Using the FE-6ABC Meter Tube

After completing the tests using the FE-5ABC meter tube, the second

4 -inch meter tube, FE-6ABC, which had remained in the flow lab since

last tested, was put into the line and tests of the FE-5/6-6A plate were

begun. The immediate result was that the value of the discharge coefficient was nearly coincident with the last values taken, i.e., the discharge coefficient values at the highest Reynolds number were 1 to 2%

above the Buckingham or Stolz values and the initial values obtained for

that plate and tube. One of the hypotheses suggested during the course

of the discussions of possible causes of the day-to-day effects was cavitation around the orifice itself. Although this did not explain the

chronological ordering of the observed effects, a short test was run. Cavitation effects could have been suppressed or reduced by increasing

the static pressure at the orifice. The normal operating pressure was

41 psig, measured at the downstream tap. The initial observations of

-460-
this investigation were made at this pressure for the 6A plate. The

pressure was raised to 60 psig and the points were repeated. The coefficient values observed at the higher back pressure closely replicated

those observed at the normal operating pressure.

The conclusions drawn from the short tests on the FE-6 meter tube were

that the day-to-day effects were much in evidence and could not be

suppressed with a rise in the system pressure by 20 psig, which was the

practical system maximum. No further changes in the flow system operating parameters could be suggested as the causal agent and the tests were stopped.

Conclusions Drawn from the Test Results

The results of the tests of the FE-5 tube showed that for all large beta

ratio plates (6A, 6B, 5A, and 5B) , the observed discharge coefficient

values were reduced to a level near the originally observed values. The

3A and 3B plates closely reproduced their previous values. The values

obtained for nominally identical beta ratio plates were similar and

generally agreed with one another within the predicted variation of the

experiment.

Further Tests

It was decided to test the FE-6ABC meter tube after it had been cleaned

by NBS personnel using a procedure as nearly identical to that used in

the refurbishing of FE-5ABC as possible. This procedure entailed the

spinning a 3 X 23 inch sander belt on a length of electrical conduit.

Belts of 60 to 120 grit were used. The belt is captured in a slot sawed

lengthwise in one end of the conduit. (Figure A6 is a photograph of the

belts and conduit.) Approximately equal lengths of the belt extend from

either side of the slot. The conduit is driven by a hand drill and spun

inside the meter tube along its entire length. Wooden spacers were used

to ensure that the conduit is near the axis of the tube at all times to

eliminate the possibility of gouging the inside surfaces of the tube

section. The belt was kept moving along the axis of the tube to reduce

the possibility of changing the diameter in one position along the tube.

Removal of all rust patches down to the bare metal at either end of the

tube was not possible with the equipment at hand. However, all the

surface rust was removed and a bright metal finish was evident in a speckled pattern of small sections of the tube interior surface, the

remaining corrosion being too hard and strongly attached to remove. The

rust removal procedures enlarged the diameters by .002 to .005 inches over the rusted diameter measurements and polished the inner surfaces

until they were smooth to the touch.

The FE-6ABC meter tube was installed in the water flow loop for tests of

several of the orifice plates. This series of short tests was designed

to determine whether removal of substantial portions of rust from the

meter tube would reduce the value of the discharge coefficients. The

large beta ratio plates were tested first since these showed the

461-
i

Figure A6. Sanding Belt and Conduit Used In Rust Removal

-462.
greatest effects. The results were dramatically changed from those

obtained in the most recent tests with the discharge coefficient values

being reduced significantly relative to the corroded tube values for all

plates tested. With these results in hand it was decided by the Orifice

Steering Committee to have all tubes reconditioned. Although it was generally agreed that a mild steel tube must not be allowed to rust to

the point of affecting the test results, the method of corrosion inhibition had not yet been decided. Consequently an extensive set of tests was performed between February and mid-June of 1985 in an attempt to

develop a procedure which would inhibit rusting of the meter tube interior surfaces without physical modification of the meter tubes, and without substantial change to the manner and conditions under which the data

were collected.

VI. The Search for Chemical Means of Corrosion Inhibition

The search for a means of chemically treating the flow facility water to

inhibit corrosion ultimately failed. Two chemicals were considered for

use, sodium silicate and zinc chromate . The sodium silicate was used in

concentrations up to approximately 100 parts per million and exhibited a level of corrosion inhibition which was not acceptable, i.e., it did not

completely stop rust formation. Additional tests with oil-treated meter

tube surfaces were performed and proved futile. Finally, the Orifice

Steering Committee agreed to electroless nickel plate one of the meter

tubes with a nominal thickness of 0.001 inch and to perform test runs on

it. This section is given as a brief record of the sequence of events

during this period of the project in the hope that future workers will

profit from it.

VI-1. Tests of FE-5ABC - No Corrosion Inhibitors

In late January and early February a short series of tests were performed to determine the operating time allowable before the effects of cor- rosion on the meter tube surfaces were detectable. The FE-5ABC meter

tube, which was still very near its refurbished state, was used. The

results reported to the Orifice Steering Committee by NBS are given

below with minor editorial changes

.

Testing of the FE-5ABC meter tube and selected plates was begun

January 31 with the testing of the 2A orifice plate. Before the meter

run was placed in the line for testing it was inspected visually. The

report of the inspectors (Sam Woo and J. Whetstone) is the following.

31 January 1985

Section 5B of meter FE-5ABC has been sealed with desiccant and oil

since 16 January 1985. Before its return to the system flow loop, it was visually inspected to note its condition. Prior to inspection,

the desiccant and oil were rinsed out using (ethyl) alcohol. Upon

inspection, the meter section was found to be in relatively clean

shape. There was some rust that had formed in the circular cut

grooves on the refurbished section of the meter tubes and it seemed to

463-
all be located on one side (as if the meter had sat in one position

and collected water) . Though the meter section had been rinsed with

alcohol, there was still a slight oil residue. Further upstream, in

the midsection of the meter section, the pipe was still dark colored.

The 2A plates were run on Thursday, January 31. The meter run was

left filled with water overnight and the upstream meter tube (FE-5B) was raised (from the test section rack) and inspected for corrosion

the following morning. The report of the inspector is the following.

Meter FE-5ABC was run 1/31/85 and left full of water overnight.

After draining the meter the morning of 2/1/85, the 5B section was lifted from the line and inspected. As the inner surface dried, a light film of rust became visible on the refurbished surface which

could be rubbed off with a finger, but the fine grooves formed by

the refurbishing could still be felt with a fingernail. The refurbished area extends 9 inches into the 5B-D end of the section and

6 inches into the 5B-U end of section 5B.

Dr. Whetstone inspected the tube also. The following is a portion of

his report entered in the notebook files on the subject.

Following the original tests in January surfaces of the meter tubes

were somewhat discolored with a light coating of rust. This coating

covered only a small fraction (25% or so) of the bright metal regions near the flanges. Also a darker color was appearing. These

darker colored regions are spreading as the testing has been con- tinued now.

The 3B and 4A plates were run February 1 and the meter run was left

filled with water over the weekend. Again the B section was inspected, as were the other sections at their open flanges. The inspection

occurred after the running of the 3B plate in the morning. A substantial increase in the level of rust in the meter tubes was generally

evident. Surface rust could be removed easily with a paper towel or

rag, but beneath this layer a harder level of corrosion had developed.

Dr. Whetstone decided that an attempt should be made to remove the

rust using 120 grit sanding belts in the manner described in the January report. This procedure succeeded in removing the large majority

of the rust and restoring the regions near the ends of the B and C

meter tube sections (sections adjacent to the orifice plate) to a bright metal finish similar to that after refurbishing. There were

some very small areas of rust in the surface grooves that were not

removed. The surfaces felt smooth and the circumferential surface

grooves could be felt easily with a fingernail.

The meter was re -installed in the test loop and the 5B, 6A, and 6B

plates were run on Feb. 4 and 5. The 6A plate was run on the morning

of Feb. 6. Then the meter tube was again taken down and inspected.

The inspection report is the following.

-464-
Sections 5B and 5C were taken down and cleaned after this morning's

pass on plate 6A. The meter sections showed substantial corrosion

as rust could be seen growing from the grooves in the refurbished

sections of pipe. The sections were cleaned using the hand drill and

120 grit sand paper. The majority of rust was removed but a thin

coating remained on the pipe. This coating could be rubbed away

using a rag. It appears that the rust is beginning to discolor the

surface of the metal. After the meter tube is cleaned, the surface

does not completely shine as brightly metallic as it did originally. Instead there are some dark patches that appear on the pipe.

The meter tube was remounted and the 4A and 5B plates were tested on February 7. Testing of the meter tube was suspended at this point due

to deterioration of the meter tube surfaces. (In the above discussion

the surfaces referred to are those at the flanges of each tube where

the refurbishing had produced a bright metallic surface two to three

diameters into the meter tube.)

Test Results

The results of this series of tests will be given by plate

chronologically and qualitatively.

Plate 2A - Jan. 31, 1985 - The discharge coefficient values

consistently fell below the previous data, taken in late

March and early April 1984, except at low Reynolds numbers.

The new data is from 3 to 15 parts in 6,000 higher than

Stolz/Buckingham.

Plate 4A - Feb. 1, 1985 - The discharge coefficient values are similar

to that of 2A and uniformly below the previous data, taken

late March to early April, by 2 to 3 parts in 600.

Feb. 7, 1985 - The data shows the between day variation

seen previously. The magnitude of the variation is

approximately 1.5 parts in 600 at the highest Reynolds

number and 0.3 parts in 600 at the lowest Reynolds number.

The variations increase uniformly with Reynolds number.

Plate 3B - Feb. 1, 1985 - The discharge coefficient values match the

previous data within the variation seen in a set of five

observations. The previous discharge coefficient values

have some significant between- day scatter at the lowest

Reynolds number.

Plate 5B - Feb. 2, 1985 - The discharge coefficient values fall within

the previous data, which has a variation of approximately

2.5 parts in 600. At higher Reynolds numbers these values

progressively drop to the lowest values of the previous

results

465-
Feb. 7, 1985 - The discharge coefficient values exhibit

the classic between-day variations seen previously, with the

low Rejmolds number values agreeing well with the Feb. 2 values with the difference between the 2 day's values

becoming progressively greater. The highest Reynolds

number values are near the top of the band of the data

taken in February, March, and April 1984

Plate 6B - Feb. 5, 1985 - The discharge coefficient values lie below

the previous values (March, May and June 1984) at low

Reynolds numbers and within the lower portion of the

previous data band at the high Reynolds numbers

.

Feb. 6, 1985 - The discharge coefficient values replicate

the Feb. 5 results and lie approximately 3 to 5 parts in

6,000 below them.

Plate 6A - Feb. 5, 1985 - The results are similar to that of 6B but

are somewhat closer to the bottom of the data band of the

early 1984 6B data.

Feb. 6, 1985 - The discharge coefficient values replicate

the Feb. 5 results but lie above them by as much as 1 part

in 600.

The FE-5ABC meter tube was taken from the test loop and dried out.

It was not sealed since considerable rust had accumulated throughout

the tube. A bright red layer of surface rust is evident on all

interior surfaces of the meter tubes.

VI-2. Test Results with N-Sodium Silicate Treated Water

In late February 1985 a quantity of N- sodium silicate had been obtained

and the water was dosed with a concentration of 25 to 30 parts per

million. This was the concentration level recommended by a corrosion

expert furnished by the API. Tests were performed using a stainless

steel 3 -inch meter tube furnished by the Gas Research Institute

through its research contract with the NBS Boulder Laboratories . Base

line data had been obtained with the meter tube before treating the

water. The discharge coefficients observed on February 27 using the

0.75 beta ratio orifice plate agreed with the base line data taken the

previous week.

The FE-5ABC meter tube was placed in the line and and test runs were made on the 0.75 beta ratio plate, 6B. The meter tube had been recon- ditioned using the sanding belt method. The first test run data with the

sodium silicate treated water was taken on March 1. Test runs were made

using the 5B plate (beta - 0.66) on March 4 and 5.

The second day's data on the 6B plate was taken on March 6. The results

showed a day-to-day effect of approximately 1% in the discharge coeffi-

•466-
cient. This set of observations was repeated March 7 after leaving the

meter tube filled overnight. The day-to-day effect was still evident

with the discharge coefficient values increasing approximately 1 to 2 parts in 600 at the highest Reynolds numbers. The meter was removed

from the flow line and visually inspected. A fine powdery coating of

rust was on the surface of the meter tubes. Distributed along the pipe

wall were grains of rust which could not be brushed off with a finger as the fine rust dust could. These grains were approximately twice the

size of a grain of table salt. Some could be dislodged with a fingernail, others with light pressure from a knife blade. Photographs were taken of the interior of the meter tube at the upstream flange. These

clearly showed the definite patterns developed on the interior surfaces

of the meter tubes. There were very definite patterns of rust grains.

The grains were disposed in roughly circular and helical patterns around

the pipe circumference with areas between the corroded areas which had

almost no rust grains in them and appeared to be very near the surface

condition before the tests were begun. Two of the more illustrative of

these photographs are given in figures A7 and A8

.

During this time a product bulletin for the inhibitor arrived from its

manufacturer which recommended concentration levels of 100 to 300 parts

per million with a pH range of 7.0 to 9.1. The concentration in the

flume water was increased from 25 to 88 parts per million, which used

the entire drum of N sodium silicate solution on hand. Also, the pH was adjusted to approximately 8.1, which matched the value for the untreated

flume water samples. FE-5ABC was conditioned again using the sanding

belts and data was taken over the full range of flow rates on March 8

.

The discharge coefficient values were very near those obtained earlier

with the refurbished surface. The meter tube was left filled with flume

water over the weekend and the second set of observations were made over

the full flow rate range on March 11. The difference in discharge

coefficient values between the 2 days at the highest Reynolds number

was 4.5 parts in 600 (approx. 0.6%).

The meter tube was removed from the test section for visual inspection.

Corrosion had once again appeared on the meter tube surface. The pattern of corroded areas was similar to the previous one. The general

appearance of the surface was different from the 25 ppm inhibitor case

in that the corroded areas had a pronounced yellow hue. Also the amount

of corrosion appeared to have diminished somewhat, but not dramatically.

With these results the use of N- sodium silicate for corrosion inhibition

was no longer considered to be a viable alternative, and the water was removed from the facility reservoir. The reservoir was refilled with

water from the municipal water mains.

The use of zinc chromate was then considered but rejected on the grounds

of difficulty of disposal. The treatment necessary to dispose of 60,000

gallons of water treated with zinc chromate was of such a magnitude that

NBS was not willing to treat the water.

-467-
Figure A7 . Corrosion Patterns in the FE-5B Meter Tube Section

After Testing with N- Sodium Silicate Treated Water.

-468.
,„ .j.^^i'^feiC«if'=fe.V.;-Ai:;,«

Figure A8 . Corrosion Patterns in the FE-5C Meter Tube Section

After Testing with N-Sodium Silicate Treated Water.

469-
VI-3. Oil Treatment and Testing of the Meter Tubes Leading to

Electroless Plating of the FE-6ABC Meter Tube

In early April 1985 the API's Orifice Meter Database Steering Committee

recommended what it termed a "pull and wipe" strategy consisting of the

following steps:

1. The meter tube would be initially wiped with a light weight oil

through its entire length before a test run.

2. It would periodically be pulled from the test rack, inspected,

and any rust removed using the sanding belt method,

3. The interior surfaces wiped with oil again, and reinstalled in

the test rack for further tests.

A test of this procedure was scheduled to begin on the morning of

April 8, 1985 with designated members of the Orifice Steering Committee

in attendance. The FE-5ABC meter tube was used. An edited version of

the report of that work is given below.

Extended Test Run ^ April 8 ^ 10^ 1985

This test was designed to simulate the operating conditions proposed

for rerunning of the orifice meter data base. The proposed schedule

involves running of the flow system on a 24-hour-a-day basis. Therefore, this test involved running of the system continuously for a period approximately equivalent to the amount of time estimated to

complete the data collection for one meter tube (all plates - one

set). The estimated time is 56 hours barring any difficulties.

April 8

The meter tube was prepared using the sanding belt technique. The

surfaces of the meter tube are a shiny dark color after passing the

spinning belts along the meter tube surface. This preparation was used along the entire length of the meter tube and produced a smooth

surface to the touch. The meter tube was wiped with an oily rag

containing lOW 40 lubricating oil. The rag was passed through the

tube sections twice. This resulted in the appearance of a shiny

surface along the entire length of the meter tube. The tube's inner

surfaces appeared to be coated uniformly with oil.

The meter tube was placed in the test rack and the beta 0.75 plate was installed in the orifice flange. Data collection was begun at 11:00

a.m. April 8, 1985. Observations were made over the range of differential pressures (0.4 to 28 psi) . A beta 0.375 plate was installed

(approx. 30 minutes was necessary to do this) and data at the highest

differential pressures were taken. The system was allowed to run unattended all night long. The measurement system was shut off for

the night while the flow system ran throughout the night.

470-
April 9

At about 8:00 a.m. the flow system was shut down and the meter tube was removed from the test rack for inspection. The Inspection report of

Mr. Sam Woo is given below.

FE-5C - "Upon initial inspection, the wet pipe showed little or no corrosion. The surface still had an oily residue along all surfaces

of the pipe (5 - 10% of the pipe surfaces have a light coat of

rust. All in all, it showed a minimal amount of corrosion.). The

surface still had an oily residue (could be smudged with fingerprints) . The rust could be wiped/rubbed out on the interior of the

pipe but not along the flange edge. There was more rust along the

bottom of the pipe than on top. The rust has a very fine

consistency.

FE-5B - "The upstream meter section doesn't look nearly as bad as the downstream section. The characteristics of the corrosion are similar to the downstream section but there is less rust."

The meter was reinstalled in the test rack with no treatment of the

tube and the water flow started by 10:30 a.m.. The beta 0.75 orifice

plate was installed and the observation points of the previous day

were repeated. Both sets of results agreed within the uncertainty of

the measurement system. That is, the mean values of each set of five

observations at a flow rate taken over the 22 -hour period reproduced

one another within 3 to 5 parts in 6,000.

The beta 0.5 orifice was placed in the meter and data were obtained

over the range of differential pressures.

The flow system was allowed to run unattended overnight.

April 10

Beginning at 11:52 a.m. data were taken on the beta 0.75 orifice plate

after it had been installed. Again the data were taken over the range

of differential pressures. The discharge coefficients calculated from

this data showed the characteristic (day-to-day) increase with

Reynolds number. The difference between the discharge coefficients at

the highest Reynolds number points (28 psi diff. press.) was .0014 or 0.23 percent.

The 0.5 beta ratio plate was installed and run at 17:00. These values

agreed with those taken the previous day (oil film assumed to be still

intact) within 0.1 percent or better which is about the reproducibility

expected of the measurement system. Both sets of values agreed with

those taken in early January 1985 when the meter tube interior

-471-
surfaces were newly refurbished and in a bright metallic condition.

The system was shut down and the plate removed at 17:30. Total

running time - approx. 56 hours.

April 11

The meter tube was inspected. Corrosion patches were evident on the

tube's interior surfaces. These were not the powdery rust observed at

the 22 -hour inspection, although such rust dust was generally present

over the surfaces of the tubes. A harder and physically larger type

of corrosion was observed which consisted of either single nodules or patches of nodules. These were rather hard, although single nodules

or small groups of nodules could be broken off the surface either

totally or partially intact with finger pressure only. It was found

that by fitting a 35 -mm camera with the proper lenses a magnified

photograph of the surface could be taken. This was done in several

places on both the C and B sections of the tube. The photographs

shown in figures A9 and AlO are representative of that series of

photographs. Both were taken of areas near the flange face of the

meter tube section. In figure A9 a tap hole (1/2 -inch diameter) is in

the center with a 0.5 millimeter (0.020 inches) length of pencil lead

placed on the surface between the tap hole and the flange face to give an impression of the scale of the rust nodules. Figure AlO shows an area to the side of the tap hole which has a somewhat greater coverage

of rust nodules occurring both singly and in multiple nodule patches.

An attempt at a quantitative measurement of the size of the nodules

was attempted. A telemicroscope was used to focus on a single nodule

formed near the top tap hole of the downstream meter section (meter

section C) . (This nodule is shown as the bright speck located at the

upper left of the pencil lead in fig. AlO.) The telemicroscope was mounted on a traversing stage having a resolution of 0.00001 inches.

The microscope stage was moved until a crosshair was tangent to one side of the nodule. The traversing stage reading was recorded and the

stage moved until the crosshair was tangent with the opposite side of

the nodule. This was repeated several times. The results of this

measurement indicate that the diameter of the nodule was of the order

of 0.001 inches. Therefore, its height above the surface would be of

the same size assuming a roughly spherical shape for the nodule.

In viewing patches of nodules with the telemicroscope the general

appearance of the patches was that of an aggregation of nodules

connected with smaller nodules forming a continuous layer. It would

be expected that the height of these patches above the surface was the same as that of a single nodule. The patches covered from 20 to 50

percent of the surface

.

Following this testing schedule it was decided that the "pull and wipe"

strategy recommended by the Orifice Meter Database Steering Committee

would be followed in subsequent tests. Running periods of 18 to 20

hours between pulling and wiping of the meter tube would be used.

-472-
Figure A9, Photograph of Corrosion Nodules Around the Tap Hole of

FE-5B After Tests Using Oiled Surfaces for Corrosion

Inhibition

-473-
Figure AlO. Photograph of Corrosion Patches to the Side of the Tap

Hole of FE-5B After Tests Using Oiled Surfaces for

Corrosion Inhibition

-474-
VI-3A. Tests of the Effect of Oiled Surfaces Using the

GRI 3 -Inch Meter Tube

NBS proposed a set of tests to determine whether the hydrophobic nature

of any oil used for wiping would affect the results of the tests.

These tests were performed with the GRI 3 -inch stainless meter tube so that removal of the oil from the surfaces would not result in corrosion

induced discharge coefficient value increases. In this way it was intended to limit the experiment to changes induced by the presence of

oil alone. Extensive testing was performed using several different

types of oils. Sets of test runs were made with the stainless steel

meter tube oiled and not oiled. These were done between May 23 through

May 29, 1985.

Three complete replicates of the data set were run consisting of all

five flow rates for both the 2A and 6A plates with the meter tube sur- faces alternately oiled and not oiled. This data has provided the

basis for an estimate of the reproducibility of the measurement system

(2A plate data) and an estimate of the magnitude of the effect that

oiling the meter tube surfaces may have on the discharge coefficient

values for the 6A plate. A rigorous statistical analysis was performed

by the NBS Center for Applied Mathematics, Statistical Engineering

Division. The major conclusions of this analysis are given below.

1. Effects of oil on the discharge coefficient

An increase in the discharge coefficient is seen at the higher

Reynolds number for the 6A plate (0.75 beta ratio) with an increase of approximately 0.004 discernible at 28 psi. For the

2A plate (0.375 beta ratio) a decrease of 0.006 in the discharge coefficient is seen at the two lowest flow rates (0.4

and 1.0 psi differential pressure) with the remainder of the

flow rates showing no discernible effect.

2No temperature dependent effects were found over the range of

26 to 38 °C.

3. A criterion for the identification of outliers in the data has

been developed. This criteria will be used in an attempt to

maintain real-time statistical control of the measurement pro- cess in the future.

4. The results of the measurements on the 6A plate show a temporal

drift of several parts in 600 across the Reynolds number range.

This drift is systematic at the higher flow rates. The 2A

plate does not show this drift. The data to be collected on

the 4- inch, stainless steel meter tube will be used to determine the magnitude of drift in the measurement system during

the remainder of the orifice meter tests.

-475-
5. Initial estimate of measurement system reproducibility

This initial estimate is based on 8 days of measurements taken on the 2A plate. These data extend over a period of approximately 5 months . Three times the total standard deviation for

these data is 0.00064 in the discharge coefficient. This is a relative uncertainty of approximately 1 part in 1,000.

From these limited tests it appeared that the presence of oil on the

surface of the 3-inch stainless meter tube could be detected in the

discharge coefficients.

VI-3B. Oiled Test of FE-5ABC Meter Tube

Since the GRI stainless steel meter tube was considerably smoother than

the typical mild steel tubes, a test was run to investigate the resid- ence time of the oil for a mild steel meter tube. The 4- inch meter

tube, FE-5ABC, was set up for a 24-hour test. The FE-5ABC mild steel

meter tube was oiled using a commercial 30-weight oil. A swab consisting of rags wrapped in a soft cloth was used to coat the interior of

the meter tube. A similar swab was passed through the meter tube sec- tions to remove the excess oil. This removal was quite thorough, caus- ing some concern over the lifetime of the oil coating. The meter tube was mounted with the 6B orifice plate (0.75 beta ratio) between the

orifice flanges and the base case data was taken beginning at 14:10 on May 16, 1985 (three observations at each of the five usual flow rates).

Following this the water flow was maintained through the night.

The next day data collection began at 10:24 at a differential pressure

of 10 psi. Data collection procedures were completed at 16:20 with a 28-psi data point. The 10- and 28-psi results are summarized below.

Date

05/16/85

05/17/85

Run No

19 20

Time

13:48

10:24

Diff.

Press

.

(psid)

10

10

Discharge Coefficients

Ruska Upper Lower

60396

60407

.60397

.60418

.60397

60419

05/16/85 16 18 15:36 28 60219 .60222 60223

05/17/85 34 - 36 12:29 28

05/17/85 52 - 54 16:05 28

.60292 .60307 .60307

.60290 .60293 .60293

As a check of these results a second test was performed beginning Monday, May 20, and completed Tuesday, May 21. The meter tube was prepared using the sanding belt method and the 30 weight non detergent motor

oil was applied using a rotating rag method. After this application a dry rag was passed through the tube sections to remove excess oil and

476-
the meter tube was mounted in the test rack with the 6B orifice plate

in place for testing. The tests were begun with the taking of the

initial data and the water flow was maintained at a significant pipe

Reynolds value throughout the night. The replicate data was taken the

following morning, the meter tube dismounted from the test rack, air

dried with compressed air and inspected. The discharge coefficient

results of this test are given below.

Date Run No Time

05/20/85 55 - 57 11:09

05/21/85 73 - 75 09:26

05/20/85 58 - 60 11:24

05/21/85 76 - 78 09:46

Diff.

Press

(psid)

10

10

28

Discharge Coefficients

Ruska Upper Lower

60341 .60345 .60346

60400 .60390 .60390

28

60183

60269

.60185

60268

.60185

.60270

Visual and tactile inspections of the meter tube surfaces were made

following each dismounting of the FE-5ABC meter tube. These inspections yielded similar observations. In both cases the meter tube did

not have substantial, newly corroded areas. The surface was mainly

smooth to the touch with isolated nodules of rust easily distinguished

by touch from the surrounding metal surface. It was noted that due to

the large number of tests which had been run on the meter tube since it

had been refurbished back to a bright metal surface, the tube surface

color had turned a dark brown color with several pits in the surface.

The abrasive treatment of the surface with the rotating sanding belts

had smoothed the surface to the point that it had a sheen to it immediately after the treatment. A light dusting of very fine rust grains

came off on the fingers. A light scrubbing action across the surface

with a finger did not remove the larger rust nodules

In both of these cases the results of the tests showed a small systematic shift upward in the value of the discharge coefficient after about

24 hours of continuous running. However, the magnitude of the shift was within the expected performance of the measurement system.

VI-3C. Initiation of Testing of the Mild Steel Meter Tubes

Even though the results of tests on the

and on the mild steel meter tube were s proceed with the generation of a viable

were made to proceed with that testing,

steel meter tubes and the 4- inch stainl

begin the week of June 3. The mild ste

mentioned earlier and had not been run

4- inch stainless meter tube had been ob

dard during this final attempt to devel

GRI stainless steel meter tube

omewhat conflicting, the need to

data base was great and plans

Testing of both 3 -inch mild

ess meter tube were scheduled to

el tubes had been refurbished as in the flow facility at all. A

tained to act as a check stanop the data base. The tests

477-
were scheduled to run on a three shift per day basis with the following

objectives

:

1. Determine the amount of time necessary to complete testing of a set

of seven plates (Beta ratio 0.1 to 0.75) with a single set-up of the

meter tube. This was expected to be 24 to 30 hours of continuous

operation based on previous, shorter-term tests.

2. Develop data on two of the mild steel meter tubes (complete two

passes on FE-6ABC)

.

3. Develop the base-line data (two replicates) for the 4- inch stainless

meter tube. This depends upon the arrival of the meter tube. If the

tube does not arrive in time to complete two replicates, the second

replicate of FE-4ABC will be done.

4. Use a replicate test of the largest beta ratio plate to determine

whether oiling of the meter tube's interior surfaces effectively

inhibits corrosion to an extent that the test results were not affected. The largest beta ratio orifice plate was selected for this

test since past results have shown that the effect of pipe corrosion

was most pronounced in the results on the large beta ratio plates.

Operating Schedule - - Week 1 - three shifts/day

Day Meter Tube Size Plate Sequence

1 FE-4 3 - inch 6,4,5,2,3,7,1,6

2 FE-6 4 - inch 6,5,1,4,2,3,7,6

3 SS-4 4 - inch 6,4,5,2,3,7,1,6

4 FE-6 4 - inch 6,4,5,2,3,7,1,6

5 SS-4 4 - inch 6,5,1,4,2,3,7,6

In preparation for continuous testing, the flow facility sump water was substantially replaced on June 2 to obtain the lowest water temperature

possible at the beginning of the test period. The tests on the GRI

stainless steel, 3 -inch meter run, in the oiled/not oiled tests, had

raised the water temperature to above 35 °C. It was expected that as the tests progressed through the week, the water temperature would

reach rather high temperatures due to the almost continual pumping.

The water change was completed early in the evening of June 2,

The first shift of the week was begun at 22:00 hours, June 2 with the

inspection (diameter measurements and visual inspection) and mounting

of the FE-4ABC meter tube. This required several hours, including the

coating of the inner surfaces of the tube with 30 -weight non detergent

lubricating oil, API Grade SB. The meter tube was first wetted with

water at approximately 03:30 on June 3, and the initial data on the 6A

orifice plate was begun at 05:30. The intervening time, 03:30 to

478-
05:30, was necessary to clear the air from the flow lines. The first

day's schedule for the week was followed and the replicate data for the

6A plate was taken at approximately 05:30 on June 4. The meter tube was immediately taken down and dried by blowing compressed air through

the meter tube sections until the inner surfaces were dry.

Results of the First Day's Testing

1. The results of the data taken at the last of the test runs on the 6A

plate were divergent by 2 to 3 parts in 600 at the highest Reynolds

number values relative to the initial values. This divergence was a clear indication that the oil coating had not prevented corrosion

from occurring in the meter tube.

2. A visual inspection of the meter tube surfaces was made. The tube's

inner surfaces were covered uniformly with a red rusty coating which

had two distinct topologies. The first was observed in the upstream

meter tube section, FE-4A, and the upstream portion of the second

section, FE-4B. The rust was formed roughly into streaks extending

longitudinally along the tube wall. These were separated by areas which had a smaller degree of corrosion, but were still lightly cov- ered with a red dusting of rust. In these areas the original tool

marks in the tube wall could be observed visually. Near the orifice

plate flanges the streaks gave way to the second topology, a speckled

pattern of rust. The speckles were separated by areas similar in

appearance to those separating the streaks in the upstream tubes

.

The downstream meter tube, FE-4C, showed a transition from the speckled pattern to the streaked pattern about midway down its length.

The position of the weld between the flange and the meter tubing was clearly marked as a continuous ring around the tube's inner circumference .

3. Pictures were taken of the corrosion patterns near the orifice meter

flanges. Figure All is one of the photographs taken of the FE-4B

meter tube. Figure A12 shows the area around the tap hole on downstream tube FE-4C.

4. Surface roughness measurements were made using a stylus -type surface

roughness measurement instrument. A measurement was made in the

location of the previous measurements for the tube , i.e., near the

tap hole on the upstream meter tube, FE-4B. Successive readings were

190, 170, and 150 microinches. These were taken with two traverses

of the stylus comprising each reading. The downward force on the

stylus is estimated equivalent to 1 to 2 grams. The stylus was probably crushing the rust progressively as it made successive

traversals over the surface. With the use of an instrument of this

type, the apparently fragile structure of the rust was seriously

affected by the roughness measurement itself and did not accurately

reflect the surface profile of the rusty meter tube.

•479-
Figure All. Photograph of Speckled Corrosion Pattern on FE-4B,

480-
Figure A12. Photograph of Speckled Corrosion Pattern on FE-4C,

481-
The testing schedule was suspended due to these results. Designated

members of the Orifice Steering Committee were present in the flow laboratory. Both observed the condition of the meter tubes and concurred

that further testing would not be advisable. Clearly the most recent

corrosion inhibiting oil had failed to deter corrosion formation and the

effects induced by it. A meeting of the Orifice Meter Database Steering

Committee was planned.

Topographical Traces of Selected Regions on FE-4B

Characterization of the topography of the surface of the meter tubes was attempted through the use of a recording topographical instrument used

at NBS for state-of-the-art surface roughness and step height measurements. This is a stylus instrument having a resolution in the submicrometer range (1 micrometer = 39.37 microinches) . In this way an estimate

of the height of the rust patches observed in the upstream (FE-4B) meter

tube section could be made. Figure A13 shows two of these traces. Each

trace was taken at a different position in the meter tube near the upstream orifice flange face. Both were taken over a traverse of approximately 750 micrometers (0.030 inches) along the axis of the meter tube.

The horizontal scale of each trace is the traverse direction. The rev- ersal of the traverse is clearly shown by the traverse direction trace

given at the top of plot. Unlike the instrument used for the measure- ment described under item 4 above, this instrument had an extremely

small down force and did not appear to disturb the major features of the

surface topography. In the top plot the surface shows abrupt changes in

height in the 40- to 50-micrometer range (0.0016 to 0.0020 inches).

Both traces show an inclined background height. This was caused by

small differences in parallelism between the motion axis of the instrument and the surface of the meter tube

.

The topography observed at the second position (bottom trace) shows less

dramatic changes in surface height. This trace was taken at a point

selected to pass through a rust- free area of the meter tube and pass

over one of the rust patches. The position of the rusty patch is shown

in the plot. The initial step at the edge of the rust patch appears to

be approximately 40 micrometers in amplitude with approximately the same level of height variation inside the patch as that observed outside the

patch. The topography outside the patch shows intermittent large height

changes of 10- to 20-micrometer amplitude. These may be the tool marks

made during the refurbishing of the meter tube. Although these are considerably larger than the 170- to 190-microinch rms average surface

roughness value observed with the instrument of item 4 above, it should

be stressed that the normally quoted surface roughness values are aver- age values over the length of the trace. Within the trace, step heights

considerably larger than the rms value will occur and are offset in the

average value by much smaller background values. This behavior is seen

in the areas between the peaks where the local topography is much smaller than the step amplitudes.

-482-
FE-4B Meter Tube Section - Position 1

FE-4B iVleter Tube Section - Position 2

TOPOGRAPHICAL TRACES OF FE-4B

Figure A13. Topographic Traces of the Speckled Corrosion Pattern

in FE-4B

-483.
These topographical measurements quantified the height of the rust patches in the meter tubes and gave some indication of the topology of

those portions of the meter tube which were essentially unaffected by

corrosion. These measurements showed clearly that even small amounts

of rust roughened the surface to a degree greater than the 300 -micro

inch level allowed for a commercial grade meter tube by AGA

Report No. 3.

Further Action by the Orifice Steering Committee

The API Orifice Meter Database Project Steering Committee met on June 5, 1985. The result of the meeting was a request by the committee

for NBS to use another oil for corrosion inhibition. This oil was nor- mally used for storing meter tubes after manufacture. It was obtained

and arrived at NBS in the late morning of June 7. The testing of the

FE-4ABC (3- inch) meter tube was scheduled for June 10. A siommary of

the report of the tests run using this oil is given below.

Summary of Data Collected on Meter Tube FE-4, Orifice Plate 6A

June 10, 1985

Tube Preparation

Recondition the meter tube surfaces using the rotating sanding belt

method.

Oil the meter tube surfaces with (the corrosion inhibiting oil)

using the paint roller method used before. (Application was done

liberally since the corrosion inhibiting oil appeared to have a viscosity near that of kerosene.)

Experiment Objective

Determine the amount of time required for the discharge coefficient

to increase due to corrosion of the meter tube surfaces after having

been coated with Rust Veto No. 377 [3].

Data Collection Procedures

Mount the meter assembly and run continuously with data collected

approximately every hour at the differential pressure (Reynolds

number) most sensitive to the effect, i.e., 28 psi, with the Beta

0.75 orifice plate.

•484-
Run No. Time Differential Discharge Coefficients

Press. (psi) Ruska Upper Lower

37 - 39 11:03 28 .60633 .60635 .60690

49 - 51 12:12 28 .60633 .60632 .60690

58 - 60 13:14 28 .60628 .60631 .60687

61 - 63 14:26 28 .60643 .60649 .60691

70 - 72 15:25 28 .60650 .60652 .60690

Run No. Time Differential Discharge Coefficients

Press. (psi) Ruska Upper Lower

73 - 75 16:07 28 .60645 .60648 .60692

79 - 81 17:18 28 .60640 .60645 .60690

82 - 84 18:33 28 .60645 .60651 .60698

85 - 87 19:19 28 .60654 .60659 .60699

88 - 90 20:25 28 .60645 .60653 .60703

91 - 92 21:22 28 .60663 .60669 .60712

21:30 to 22:45 - Meter Tube Taken Down for Inspection - The tube was

air dried with compressed air as soon as possible after removing it

from the test rack. Very little rust could be seen. The tube sur- faces were 85 to 95% bright metal. The effects of the previous

rusting were evident visually in the small pitting of the tube wall.

Small flecks of rust could be observed in an approximately random

pattern uniformly along the wall. These flecks were not prominent.

No rust patches of any size could be seen.

Run No. Time Differential

Press, (psi)

Discharge Coefficients

Ruska Upper Lower

93 - 95 23:05 28 60653 60659 60705

The differential pressure was reduced to 0.4 psi or below and the

system was allowed to run for approximately 6 or 7 hours.

6/11/85 - Continuation of observations

98 - 100 06:07 28 .60786 .60787 .60858

Meter Taken Down for Inspection - The coverage of rust had

increased. Although the general appearance was of a larger coverage

of the rust than the previous inspection, the amount of bright metal

surface was definitely the majority of the meter tube surface.

Pictures of all tubes in the vicinity of the flanges were taken.

The tube was air dried using compressed air as soon as possible

after removing from the test rack. The meter tube was replaced in

the test rack and the following results were obtained to insure that

the previous values were not a fluke.

485-
101 - 103 10:24 28 .60794 60795 60855

The meter tube was dismounted from the test rack and inspected,

tube surfaces were essentially unchanged from the previous

observation.

The

Since the majority of this test had been run with the pipe Reynolds

number at the maximum value for this beta ratio, and the stability

of the discharge coefficient values did not degrade until the

Reynolds number was reduced, a second test was begun. The Reynolds

number was to be set to a low value for the beta 0.75 plate, but in

the region where a substantial number of tests would be needed for

the smaller beta ratio plates. This flow rate was to be maintained

except for the period of data collection at 28 psi. The meter tube was again treated with the sanding belts to remove the rust, thereby

returning the meter tube surface to a nearly 100% bright metallic

color, the diameter was measured, the rust inhibiting oil was applied to all meter tube inner surfaces, and the test was started.

The following table lists the results.

Run No. Time Differential Discharge Coefficients

Press, (psi) Ruska Upper Lower

107 - 109 12:46 28 .60608 .60609 .60644

110 - 112 13:36 28 .60612 .60615 .60654

113 - 115 14:45 28 .60607 .60614 .60651

116 - 118 15:40 28 .60613 .60615 .60656

119 - 121 16:39 28 .60623 .60625 .60667

122 - 124 20:02 28 .60679 .60706 .60728

125 - 127 23:07^ 28 .60821 .60843 .60855

128 - 130 00:29^ 28 .60811 .60829 .60845

^ Reynolds Number maintained near 28 psi shortly before run no. 125 through the end of this test.

The NBS principal investigator visually inspected the meter tube.

The following are his observations.

The interior surfaces of the meter tube had a very different

appearance compared with that observed in this meter tube following the runs of June 3 and 4. In this case the meter tube con- tained two very distinct regions with disparate corrosion topographies. As with the previous rusting topography (June 3 & 4)

,

•486-
the two distinctive regions were characterized by streaked and

speckled patterns. The streaked pattern was the most pronounced,

covering all of the two upstream sections, FE-4A and B. The

speckled region extended several diameters from the face of the

orifice flange of the C tube section with streaks forming in its

downstream half. The predominant feature was the streaked region.

The streaks are quite prominent because the areas separating them

are brightly metallic with essentially no rust on them, much as they appeared before starting the test. The streaks themselves

are comprised of a continuous patch of closely spaced rust nodules

in a contiguous line parallel to the axis of the tube. The width

of the streaks is approximately 1/8 to 3/16 of an inch. There are

24 of them distributed around the circumference of FE-4B viewed

from the upstream orifice plate flange. All of the streaks

terminate at a distance of 5/8 of an inch from the upstream

orifice plate flange face. The variation in this distance is very

small, 1/16 of an inch or less. A well defined, continuous ring

of corrosion is seen at the position of the weld between the tube

and the flange. I would emphasize that the areas between these

streaks are essentially free of corrosion and bright metallic in

color. There are a few isolated rust nodules in these areas, but

their coverage is a quite small percentage of the bright areas.

The appearance of FE-4C, at the downstream orifice plate flange,

is quite different. There are patches of rust, comprised of the same type of nodules making up the streaks, randomly placed along

and around the tube for the first 3 to 5 diameters of the tube.

There are three prominent patches between the flange face and the

tap holes with other smaller patches or single nodules and flecks

of rust on the basic bright metallic surface. I would estimate

roughly that the corrosion coverage is 2 to 5% of the total interior surface area of this region of FE-4C.

The streaks seen in the middle tube section, FE-4B, are continued

through FE-4A along its entire length and appear to continue

across the surface of the beta 1.0 sealing plate between the A and

B sections.

The results of these tests were communicated to the API Program Manager

as the testing progressed. A meeting of the Orifice Meter Database

Steering Committee and NBS personnel was held at 9:00 a.m., June 14.

The results discussed above were presented to the committee by the NBS

Principal Investigator. NBS proposed that the meter tube surface

roughness level be stabilized by electroless nickel plating the meter

tubes; a plating thickness of 0.001 inch was recommended.

VI. Nickel plating of FE-6: The End of Corrosion- Induced Effects on

the Database

As part of the NBS proposal to the API Orifice Meter Database Steering

Committee it was agreed that should the orifice project steering com487'
mittee agree with the NBS proposal to electroless nickel plate the 4-

inch meter tube, FE-6ABC, control tests of the meter tube, subsequently

termed bare tube tests , would be run on the largest beta ratio plate

prior to plating. These tests would be run in the shortest amount of

time possible to minimize the potential for corrosion of the tube sur- faces . The reason for taking this data was to provide data with which

to determine whether plating of the meter tube caused any detectable

difference in the resulting discharge coefficient values.

On June 17,1985 the final approval for plating of the FE-6ABC meter

tube was given. The bare tube tests were completed the morning and

early afternoon of June 18 and the meter tube taken to be plated the

following day. The meter tube was plated with a nominal thickness of

0.001 inches of nickel and returned to the NBS site Friday, June 21.

The FE-6ABC meter tube was inspected after the bare tube test. No sign

of corrosion was noted on the inner surfaces after the 3-hour test was

completed. At that time the tube surface was a bright metallic color

on which there were isolated pits having a dark color. These were very

shallow and thought to be remaining from the original pitting of the

meter tube. The entire meter tube was electroless nickel plated. The

appearance of the inside surfaces were very similar to the appearance

before plating, i.e., the tool marks made during the honing process

were visually unchanged. The color of all tube surfaces was a silver

matte finish. The internal diameter measurements were repeated. These

showed a very small decrease in the mean value of the diameter.

Surface topography traces were made on PE-6B before it was run. One of

these is shown in figure A14. Although there are steps of approximately 300-microinch height observed in the surface structure, probably the

tool marks developed during refurbishment, the structure is more uniform in character and has a generally smaller amplitude than the traces

of the rusted tube shown in figures A12 and A13. The photograph in

figure A15 shows the interior surface near one of the tap holes. The

surface is evenly finished with the tool marks clearly visible.

The PE-6ABC meter tube was mounted in the water flow facility test rack

and tests of the 6C plate were begun June 24. The preliminary results

of these tests showed no discernible change from the bare meter tube

results. A second plate was also run that day. The meter tube was opened for inspection at the end of the day. After approximately 8

hours of running the meter tube showed some minor discoloration of the

surface where rusting had occurred through a few pin holes in the plating, and a small section in the downstream meter tube section, PE-6C,

which was discolored, as if the plating was breached in a one-half by 5- or 6 -inch long strip. No change in the surface finish was evident to

the touch. These results were reported to the Orifice Steering

Committee in a conference call June 27. NBS proposed that one meter

tube of each size be plated. Additionally, the scope of the bare meter

-488-
cgo

0)

<D

«-•

CD

COI LU

Q.

aoC

•H

•u

CO .H

PhiH

Q) ^ o V z

•H

h- CO < cn _l

Q. o

1-1 _J •u LU 0) my W ^ z

^co

C/5 >^

LLI LJJ r-i o pJ 4-1 < 2

n3 •H oc F 13 ^= .^

CUe o 1 >- LU 1—1 X -1 c Q. Ill CU

OGRA

FTER

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cn

0)a

to

O ^ H H >. u

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•H

Ph pq h- CO >X) U 1 < bO W O Ph Q fX LU H O

60

•H

-489-
-!^^SS^s":*^^

^•:3^^*^1

Figure A15. Photograph of the Tap Hole of PE-6B.

490-
tube testing was proposed to be enlarged to 6 hours to include an orifice plate of nominal beta ratio 0.375 in order to cover the

envelope of observed, corrosion induced effects.

Testing of all of the C series plates (beta ratio 0.1 to 0.75) in

PE-6ABC was completed July 1. Additional tests of the 6C plate (beta

ratio 0.75) were included to test for the effects of changes in the

surface roughness from corrosion. During these tests the meter tube was opened frequently for visual inspections. The results of these

inspections were that the appearance of the inner meter tube surface

did not change from the initial rust staining at the pin holes which

occurred during the first day of running. Additionally, the light

dusting of rust which had always appeared on the orifice plate surfaces

after previous tests with the mild steel meter tubes, was absent. The

data for all plates replicated itself very well with the exception of one pass on one plate. A third pass on the beta 0.75 plate resulted in

the third pass replicating the initial pass very well.

VIII. Completion of the Database and the Project

The remainder of the meter tubes were plated with a 0.001 nominal

thickness of electroless nickel much as FE-6ABC was. The two plate,

bare tube test schedule was run on each. The bare tube tests were denoted with the FE designation. The designation of the meter tubes was changed to PE-6ABC, etc. to denote the addition of the nickel

plating. Completion of the data collection phase occurred in December

1985. Upon the advice of the NBS Statistical Engineering Division

observations on two plates of the PE-lABC meter tube were repeated in

January 1986. The analysis of the data base by NBS occurred over the

remainder of 1986. The API requested the rerunning of certain of the

small beta ratio plates. This occurred in early 1987.

IX. References

[Al] American Gas Association Report No. 3., Amer. Gas Assoc, Catalog

No. XQ0178, Arlington, VA, also American National Standard

Institute/American Petroleum Institute 2530.

[A2] Stolz, J., "A Universal Equation for the Calculation of Discharge

Coefficients of Orifice Plates," FLOMEKO 1978, IMEKO Conference on Flow Measurement of Fluids, Groningen, North-Holland, Amsterdam,

1978; also found in ISO 5167.

[A3] Beitler, S. R. , "The Flow of Water Through Orifices," The Ohio

State University, Engineering Experiment Station Bulletin 89,

73 pgs. , May 1935.

-491-
II
APPENDIX B

Water Density Measurements

Measurements of the density of samples of the water flowing in the NBS

flow facility were made using a vibrating tube technique [Bl] . This is a comparative technique requiring two liquids of known density over the

range of temperatures used. The equation governing the operation of the

comparator is the following:

p^ - P2 = K (T^ - T^)

where p^ = Density of liquid 1 P2 = " " " 2 T, = Period of Oscillation for liquid 1

T^ = Period of Oscillation for liquid 2

Calibration of the comparator must be done for each measurement temperature. This temperature is maintained very near a constant value set

by a thermostatic jacket surrounding the measurement cell. Temperature

measurements of the cell are made by placing a suitable thermometer in a re-entrant tube of the cell. A thick film platinum resistance thermometer (PRT) , which had been previously calibrated against a standard

platinum resistance thermometer, was used for this purpose. The uncer- tainty in the temperature measurement using the thick film PRT is

estimated to be approximately 0.12 degrees Celsius.

The calibration liquids used were distilled water and a sample of xylene

having previously assigned density values over this temperature range

[B2] . Computation of the density of distilled water was made using the

correlation of Kell [B3]. For both liquids the density is computed from

the temperature of the measurement, T, as determined from the thick film

platinum resistance thermometer. The mathematical relations used are

the following:

Xylene Density p = 884.671 - 0.86147 T

Distilled Water Density

p = ) n

'^w /

A T^

n=0

1 -I- CT

where A = 999,,83952

A^ -

16,

-7,

-46,

105,

,945176

.9870401 X

.170461 X

,56302 X

10'

10'

10"

3

6

9

•12

^=:

-208,

16,

.54253 X

.879850 X

10'

10"3

3 The density of both is given in units of kg/m . Temperature values are

in degrees Celsius.

-493-
The measurement sequence consisted of observation of the comparator

response, or period value, beginning with the distilled water and

xylene. These observations allowed the value of the instrument

constant, K, to be determined. Subsequently, the samples of unknown

density were loaded into the comparator cell and several successive

observations of the period values for each were made after stabilization

of the PRT resistance value. The period was judged to be valid if

successive period values repeated one another within two to four counts

of the device. (One count of the device corresponds to approximately

0.001 kg/m or approximately 1 part per million for these water

samples . ) Table Bl gives the mean values of the observations for the

calibration liquids and the water samples and the results of the

measurements. The column labeled Diff. is the difference between the

density of the reservoir sample and that of distilled water at the

temperature at which the reservior sample is measured. The average

value is given at the bottom of the table. This value represents the

average offset between the density of distilled water and the water

obtained periodically from the local city water supply used to fill the

reservior. This difference is attributable to the dissolved mineral

content of the water. Its effect is considered not to be temperature

dependent. In computing the density of the water used in this test this

value will be used.

Table Bl . Measured Density Values for Water Samples

Sample Type Period PRT Temperature Density Diff

Value Resistance

(sec) ( ohms (kg/m^ (kg/m

)

(Deg. C)

Dist. Water 38.67970 1086.06 22.191 997.728

Xylene 37.37086 1086.04 22.186 865.555

8/02/85 38.68136 1086.03 22.184 997.898 0.182

7/18/85 38.68145 1086.03 22.184 997.910 0.170

6/25/85 38.68142 1086.00 22.176 997.908 0.178

8/02/85 38.68142 1086.05 22.189 997.905 0.177

1/09/85 38.68109 1086.05 22.189 997.871 0.143

10/20/83 38.68174 1086.04 22.186 997.938 0.209

7/24/85 38.68140 1086.05 22.186 997.903 0.175

12/27/84 38.68212 1086.05 22.186 997.977 0.250

4/05/86 38.68224 1086.06 22.191 997.989 0.262

Computed Instrument Constant = 1.3278645 Average Diff. 0.194

The uncertainty in these density measurements is composed of three

components, the precision of the comparator, the uncertainty of the

standard liquids, and the uncertainty in the temperature measurement.

The precision of the comparator appears to be approximately 1 to 2 counts in the period value. This corresponds to approximately 0.001 to

0.002 kg/m . The uncertainty in the density of distilled water as computed from the Kell formula is estimated by Kell to be approximately

0.010 kg/m . A similar value is the case for the xylene. The largest

contributor to the uncertainty in this series of density measurements is

•494-
due to the platinum resistance thermometer used. This was a 1000 ohm

device which had been calibrated previous to its use. A fit of its

resistance as a function of temperature in degrees Celsius was made

resulting in the following relation:

Temperature = -260.548 + 0.260355 x Resistance

The residual standard deviation of this fit is 0.040 degrees. This

value is tripled to obtain the 99% confidence level, and the uncertainty

in the temperature measurement is taken to be 0.120 degrees Celsius.

The effect of this uncertainty in the temperature on the density values

of the standard liquids is approximately 0.034 kg/m for the distilled

water and 0.106 kg/m for the xylene. These are treated as systematic

errors in the measurement and are considerably larger than the comparative uncertainty. These uncertainties must be applied to the absolute

values of the density assigned to each sample. However, the difference

values between the reservoir samples and distilled water are primarily

influenced by the uncertainty in the distilled water density value

computed from the temperature measurements and by the comparative pre- ^ cision. These are combined additively to give approximately 0.045 kg/m

in the difference value

.

References

[Bl] Kratky, 0., Leopold, H. , and Stabinger, H. , Angew. Phys . 27,

(1969).

[B2] Whetstone, J. R. , et al .

, National Bureau of Standards Internal

Report 78-1533, 1978.

[B3] Kell, G. S., "Density, Thermal Expansivity, and Compressibility of

Liquid Water from to 150°C: Correlations and Tables for

Atmospheric Pressure and Saturation Reviewed and Expressed on 1968

Temperature Scale," J. Chem. and Eng. Data, Vol. 20, No.l (1975).

495-

APPENDIX C

Differential Pressure Transducer Coefficient Values

Table CI. Response Model Coefficients for the Ruska Transducer

Serial Number 30827 Connected to the Upper Orifice

Meter Taps

Date Zero AP

Response

^1 S

Residual

Std. Dev

(volts.) (psid) (psid/volt) (psid)

06/10/85 0.0054 0.00086 2.88919 0.00044

06/14/85 0.0048 0.00055 2.88933 0.00094

06/17/85 0.0051 0.00128 2.88929 0.00043

06/18/85 0.0051 0.00178 2.88922 0.00082

06/24/85 0.0053 0.00100 2.88912 0.00088

06/25/85 0.0051 0.00060 2.88913 0.00070

06/26/85 0.0052 0.00017 2.88917 0.00067

07/01/85 0.0020 0.00078 2.88927 0.00076

07/02/85 0.0020 0.00078 2.88927 0.00076

07/03/85 0.0038 0.00038 2.88919 0.00046

07/05/85 0.0045 0.00102 2.88909 0.00049

07/08/85 0.0050 0.00100 2.88912 0.00069

07/09/85 0.0046 0.00077 2.88914 0.00052

07/12/85 0.0050 0.00129 2.88911 0.00040

07/15/85 0.0049 0.00116 2.88922 0.00108

07/16/85 0.0053 0.00204 2.88913 0.00102

07/17/85 0.0041 0.00102 2.88921 0.00055

07/18/85 0.0044 0.00100 2.88927 0.00082

07/24/85 0.0040 0.00081 2.88920 0.00051

07/25/85 0.0045 0.00040 2.88928 0.00114

07/26/85 0.0041 0.00047 2.88921 0.00101

07/29/85 0.0046 -0.00049 2.88930 0.00080

07/30/85 0.0046 -0.00009 2.88920 0.00120

07/31/85 0.0045 -0.00060 2.88935 0.00090

08/01/85 0.0045 0.00022 2.88927 0.00064

08/02/85 0.0042 -0.00042 2.88927 0.00123

08/05/85 0.0041 -0.00000 2.88916 0.00103

08/06/85 0.0042 0.00065 2.88912 0.00053

08/07/85 0.0043 -0.00097 2.88930 0.00073

08/08/85 0.0043 -0.00030 2.88923 0.00061

08/09/85 0.0042 -0.00014 2.88927 0.00115

08/12/85 0.0021 0.00172 2.88906 0.00064

08/13/85 0.0048 0.00081 2.88904 0.00082

08/14/85 0.0079 0.00160 2.88925 0.00108

08/19/85 0.0049 0.00069 2.88902 0.00078

08/23/85 0.0023 -0.00064 2.88908 0.00062

08/26/85 0.0016 0.00003 2.88897 0.00087

08/27/85 0.0004 -0.01179 2.88952 0.01665

08/28/85 0.0051 -0.00080 2.88948 0.00201

08/29/85 0.0008 -0.00236 2.88907 0.00086

08/30/85 0.0017 -0.00004 2.88906 0.00067

09/03/85 0.0003 -0.00253 2.88921 0.00064

497-
Table CI. Response Model Coefficients for the Ruska Transducer

Serial Number 30827 Connected to the Upper Orifice

Meter Taps -- Continued

Date Zero AP

Response

h =2 Residual

Std. Dev

(volts.

)

(psid) (psid/volt) (psid)

09/04/85 0.0001 -0.00188 2.88910 0.00048

09/05/85 0.0002 -0.00065 2.88896 0.00058

09/06/85 -0.0001 0.00036 2.88906 0.00055

09/09/85 -0.0011 0.00000 2.88919 0.00081

09/10/85 -0.0009 0.00107 2.88911 0.00053

09/11/85 -0.0010 0.00159 2.88904 0.00069

09/13/85 -0.0011 0.00012 2.88906 0.00058

09/17/85 -0.0012 -0.00031 2.88901 0.00070

09/18/85 -0.0012 -0.00047 2.88909 0.00061

09/19/85 -0.0014 0.00008 2.88899 0.00061

09/20/85 -0.0013 0.00003 2.88915 0.00037

09/24/85 -0.0013 0.00102 2.88917 0.00070

09/25/85 0.0043 0.00657 2.88995 0.00604

09/26/85 0.0044 0.00076 2.88892 0.00073

09/27/85 0.0050 0.00118 2.88905 0.00084

09/30/85 0.0050 -0.00012 2.88896 0.00094

10/09/85 0.0039 0.00104 2.88904 0.00037

10/09/85 0.0039 0.00104 2.88904 0.00037

10/11/85 0.0042 0.00169 2.88909 0.00173

10/15/85 0.0044 0.00150 2.88900 0.00041

10/16/85 0.0045 0.00149 2.88903 0.00090

10/17/85 0.0044 0.00025 2.88904 0.00038

10/22/85 0.0043 -0.00000 2.88894 0.00111

10/23/85 0.0042 0.00068 2.88895 0.00035

10/24/85 0.0043 0.00096 2.88902 0.00060

11/06/85 0.0267 0.01326 2.89737 0.00497

11/07/85 0.0049 0.00098 2.88895 0.00077

11/08/85 0.0046 0.00071 2.88895 0.00066

11/12/85 0.0042 0.00070 2.88898 0.00067

11/13/85 0.0041 0.00075 2.88897 0.00080

11/14/85 0.0040 0.00168 2.88897 0.00048

11/15/85 0.0040 0.00173 2.88892 0.00070

11/18/85 0.0037 0.00054 2.88902 0.00047

11/19/85 0.0036 0.00061 2.88905 0.00078

11/20/85 0.0035 0.00177 2.88894 0.00065

11/21/85 0.0032 -0.00035 2.88898 0.00088

11/22/85 0.0000 0.00000 0.00000 0.00000

12/04/85 0.0045 -0.00004 2.88899 0.00025

12/05/85 0.0042 -0.00077 2.88895 0.00057

12/06/85 0.0045 -0.00055 2.88899 0.00050

12/09/85 0.0044 -0.00034 2.88898 0.00061

12/10/85 0.0043 -0.00126 2.88887 0.00070

12/30/85 0.0035 -0.00063 2.88897 0.00074

01/07/86 0.0039 -0.03044 2.90353 0.09070

498
Table C2

Date

06/03/85

06/10/85

06/14/85

06/17/85

06/18/85

06/24/85

06/25/85

06/26/85

07/01/85

07/02/85

07/03/85

07/05/85

07/08/85

07/09/85

07/12/85

07/15/85

07/16/85

07/17/85

07/18/85

07/24/85

07/25/85

07/26/85

07/29/85

07/30/85

07/31/85

08/01/85

08/02/85

08/05/85

08/06/85

08/07/85

08/08/85

08/09/85

08/12/85

08/13/85

08/14/85

08/16/85

08/19/85

08/23/85

08/26/85

08/27/85

08/28/85

08/29/85

08/30/85

Response Model Coefficients for the Paros Transducer

Serial Niimber 13150 Connected to the Upper Orifice

Meter Taps

Zero AP

Response

(microsec .

)

25.59684

25.59669

25.59776

25.59778

25.59776

25.59767

25.59751

25.59751

25.59732

25.59732

25.59736

25.59743

25.59743

25.59735

25.59736

25.59735

25.59740

25.59747

25.59750

25.59738

25.59749

25.59723

25.59736

25.59736

25.59727

25.59734

25.59736

25.59739

25.59739

25.59745

25.59743

25.59744

25.59737

25.59755

25.59744

25.59741

25.59739

25.59752

25.59756

25.59750

25.59762

25.59757

25.59760

(psid)

0.00095

0.00023

0.00067

0.00135

0.00220

0.00033

•0.00162

•0.00129

0.00006

0.00006

0.00044

0.00173

0.00116

0.00053

0.00132

0.00100

0.00173

0.00200

0.00152

0.00053

0.00097

0.00109

0.00036

0.00061

0.00205

0.00072

0.00148

0.00052

0.00010

0.00070

-0.00066

0.00012

0.00082

0.00187

0.00103

0.00050

0.00058

0.00047

0.00031

0.00030

0.00031

-0.00035

0.00024

B

(psid)

448.7446

448.6931

449.0188

449.0262

449.0067

449.0287

448.9875

448.9802

449.0227

449.0227

448.9887

448.9725

448.9723

448.9830

448.9643

449.0201

449.0620

449.0032

449.0750

448.9635

448.9855

449.0392

449.0013

449.0097

449.0534

448.9954

449.0253

449.0149

448.9466

448.9735

449.0058

448.9768

448.8544

448.9474

448.9851

448.9158

448.8405

448.8501

448.7809

448.8625

448.8756

448.8288

448.8561

(psid)

•121.940

•121.516

•117.534

•117.877

•117.964

•118.668

•118.331

•118.100

•118.628

•118.628

•118.112

•117.925

•117.665

•117.984

•117.838

•118.573

•119.310

•118.117

•119.233

•118.045

•117.735

•119.145

•118.679

•118.693

•119.158

•118.232

119.061

•119.688

•118.374

•118.211

•119.004

118.810

•117.971

•119.279

•119.816

•119.388

•118.598

117.922

•117.840

119.810

119.827

119.248

119.712

Residual

Std. Dev.

(psid)

0.00088

0.00070

0.00067

0.00059

0.00079

0.00097

0.00133

0.00109

0.00093

0.00093

0.00066

0.00074

0.00086

0.00059

0.00055

0.00108

0.00080

0.00069

0.00086

0.00066

0.00119

0.00089

0.00071

0.00138

0.00099

0.00082

0.00156

0.00130

0.00063

0.00060

0.00069

0.00117

0.00113

0.00090

0.00084

0.00094

0.00095

0.00084

0.00078

0.00105

0.00101

0.00072

0.00043

•499-
Table C2 . Response Model Coefficients for the Paros Transducer

Serial Number 13150 Connected to the Upper Orifice

Meter Taps - - Continued

Date

09/03/85

09/04/85

09/05/85

09/06/85

09/09/85

09/10/85

09/11/85

09/13/85

09/16/85

09/17/85

09/18/85

09/19/85

09/20/85

09/24/85

09/25/85

09/26/85

09/27/85

09/30/85

10/09/85

10/09/85

10/11/85

10/15/85

10/16/85

10/17/85

10/22/85

10/23/85

10/24/85

11/06/85

11/07/85

11/08/85

11/12/85

11/13/85

11/14/85

11/15/85

11/18/85

11/19/85

11/20/85

11/21/85

11/22/85

Zero AP

Response

(microsec.

)

25, 59752

25.59756

25.59767

25.59763

25.59762

25.59768

25.59767

25.59760

25.59761

25.59768

25.59764

25.59767

25.59763

25.59761

25.59768

25.59764

25.59767

25.59755

25.59755

25.59755

25.59757

25.59756

25.59760

25.59767

25.59751

25.59754

25.59756

25.59762

25.59763

25.59764

25.59765

25.59761

25.59759

25.59758

25.59755

25.59761

25.59749

25.59757

25.59762

(psid)

0.00246

0.00172

0.00065

0.00006

0.00051

0.00077

0.00114

0.00035

0.00090

0.00042

0.00025

0.00026

0.00020

0.00040

0.00089

0.00075

0.00095

0.00064

0.00110

0.00110

0.00159

0.00172

0.00108

0.00043

0.00013

0.00066

0.00125

0.00164

0.00087

0.00090

0.00148

0.00067

0.00169

0.00136

0.00068

0.00033

0.00129

0.00102

0.00069

B

(psid)

448.8151

448.8282

448.8135

448.8053

448.7766

448.7926

448.8131

448.7672

448.7689

448.8028

448.7461

448.7910

448.7845

448.8559

448.8476

448.7944

448.8900

448.8541

448.7829

448.7829

448.8263

448.7854

448.8554

448.8204

448.8612

448.7871

448.8096

448.8437

448.8750

448.8481

448.8444

448.8881

448.8601

448.8471

448.8324

448.9084

448.8292

448.9148

448.8521

(psid)

•119.298

119.835

120.192

120.093

119.773

119.796

120.228

119.659

119.546

120.300

119.045

120.064

119.359

•120.301

120.333

119.599

120.563

121.114

119.424

119.424

120.277

119.751

•120.631

119.813

121.473

119.854

120.034

120.744

120.862

120.240

120.182

•120.641

120.331

120.217

120.123

121.059

120.024

121.369

120.079

Residual

Std. Dev.

(psid)

0.00074

0.00042

0.00054

. 00044

0.00087

0.00071

0.00037

0.00076

0.00105

0.00083

0.00088

0.00066

0.00062

0.00062

0.00054

0.00054

0.00062

0.00080

0.00066

0.00066

0.00068

0.00046

0.00043

0.00035

0.00094

0.00060

0.00092

0.00051

0.00050

0.00048

0.00075

0.00064

0.00040

0.00061

0.00053

0.00045

0.00055

0.00088

0.00033

-500^
Table C2 . Response Model Coefficients for the Paros Transducer

Serial Number 13150 Connected to the Upper Orifice

Meter Taps - - Continued

Date

12/04/85

12/05/85

12/06/85

12/09/85

12/10/85

12/30/85

01/07/86

Zero AP

Response

(microsec .

)

25.59748

25.59746

25.59742

25.59737

25.59737

25.59710

25.59724

(psid) (psid)

0.00108

0.00009

0.00014

0.00039

0.00077

0.00036

0.00041

449.0544

449.1114

449.1095

449.1084

449.1702

449.0776

449 . 1444

(psid)

•119.458

119.668

119.257

•119.196

•120.004

•119.195

119.541

Residual

Std. Dev.

(psid)

0.00042

0.00028

0.00046

0.00056

0.00066

0.00030

0.00053

-501-
Table C3

Date

06/03/85

06/10/85

06/14/85

06/17/85

06/18/85

06/24/85

06/25/85

06/26/85

07/01/85

07/02/85

07/03/85

07/05/85

07/08/85

07/09/85

07/12/85

07/15/85

07/16/85

07/17/85

07/18/85

07/24/85

07/25/85

07/26/85

07/29/85

07/30/85

07/31/85

08/01/85

08/02/85

08/05/85

08/06/85

08/07/85

08/08/85

08/09/85

08/12/85

08/13/85

08/14/85

08/16/85

08/19/85

08/23/85

08/26/85

08/27/85

08/28/85

08/29/85

Response Model Coefficients for the Paros Transducer

Serial Number 12200 Connected to the Lower Orifice

Meter Taps

Zero AP

Response

(microsec .

)

25.21105

25.21102

25.21104

25.21108

25.21108

25.21105

25.21098

25.21093

25.21107

25.21107

25.21113

25.21120

25.21118

25.21113

25.21118

25.21122

25.21124

25.21131

25.21135

25.21140

25.21133

25.21120

25.20285

25.20285

25.20279

25.20283

25.20290

25.20299

25.20294

25.20299

25.20301

25.20305

25.20306

25.20319

25.20312

25.20322

25.20335

25.20344

25.20347

25.20344

25.20352

25.20351

B

(psid) (psid)

0.00007

0.00036

0.00073

0.00138

0.00230

0.00061

0.00067

0.00078

0.00007

0.00007

0.00075

0.00216

0.00127

0.00094

0.00139

0.00157

0.00176

0.00219

0.00160

0.00106

0.00067

-0.00072

0.00024

0.00032

0.00162

-0.00048

0.00096

0.00024

0.00026

0.00061

0.00052

0.00007

0.00129

0.00180

0.00116

0.00093

0.00125

-0.00191

0.00047

0.00051

0.00079

0.00002

512.7597

512.7783

512.8116

512.8181

512.7912

512.8100

512.7602

512.7477

512.8270

512.8270

512.7840

512.7562

512.7567

512.7656

512.7499

512.8071

512.8758

512.8037

512.8867

512.7867

512.8087

512.8676

512.8383

512.8519

512.9070

512.8560

512.8989

512.8953

512.8221

512.8538

512.8804

512.8651

512.7378

512.8442

512.8990

512.8139

512.7312

512.8495

512.7024

512.8297

512.8485

512.8010

(psid)

150.197

150.764

150.284

150.614

150.561

151.419

150.664

150.557

151.406

151.406

150.682

•150.473

150.108

150.538

150.263

151.193

152.371

150.695

151.882

150.526

150.090

151.966

-150.772

150.730

-151.546

-150.468

-151.262

-152.291

-150.584

-150.309

-151.164

-150.962

-149.960

-151.363

-152.317

-151.520

-150.401

-150.927

-149.415

-151.876

-151.627

-151.029

Residual

Std. Dev.

(psid)

0.00071

0.00037

0.00065

0.00032

0.00063

0.00061

0.00086

0.00069

0.00055

0.00055

0.00035

0.00041

0.00049

0.00038

0.00030

0.00061

0.00062

0.00042

0.00043

0.00038

0.00098

0.00058

0.00054

0.00119

0.00087

0.00072

0.00135

0.00107

0.00039

0.00069

0.00049

0.00112

0.00083

0.00077

0.00069

0.00070

0.00088

0.00032

0.00094

0.00081

0.00081

0.00056

502-
Table C3 . Response Model Coefficients for the Paros Transducer

Serial Number 12200 Connected to the Lower Orifice

Meter Taps - - Continued

Date

08/30/85

09/03/85

09/04/85

09/05/85

09/06/85

09/09/85

09/10/85

09/11/85

09/13/85

09/16/85

09/17/85

09/18/85

09/19/85

09/20/85

09/24/85

09/25/85

09/26/85

09/27/85

09/30/85

10/09/85

10/09/85

10/11/85

10/15/85

10/16/85

10/17/85

10/22/85

10/23/85

10/24/85

11/06/85

11/07/85

11/08/85

11/12/85

11/13/85

11/14/85

11/15/85

11/18/85

11/19/85

11/20/85

11/21/85

11/22/85

Zero AP

Response

(microsec .

)

25.20355

25.20361

25.20361

25.20371

25.20372

25.20382

25.20387

25.20393

25.20405

25.20425

25.20431

25.20433

25.20434

25.20432

25.20440

25.20443

25.20444

25.20449

25.20453

25.20458

25.20458

25.20462

25.20483

25.20477

25.20489

25.20484

25.20487

25.20495

25.20524

25.20515

25.20515

25.20607

25.20602

25.20602

25.20595

25.20620

25.20618

25.20605

25.20618

25.20626

(psid)

•0.00015

•0.00230

•0.00174

•0.00072

0.00005

•0.00036

0.00103

0.00134

0.00008

•0.00050

•0.00006

0.00033

0.00082

0.00012

0.00059

0.00067

0.00070

0.00088

0.00054

0.00103

0.00103

0.00170

0.00227

0.00109

0.00060

0.00012

0.00091

0.00177

0.00211

0.00119

0.00132

0.00161

0.00099

0.00182

0.00115

0.00114

0.00073

0.00150

0.00106

0.00076

(psid)

512.8241

512.7818

512.8185

512.8261

512.8242

512.7705

512.7967

512.8228

512.7668

512.7913

512.8236

512.7798

512.8005

512.7816

512.8194

512.8135

512.7285

512.8356

512.7771

512.6816

512.6816

512.7511

512.6942

512.7811

512.7797

512.7474

512.6684

512.7128

512.7809

512.8041

512.7560

512.7314

512.7867

512.7578

512.7405

512.7127

512.7904

512.6896

512.8356

512.7245

(psid)

•151.568

151.257

152.000

152.196

152.239

151.619

151.776

152.455

151.691

151.908

152.883

151.633

152.549

151.558

152.747

152.570

151.446

152.894

153.466

151.518

151.518

152.551

151.985

153.065

152.481

154.017

151.857

152.411

153.970

153.937

153.085

152.825

153.422

153.201

152.932

152.904

154.012

152.638

154.946

•152.869

Residual

Std. Dev.

(psid)

0.00035

0.00067

0.00045

0.00036

0.00035

0.00062

0.00042

0.00031

0.00055

0.00099

0.00072

0.00072

0.00058

0.00047

0.00048

0.00038

0.00055

0.00051

0.00062

0.00036

0.00036

0.00047

0.00058

0.00034

0.00026

0.00061

0.00038

0.00059

0.00049

0.00033

0.00047

0.00061

0.00065

0.00024

0.00049

0.00040

0.00036

0.00051

0.00069

0.00031

503-
Table C3. Response Model Coefficients for the Paros Transducer

Serial Number 12200 Connected to the Lower Orifice

Meter Taps - - Continued

i

Date Zero AP

Response

(microsec.

)

B

(psid) (psid)

C Residual

Std. Dev.

(psid) (psid) i

12/04/85

12/05/85

12/06/85

12/09/85

12/10/85

12/30/85

01/07/86

25.20767

25.20770

25.20772

25.20787

25.20785

25.20758

25.20791

0.00148

•0.00024

0.00002

0.00067

0.00075

0.00015

0.00040

512.7023

512.7867

512.7631

512.7306

512.8034

512.6372

512.7819

152.694

153.616

153.056

153.478

154.508

152.997

154.350

0.00041

. 00040

0.00050

0.00070

0.00050

0.00053

0.00049

-504-
APPENDIX D

Archival Data Base Format

Intermediate Reynolds Number Project

Format for raw data, for the Intermediate Reynolds Ntimber Data Base

Project

1. Differential pressure transducer coefficient data blocks.

The coefficient data necessary to convert the recorded pressure

transducer readings to pressure units for the water data are recorded in a series of 3 record pairs . The format for each record pair is given

here:

Record # or description Columns Format Comments

record I

transducer ID

date

observation time

fit date

transducer zero

record II

constant coefficient

linear coefficient

quadratic coefficient

fit residual standard

deviation

1

- 11 XXXXXXXXXXX

12 blank

13 - 20 MM/DD/YY

21 blank

22 - 29 HH:MM:SS

30 blank

31 - 38 MM/DD/YY

39 - 40 blank

41 - 48 +N.NNNNN

49 - 80 blank

units of /isec

for Paros-type

transducers

(upper and

lower) or volts

for the Ruska

transducer

1

- 17 +N . NNNNNNNNNNE+NN

18 - 20 blank

21 - 37 +N . NNNNNNNNNNE+NN

38 - 40 blank

41 - 57 +N . NNNNNNNNNNE+NN

58 - 60 blank

61 - 77 +N . NNNNNNNNNNE+NN

78 - 80 blank

•505-
2. Test run header data blocks.

The header data for the water data collection are recorded in five-record

blocks. The header includes the number of pressure records which follow

the header records. The format of the header records is given here:

Record # or description Columns Format Comments

record I

run number

system ID

date

time

tube

plate

upper transducer ID

lower transducer ID

1

- 4 NNNN

5

- 6 NN

7

- 14 MM/DD/YY

15 blank

16 - 23 HH:MM:SS

24 - 30 XXXXXXX

31 - 38 blank

39 - 47 XXXXXXXXX

48 - 53 blank

54 - 64 XXXXXXXXXXX

65 - 66 blank

67 - 77 XXXXXXXXXXX

78 - 80 blank

record II

tare weight (Ibm)

gross weight (Ibm) no flow correction

factor (upper, /xsec) no flow correction

factor (lower, /zsec) no flow correction

factor (Ruska, volts)

diverter time (sec)

flow temp (deg. C)

tank temp (deg. C)

air temp (deg. C)

1

- 11 NNNNNN.NNNN

12 - 22 NNNNNN.NNNN

23 - 32 NNN.NNNNNN

33 - 42 NNN.NNNNNN

43 - 52 NNN . NNNNNN

53 - 62 NNNNN . NNNN

63 - 68 NNN . NN

69 - 74 NNN.NN

75 - 80 NNN . NN

506-
Record # or description Columns Format Comments

record III

system 1 X

2

- 4 blank

upper transducer zero 5

- 14 NNN . NNNNNN

(/isec)

lower transducer zero 15 - 24 NNN . NNNNNN

(/Ltsec)

Ruska transducer zero 25 - 34 NNN . NNNNNN

(volts)

Paros offset 35 - 39 NNN.N

(//sec)

barometer 40 - 45 NNN . NN

(cm Hg)

relative humidity (%) 46 - 51 NNN . NN

52 - 54 blank

turbine count 55 - 61 NNNNNNN

62 blank

tube diameter (in.) 63 - 69 NN . NNNN

70 blank

plate diameter (in.) 71 - 77 NN . NNNN

78 - 80

record IV

check string 1 - 80 XXXX. . .XXXX Many test runs had no check

string stored.

In these cases

,

the string "NO

Check String

Recorded"

appears in

record IV and

record V does

not appear.

record V

check string (contd.) 80 XXXX. . .XXXX

•507-
3. Test run differential pressure transducer observation data blocks.

The differential pressure transducer observation data for the

Intermediate Reynolds Number data base are recorded in three blocks, one for each differential pressure transducer. Each block consists of a single identification record followed by a variable number of data

records. Each complete data record contains eight observed values, and

the last data record contains from one to eight observed values. The

header record contains the actual total number of observations to follow,

and the number of records is computed from this value. The format of the

record block is given here:

Record # or description Columns Format Comments

record I

run number

transducer

date

plate

number of observations

record II - record N

1

- 4 NNNN

5 blank

6

7

X

blank

8

- 15 MM/DD/YY

16 blank

17 - 25 NNNNNNNNN

26 blank

27 - 29 NNN

R=Ruska

,

U=upper

,

L=lower

pressure reading i

pressure

pressure

pressure

pressure

pressure

pressure

pressure

reading i + 1 reading i + 2 reading i + 3 reading i + 4

reading i + 5 reading i + 6 reading i + 7

1 - 2

3 - 11

blank

NNN . NNNNN

12 -- 20 NNN . NNNNN

21 - 29 NNN . NNNNN

30 -- 38 NNN . NNNNN

39 -- 47 NNN . NNNNN

48 - 56 NNN . NNNNN

57 -- 65 NNN . NNNNN

66 - 74 NNN . NNNNN

75 -

- 80 blank

units of /isec

for Paros-type

transducers

(upper and

lower) or volts

for the Ruska

transducer

•508-
Format for the Auxiliary File of the Intermediate Reynolds Number Project

For the Intermediate Reynolds Number data base, the auxiliary file

contains the zero differential pressure observations and the daily

transducer calibration data.

1. Differential pressure transducer zero observation data blocks.

The zero differential pressure observation file contains information

taken daily consisting of 25 observed values each for the no-flow

transducer observations and the zero differential pressure observations.

The data are recorded in four record blocks for each transducer. The

format of these records is given here:

Record # or description Columns Format Comments

record I observation type XXXXXX

transducer ID

7 blank

8-18 XXXXXXXXXXX

date

time

reading 1

record II

reading 2

reading 3

reading 4

reading 5

reading 6

reading 7

reading 8

reading 9

19 blank

20 - 27 MM/DD/YY

28 blank

29 - 36 HH:MM:SS

37 blank

38 - 45 +N . NNNNN

46 - 80 blank

1

- 8 +N. NNNNN

9 blank

10 - 17 +N . NNNNN

18 blank

19 - 26 +N . NNNNN

27 blank

28 - 35 +N . NNNNN

36 blank

37 - 44 +N . NNNNN

45 blank

46 - 53 +N . NNNNN

54 blank

55 - 62 +N . NNNNN

63 blank

64 - 71 +N . NNNNN

72 - 80 blank

units of /isec

for Paros-type

transducers

(upper and

lower) or volts

for the Ruska

transducer

-509-
Record # or description Columns Format Comments

record III

reading 10

reading 11

reading 12

reading 13

reading 14

reading 15

reading 16

reading 17

record IV

reading 18

reading 19

reading 20

reading 21

reading 22

reading 23

reading 24

reading 25

1

- 8 +N . NNNNN

9 blank

10 - 17 +N . NNNNN

18 blank

19 - 26 +N . NNNNN

27 blank

28 - 35 +N . NNNNN

36 blank

37 - 44 +N . NNNNN

45 blank

46 - 53 +N . NNNNN

54 blank

55 - 62 +N . NNNNN

63 blank

64 - 71 +N . NNNNN

72 - 80 blank

1

- 8 +N . NNNNN

9 blank

10 - 17 +N . NNNNN

18 blank

19 - 26 +N . NNNNN

27 blank

28 - 35 +N . NNNNN

36 blank

37 - 44 +N . NNNNN

45 blank

46 - 53 +N . NNNNN

54 blank

55 - 62 +N . NNNNN

63 blank

64 - 71 +N. NNNNN

72 - 80 blank

-510-
2. Differential pressure transducer calibration data blocks.

The transducer calibration data files for the Intermediate Reynolds

Number data base are recorded as a series of five record groups . Each

group contains the data for a single observation in the calibration

procedures for all three transducers. The format of the records is given

here:

record I

calibration observation

number

date

time

reference dead weight

tester serial number

test dead weight tester

serial number

test weight stack

test pressure (psig)

record II

NN

3 blank

4 - 11 MM/DD/YY

12 blank

13 - 20 HH:MM:SS

21 - 25 XXXXX

26 blank

27 - 31 XXXXX

32 blank

33 - 72 XXXX. . .XXXX . . . indicates

characters left

out

73 - 80 +NN . NNNN

reference weight stack 1-12

reference pressure (psig) 13 - 20

21

weight carrier 22 - 29

30

barometric pressure 31 - 36

(cm of Hg)

37

air temperature (deg. F) 38 - 42

43

relative humidity (%) 44-48

49

Paros offset (/isec) 50 - 54

55 - 80

xxxxxxxxxxxx

+NN . NNNN

blank xxxxxxxx blank

+NN . NN

blank

NN.NN

blank

NNN.N

blank

NNN.N

blank

511-
Record # or description Columns Format Comments

record III

transducer 1 ID

transducer 1 zero

1 - 11 xxxxxxxxxxx

12 blank

13 - 21 +NN.NNNNN

22 blank

transducer 1 response 23 - 31 +NN . NNNNN

32 - 80 blank

record IV

transducer 2 ID 1

- 12

11 XXXXXXXXXXX

blank

transducer 2 zero 13

22

- 21 +NN . NNNNN

blank

transducer 2 response 23 - 31 +NN . NNNNN

32 - 80 blank

record V

transducer 3 ID 1

- 12

11 XXXXXXXXXXX

blank

transducer 3 zero 13

22

- 21 +NN . NNNNN

blank

transducer 3 response 23 - 31 +NN . NNNNN

32 - 80 blank

/isec for Paros

(upper or lower) , volts

for Ruska

512-
APPENDIX E

Measurements of Orifice Plate Edge Sharpness

Measurements of the sharpness of the orifice edge of most of the plates

used in this series of tests were made using the lead foil technique.

This method was initially described by Herning [El] and has been improved by later investigators [E2, E3 , E4] . This method uses a fixture

holding the orifice plate in place relative to an arm carrying a 0.005

inch thick lead foil in a holder. The holder and foil are pressed

against the orifice edge thereby recording the shape edge in the foil.

Typical indentation depths are 0.3 mm. The lead foil is then inspected

with an optical comparator having a magnification of 250. This allows

the radius of the edge and the indentation depth to be estimated. The

radius of the indentation in the foil was measured using an optical

microscope having a magnification of 304. The image of the foil was projected onto a ground glass screen and the radius of this image was measured with a normal radius gauge.

Table El lists the results of the edge sharpness measurements for those

plates measured. Not all of the plates involved in the testing were

measured. The authors would like to express their appreciation to Dr.

R. Teysanndier, Mr. E. L. Upp , and Mr. D. Goodson of Daniels Industries,

Inc., Houston, Texas for their cooperation in making most of these

measurements. One of the authors (WGC) made the initial measurement at

Daniels (Sept. 1983). The majority of the measurements were made

shortly before beginning the data collection for the final data base on

the nickel meter tubes. The acceptance tolerance, 0.0004 x orifice

diameter, as defined by the International Standards Organization

Standard 5167, is listed for each plate.

Additionally, observations were made on each plate using a light

scattering method in accordance with the ANSI/API 2530, [E5] which

states

,

"(e) The inlet edge of the orifice shall be square and sharp, free

from either burrs or rounding, so that when viewed without

magnification a beam of light is not reflected visibly by the

edge .

Comparison of the initial and final sharpness observations show a scatter in the differences which seem to be normally distributed about a zero difference value. It is assumed that this difference gives a measure of the precision of the measurements process than a degradation

of the edge sharpness of the orifice plates.

Orifice plates having orifice diameters of 0.5 inches or less were considered to be too small to measure accurately. These are marked with

asterisks in table E2

.

•513-
ble El. Initial Ori fice Plate Edge Sharpness Measurement Results

Plate Obser. Norn. Nom. Plate Measured ISO-5167

Date Meter Orifce Thickness Edge Tol.

Dia. Dia. Radius Radius

(In.) (In.) (In.) (In.)

FE-1/2-1A 06/17/85 2 -INCH 0.500 0.125 0.000154 0.000200

FE-1/2-1B 06/17/85 2 -INCH 0.500 0.125 0.000167 0.000200

FE-1/2-2A 06/17/85 2 -INCH 0.750 0.125 0.000193 0.000300

FE-1/2-2B 06/17/85 2 -INCH 0.750 0.125 0.000115 0.000300

FE-1/2-3A 06/17/85 2 - INCH 1.000 0.125 0.000141 0.000400

FE-1/2-3B 06/17/85 2 -INCH 1.000 0.125 0.000089 0.000400

FE-1/2-4A 06/17/85 2 - INCH 1.125 0.125 0.000115 0.000450

FE-1/2-4B 06/17/85 2 -INCH 1.125 0.125 0.000115 0.000450

FE-1/2-5A 06/17/85 2 -INCH 1.375 0.125 0.000102 0.000550

FE-1/2-5B 06/17/85 2 -INCH 1.375 0.125 0.000102 0.000550

FE-1/2-6A 06/17/85 2 -INCH 1.500 0.125 0.000090 0.000600

FE-1/2-6B 06/17/85 2 -INCH 1.500 0.125 0.000128 0.000600

FE-1/2-7A 06/17/85 2 -INCH 0.250 0.125 0.000167 0.000100

FE-1/2-7B 06/17/85 2 -INCH 0.250 0.125 0.000141 0.000100

FE-5/6-1A 06/19/85 4- INCH 0.875 0.125 0.000103 0.000350

FE-5/6-1B 09/20/83 4 -INCH 0.875 0.125 0.000090 0.000350

FE-5/6-1C 04/15/85 4 -INCH 0.875 0.125 0.000090 0.000350

FE-5/6-2A 06/19/85 4 -INCH 1.500 0.125 0.000103 0.000600

FE-5/6-2B 09/20/83 4 -INCH 1.500 0.125 0.000180 0.000600

FE-5/6-2C 04/15/85 4- INCH 1.500 0.125 0.000218 0.000600

FE-5/6-3A 06/19/85 4 -INCH 2.000 0.125 0.000103 0.000800

FE-5/6-3B 09/20/83 4 -INCH 2.000 0.125 0.000103 0.000800

FE-5/6-3C 04/15/85 4 -INCH 2.000 0.125 0.000180 0.000800

FE-5/6-4A 06/19/85 4 -INCH 2.250 0.125 0.000128 0.000900

FE-5/6-4B 09/20/83 4 -INCH 2.250 0.125 0.000128 0.000900

FE-5/6-4C 04/15/85 4 -INCH 2.250 0.125 0.000150 0.000900

FE-5/6-5A 06/19/85 4 -INCH 2.625 0.125 0.000231 0.001050

FE-5/6-5B 09/20/83 4 -INCH 2.625 0.125 0.000310 0.001050

FE-5/6-5C 04/15/85 4 -INCH 2.625 0.125 0.000190 0.001050

FE-5/6-6A 06/19/85 4 -INCH 3.000 0.125 0.000154 0.001200

FE-5/6-6A 09/20/83 4 -INCH 4.500 0.125 0.000130 0.001200

FE-5/6-6B 09/20/83 4 -INCH 4.500 0.125 0.000218 0.001200

FE-5/6-6C 04/15/85 4 -INCH 3.000 0.125 0.000257 0.001200

FE-5/6-7A 06/19/85 4- INCH 0.375 0.125 0.000090 0.000150

FE-5/6-7C 04/15/85 4- INCH 0.375 0.125 0.000077 0.000150

FE-5/6-8A 06/19/85 4- INCH 0.250 0.125 0.000141 0.000100

FE-7/8-2A 09/20/83 6 -INCH 2.250 0.125 0.000051 0.000900

FE-7/8-3A 09/20/83 6 -INCH 3.000 0.125 0.000120 0.001200

FE-7/8-4A 09/20/83 6 -INCH 3.500 0.125 0.000140 0.001400

FE-7/8-5A 09/20/83 6 -INCH 4.000 0.125 0.000100 0.001600

FE-7/8-6A 09/20/83 6 -INCH 4.500 0.125 0.000130 0.001800

•514-
Table El. Initial Orifice Plate Edge Sharpness

Measurement Results -- Continued

Plate Obser. Nom. Nom. Plate Measured ISO-5167

Date Meter Orifce Thickness Edge Tol.

Dia. Dia. Radius Radius

(In.) (In.) (In.) (In.)

FE-9/0-1A 06/19/85 10 -INCH 2.000 0.250 0.000154 0.000800

FE-9/0-1B 06/19/85 10 -INCH 2.000 0.250 0.000141 0.000800

FE-9/0-2A 06/19/85 10 -INCH 3.750 0.250 0.000257 0.001500

FE-9/0-2B 06/19/85 10 -INCH 3.750 0.250 0.000128 0.001500

FE-9/0-3A 06/19/85 10 -INCH 5.000 0.250 0.000116 0.002000

FE-9/0-3B 06/19/85 10 -INCH 5.000 0.250 0.000154 0.002000

FE-9/0-4A 06/19/85 10 -INCH 5.750 0.250 0.000128 0.002300

FE-9/0-4B 06/19/85 10 -INCH 5.750 0.250 0.000141 0.002300

FE-9/0-5A 06/19/85 10 -INCH 6.625 0.250 0.000192 0.002650

FE-9/0-5B 06/19/85 10 -INCH 6.625 0.250 0.000179 0.002650

FE-9/0-6A 06/19/85 10 -INCH 7.500 0.250 0.000179 0.003000

FE-9/0-6B 06/19/85 10 -INCH 7.500 0.250 0.000167 0.003000

FE-9/0-7A 06/19/85 10 -INCH 1.000 0.250 0.000090 0.000400

FE-9/0-7B 06/19/85 10 -INCH 1.000 0.250 0.000156 0.000400

515-
Table E2

.

Final Orifice Plate Edge Sharpness Measurement Results

Plate Obser. Nom. Nom. Plate Measured ISO-5167

Date Meter Orifce Thickness Edge Tol.

Dia. Dia. Radius Radius

(In.) (In.) (In.) (In.) (In.)

FE-1/2-1A 09/25/87 2 0.500 0.125 0.000064 0.000200

FE-1/2-2A 09/25/87 2 0.750 0.125 0.000128 0,000300

FE-1/2-3A 09/25/87 2 1.000 0.125 0.000128 0.000400

FE-1/2-4A 09/25/87 2 1.125 0.125 0.000090 0.000450

FE-1/2-5A 09/25/87 2 1.375 0.125 0.000154 0.000550

FE-1/2-6A 09/25/87 2 1.500 0.125 0.000128 0.000600

FE-1/2-7A 09/25/87 2 0.250 0.125 ** 0.000100

FE-1/2-1B 09/28/87 2 0.500 0.125 0.000154 0.000200

FE-1/2-2B 09/28/87 2 0.750 0.125 0.000154 0.000300

FE-1/2-3B 09/28/87 2 1.000 0.125 0.000103 0.000400

FE-1/2-4B 09/28/87 2 1.125 0.125 0.000115 0.000450

FE-1/2-5B 09/28/87 2 1.375 0.125 0.000103 0.000550

FE-1/2-6B 09/25/87 2 1.500 0.125 0.000128 0.000600

FE-1/2-7B 09/25/87 2 0.250 0.125 ** 0.000100

FE-3/4-1A 09/11/87 3 0.625 0.125 0.000077 0.000250

FE-3/4-2A 09/11/87 3 1.125 0.125 0.000141 0.000450

FE-3/4-3A 09/11/87 3 1.500 0.125 0.000128 0.000600

FE-3/4-4A 09/11/87 3 1.750 0.125 0.000102 0.000700

FE-3/4-5A 09/11/87 3 2.000 0.125 0.000205 0.000800

FE-3/4-6A 09/11/87 3 2.250 0.125 0.000115 0.000900

FE-3/4-7A 09/11/87 3 0.375 0.125 0.000154 0.000150

FE-3/4-8A 09/11/87 3 0.250 0.125 ** 0.000100

FE-3/4-1B 09/11/87 3 0.625 0.125 0.000141 0.000250

FE-3/4-2B 09/11/87 3 1.125 0.125 0.000077 0.000450

FE-3/4-3B 09/11/87 3 1.500 0.125 0.000089 0.000600

FE-3/4-4B 09/11/87 3 1.750 0.125 0.000128 0.000700

FE-3/4-5B 09/11/87 3 2.000 0.125 0.000115 0.000800

FE-3/4-6B 09/11/87 3 2.250 0.125 0.000141 0.000900

FE-3/4-7B 09/11/87 3 0.375 0.125 0.000128 0.000150

FE-3/4-8B 09/11/87 3 0.250 0.125 ** 0.000100

! - two bad spots noted on the edge at the 1 and 5 o'clock positions

viewing the inlet face of the plate.

516-
Table E2 . Final Orifice Plate Edge Sharpness

Measurement Results -- Continued

Plate Obser

.

Nom, Nom. Plate Measured ISO-5167

Date Meter Orifce Thickness Edge Tol.

Dia. Dia. Radius Radius

(In.) (In.) (In.) (In.) (In.)

FE-5/6-1A 09/18/87 4 0.875 0.125 0.000141 0.000350

FE-5/6-2A 09/18/87 4 1.500 0.125 0.000115 0.000600

FE-5/6-3A 09/18/87 4 2.000 0.125 0.000115 0.000800

FE-5/6-4A 09/18/87 4 2.250 0.125 0.000154 0.000900

FE-5/6-5A 09/18/87 4 2.625 0.125 0.000205 0.001050

FE-5/6-6A 09/18/87 4 3.000 0.125 0.000089 0.001200

FE-5/6-7A 09/18/87 4 0.375 0.125 0.000115* 0.000150

FE-5/6-8A 09/18/87 4 0.250 0.125 ** 0.000100

FE-5/6-1B 09/18/87 4 0.875 0.125 0.000077 0.000350

FE-5/6-2B 09/18/87 4 1.500 0.125 0.000218 0.000600

FE-5/6-3B 09/18/87 4 2.000 0.125 0.000193 0.000800

FE-5/6-4B 09/18/87 4 2.250 0.125 0.000167 0.000900

FE-5/6-5B 09/18/87 4 2.625 0.125 0.000231 0.001050

FE-5/6-6B 09/18/87 4 3.000 0.125 0.000103 0.001200

FE-5/6-7B 09/11/87 4 0.375 0.125 0.000064* 0.000150

FE-5/6-8B 09/11/87 4 0.250 0.125 ** 0.000100

FE-5/6-1C 09/17/87 4 0.875 0.125 0.000077 0.000350

FE-5/6-2C 09/17/87 4 1.500 0.125 0.000179 0.000600

FE-5/6-3C 09/17/87 4 2.000 0.125 0.000103 0.000800

FE-5/6-4C 09/17/87 4 2.250 0.125 0.000179 0.000900

FE-5/6-5C 09/17/87 4 2.625 0.125 0.000154 0.001050

FE-5/6-6C 09/17/87 4 3.000 0.125 0.000179 0.001200

FE-5/6-7C 09/18/87 4 0.375 0.125 0.000090* 0.000150

FE-7/8-1A 09/29/87 6 1.250 0.125 0.000103 0.000500

FE-7/8-2A 10/19/87 6 2.250 0.125 0.000103 0.000900

FE-7/8-3A 10/19/87 6 3.000 0.125 0.000154 0.001200

FE-7/8-4A 10/19/87 6 3.500 0.125 0.000141 0.001400

FE-7/8-5A 10/19/87 6 4.000 0.125 0.000103 0.001600

FE-7/8-6A 10/19/87 6 4.500 0.125 0.000154 0.001800

FE-7/8-7A 09/11/87 6 0.625 0.125 0.000103 0.000250

FE-7/8-8A 10/19/87 6 1.250 0.125 0.000141 0.000500

517-
Table E2 . Final Ori fice Picite Edge Sharpness

Measurement Results - - Cont inued

Plate Obser

.

Nom. Nom. Plate Measured ISO-5167

Date Meter Orifce Thickness Edge Tol.

Dia. Dia. Radius Radius

(In.) (In.) (In.) (In.) (In.)

FE-7/8-1B 09/29/87 6 1.250 0.125 0.000090 0.000500

FE-7/8-2B 09/11/87 6 2.250 0.125 0.000167 0.000900

FE-7/8-3B 09/11/87 6 3.000 0.125 0.000103 0.001200

FE-7/8-4B 09/11/87 6 3.500 0.125 0.000116 0.001400

FE-7/8-5B 09/11/87 6 4.000 0.125 0.000103 0.001600

FE-7/8-6B 09/11/87 6 4.500 0.125 0.000128 0.001800

FE-7/8-7B 09/11/87 6 0.625 0.125 0.000141 0.000250

FE-7/8-8B 09/11/87 6 0.625 0.125 0.000141 0.000250

FE-7/8-1C 09/03/87 6 1.250 0.125 0.000308 0.000500

FE-7/8-3C 09/11/87 6 3.000 0.125 0.000193 0.001200

FE-7/8-5C 09/11/87 6 4.000 0.125 0.000167 0.001600

FE-9/0-1A 10/19/87 10 2.000 0.250 0.000154 0.000800

FE-9/0-2A 09/29/87 10 3.750 0.250 0.000154 0.001500

FE-9/0-3A 10/19/87 10 5.000 0.250 0.000167 0.002000

FE-9/0-4A 10/19/87 10 5.750 0.250 0.000128 0.002300

FE-9/0-5A 10/19/87 10 6.625 0.250 0.000179 0.002650

FE-9/0-6A 09/29/87 10 7.500 0.250 0.000141 0.003000

FE-9/0-7A 10/19/87 10 1.000 0.250 0.000141 0.000400

FE-9/0-7A 10/19/87 10 1.000 0.250 0.000128 0.000400

FE-9/0-1B 09/29/87 10 2.000 0.250 0.000167 0.000800

FE-9/0-2B 09/29/87 10 3.750 0.250 0.000141 0.001500

FE-9/0-3B 09/29/87 10 5.000 0.250 0.000193 0.002000

FE-9/0-4B 09/29/87 10 5.750 0.250 0.000115 0.002300

FE-9/0-5B 09/29/87 10 6.625 0.250 0.000154 0.002650

FE-9/0-6B 09/29/87 10 7.500 0.250 0.000115 0.003000

FE-9/0-7B 09/29/87 10 1.000 0.250 0.000128 0.000400

•518-
References:

[El] Herning, von Fr. , "Untersuchen zum Problem der Kantehunscharfe Bei

Normblenden und die Segmentblenden. " (Experiments on the Problem

of the Edge Sharpness of Standard and Segmental Orifice Plates.)

Brenns-Warme -Kraft, 14(3), 119-126, 1962.

[E2] Jepson, P., and Johnson, E. P., "A Method of Measuring Orifice

Edge Sharpness (ORIS)." Tech. Rept-ERS .T.415 . Killingworth,

Newcastle, Gas Council Engineering Research Station, 1971.

[E3] Brain, T. J. S., and Reid, J., "Measurement of Orifice Plate Edge

Sharpness," Measurement and Control, 9), 377-383, 1973.

[E4] Benedict, R. P., Wyler, J. S. and Brandt, G. B. , "The Effect of

Edge Sharpness on the Discharge Coefficient of Orifice Plates,"

Trans. ASME, J. Eng. for Power, paper no. 74-WA/FM-4, 1974.

[E5] American National Standard/American Petroleum Institute 2530,

American Petroleum Institute, Washington, DC.

-519-

APPENDIX F

Velocity Profile Measurements*

Although main stream velocities and their distributions reflect only the

parameters of the macroscale turbulence, they may affect orifice meter

performance if not controlled by proper upstream installations [F1-F3]

.

For this reason, velocity distributions involved in this orifice testing

program were checked to determine if upstream piping elements produced

significantly anomalous flow profiles at the orifice union, i.e. at the

orifice plate position in the meter tube assembly.

For specific initial or inlet flows, the factors that control velocity

profile variations, with downstream distance, are the fluid inertial and

viscous effects and the roughness and size of the piping. The presence

of flow conditioners and piping geometries can also affect velocity

profiles. In dimensionless terms and for specific pipe geometry, the

pertinent flow parameters describing pipe flow development to equilibrium conditions, i.e., "fully developed," are Rejmolds number and the

relative roughness [F3-F5]

.

To efficiently check the numerous pipe flow conditions that were involved in this orifice testing program, the strategy adopted was to

obtain velocity profiles for the "worst case" condition. If for this

condition the profiles were satisfactory, there would be no need to test

any other.

It is well known that anomalous flow effects propagate into downstream

piping with diametral distances that increase with Reynolds Number and

decrease with relative roughness, [F4-F6] . Therefore, the largest,

smoothest pipe, at the highest flowrate is the configuration considered

"worst" - i.e., most likely to permit undesirable upstream conditions to

produce anomalous profiles at the orifice union. Following this reasoning, and after careful visual inspection, the PE-0 tube was selected for

the velocity profile tests in February 1987. Although the PE-9 tube was originally determined as having the lowest internal wall roughness , it was rejected for the velocity profile measurements because significant

patches of rust developed on the inner surface after the completion of

the discharge coefficient measurements.

To measure the time -averaged velocity distribution at the orifice union,

the pitot tube technique was selected; see [F2]. A pitot-tube traversing fixture was designed and installed in the flow at the orifice union.

Two pitot tubes of slightly different construction were used during the

measurements to test for possible system errors; both instruments gave

coincidental results. For these tests, orifice plates were removed from

the pipeline. Two diametral traversing positions (vertical and

horizontal) were selected, with measurements repeated on different days.

*Dr. G. E. Mattingly and G. P. Baumgarten performed the work described

here. Dr. J. J. Ulbrecht assisted Dr. Mattingly in writing this

appendix

.

-521-
The vertical traversing plane was that of the orifice union tappings.

The horizontal traversing plane was normal to the vertical plane. The

dynamic pressure differences were measured using the same differential

pressure transducers and data acquisition system described in the main

body of this report. The pitot tube was positioned by means of a graduated- scale indexed to the probe traversing plate.

Results are given in tables Fl and F2 , and in the form of the dimensionless plots shown in figure Fl for both traverse orientations. The

profiles show no inflection points. The high degree of repeatability

evident from the data taken over several days confirms the credibility

of these results.

The slight asymmetry of the velocity profiles can be evaluated by

analyzing the orifice differential pressure measurements acquired using

the same meter tube geometry and the same flow conditions . By examination of the data in table 47F it appears that there is only one set of

conditions, namely the highest beta ratios and the highest Reynolds

numbers in the PE-0 tube, when consistently higher pressure readings

were obtained from the upper pressure tap. This trend is perfectly

consistent with the apparent asymmetry of the velocity profile.

However, this difference (between upper and lower pressure tap readings)

is also observed to be numerically small in comparison with the measure- ment uncertainty associated with each data point. For example, the

difference between upper and lower pressure tap readings under the worst

conditions (Reynolds Number = 2.7 x 10 and /3 = 0.75) does not exceed 6

parts in 2800 (0.21%). In addition to this visual inspection of the

data in table 47F, statistical analyses have not shown any consistent

trends in differences between the upper and lower pressure tap readings

throughout the entire data base (all meter tubes, orifice plates, run

conditions, etc.). This, in turn, testifies to the insignificance of

the observed asymmetry of the profile.

When power- law formulae are fitted, via the least- squares method, to the

data shown in figure Fl , the exponent n=8+0.4 is determined. This value

is appropriate for the pipe Reynolds number and the mean relative

roughness (based on rms roughness measurements) for this pipeline- -see References [F4,F5]. The relative roughness (e/D) was 0.000024, obtained

by averaging all rms roughness measurements recorded in table 25 and

using the tube diameter given in table 24.

522-
Horizontal Plane Velocity Profile

1.0

o

ft;^0.8

o

o

0.6

I

0.4

-\—I

\—\—I—I\—f\—f—I\—I—I—I—1—I—I—I—

I

iv \\ —^

IL.

^,

1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Vertical Plan Velocity Profile

1.0

o

ft;7^0.8

o

I 0.6

I

0.4

~]—\—

I—

I—I

\—I f I t I 1 I—\—\—

I—I—I—

I—

I

ih

^ ^^IL

i^

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Position Relative to the Center Line

Figure Fl . Horizontal and Vertical Velocity Profiles

523-
Table Fl. Summary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Horizontal Traverses

The relative position, Y/R, is the radial distance from the

meter tube center. Looking downstream Y/R < denotes the

upper left portion of the flow field.

The relative velocity V/Vcl is the velocity non-dimensionalized by the velocity measured on the meter tube

centerline.

Date Run Relative Rel. Velocity

No. Position Tr. 1 Tr. 2

-- Impact Pressure (psi) -

Transducer 1 Tranducer 2

Mean SD Mean SD

04/16/87 37 -.9178 0.7529 0,,7527 3,.582 0.0663 3,.582 0.0578

04/16/87 38 -.9178 0.7520 0,,7518 3,.573 0.0658 3..572 0.0594

04/17/87 81 -.9178 0.7518 0,,7523 3,.409 0.0736 3,.415 0.0599

04/17/87 82 -.9178

mean

std. dev.

0.7536

0.7526

0.0008

0,,7539 3,.428 0.0587 3,.433 0.0524

04/16/87 35 -.8779 0.7837 0,,7836 3..898 0.0682 3..899 0.0613

04/16/87 36 -.8779 0.7837 0,,7837 3,.892 0.0702 3..894 0.0645

04/17/87 79 -.8779 0.7841 0,,7842 3..735 0.0609 3..737 0.0503

04/17/87 80 -.8779

mean

std. dev.

0.7824

0.7835

0.0007

0,,7826 3,.720 0.0557 3,.723 0.0482

04/16/87 33 -.8380 0.8060 0,,8063 4..121 0.0696 4,.126 0.0603

04/16/87 34 -.8380 0.8066 0,,8067 4,.128 0.0608 4,.132 0.0483

04/17/87 77 -.8380 0.8073 0,,8075 3,.962 0.0541 3,.965 0.0454

04/17/87 78 -.8380

mean

std. dev.

0.8068

0.8067

0.0005

0,,8070 3,.956 0.0608 3,.961 0.0543

04/16/87 31 -.7981 0.8267 0..8267 4..353 0.0750 4.,354 0.0688

04/16/87 32 -.7981 0.8287 0,.8288 4,.370 0.0520 4.,373 0.0441

04/29/87 166 -.7981 0.8277 0,,8276 5,.118 0.0680 5.,119 0.0585

04/29/87 167 -.7981 0.8295 0,,8296 5,.144 0.0720 5,,147 0.0639

04/30/87 204 -.7981 0.8321 0,,8319 5,.123 0.0618 5,,124 0.0521

04/30/87 205 -.7981

mean

std. dev.

0.8281

0.8288

0.0019

0,,8283 5,.072 0.0667 5.,077 0.0630

524-
Table Fl . Summary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Horizontal Traverses - - Continued

Date Run Relative

No. Position

Rel. Velocity

Tr. 1 Tr. 2

-- Impact Pressure (psi) -

Transducer 1 Tranducer 2

Mean SD Mean SD

04/16/87

04/16/87

04/17/87

04/17/87

04/29/87

04/29/87

04/30/87

04/30/87

29

30

73

74

164

165

198

199

-.5986

-.5986

-.5986

-.5986

-.5986

-.5986

-.5986

-.5986

mean

std. dev.

0.9067 0. 0.9097 0,

0.9095 0. 0.9086 0,

0.9054 0,

0.9051 0,

0.9054 0,

0.9053 0,

0.9070

0.0020

9067 5.255 0.0478

9098 5.281 0.0632

9096 5.033 0.0365

9087 5.019 0.0467

9055 6.097 0.0509

9051 6.101 0.0533

9054 6.051 0.0529

9054 6.042 0.0480

257 0.0406

285 0.0567

036 0.0305

023 0.0415

101 0.0452

104 0.0484

055 0.0471

6.047 0.0443

04/16/87

04/16/87

04/17/87

04/17/87

04/29/87

04/29/87

04/30/87

04/30/87

27

28

71

72

158

159

196

197

-.3990

-.3990

-.3990

-.3990

-.3990

-.3990

-.3990

-.3990

mean

std. dev.

0.9684

0.9679

0.9660

0.9677

0.9653

0.9649

0.9637

0.9647

0.9661

0.0017

0.9683

0.9677

0.9659

0.9677

0.9653

0.9649

0.9637

0.9646

009 0.0348

000 0.0440

776 0.0379

795 0.0360

939 0.0420

921 0.0437

844 0.0408

6.857 0.0451

010 0.0309

000 0.0409

778 0.0304

798 0.0305

942 0.0364

923 0.0392

849 0.0383

861 0.0408

04/16/87

04/16/87

04/17/87

04/17/87

04/29/87

04/29/87

04/29/87

04/29/87

04/29/87

04/29/87

04/30/87

04/30/87

25

26

69

70

156

157

176

177

184

185

190

191

-.1995

-.1995

-.1995

-.1995

-.1995

-.1995

-.1995

-.1995

-.1995

-.1995

-.1995

-.1995

mean

std. dev.

1.0005

1.0009

0.9988

0.9998

0.9985

0.9984

0.9981

0.9983

0.9982

0.9992

0.9987

0.9980

0.9990

0.0010

1.0005

1.0009

0.9990

0.9999

0.9984

0.9986

0.9982

0.9983

0.9982

0.9992

0.9985

0.9979

,426

,444

,182

,188

,377

7.373

7.317

7.307

7.309

7.320

7.338

7.334

0.0261

0.0320

0.0245

0.0295

0.0267

0.0313

0.0348

0.0286

0.0413

0.0312

0.0335

0.0403

6.429

6.447

6.186

6.191

7.379

7.378

7.322

7.310

7.311

7.323

7.341

7.338

0.0206

0.0269

0.0224

0.0262

0.0223

0.0265

0.0320

0.0248

0.0366

0.0270

0.0305

0.0373

525-
Table Fl . Summary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Horizontal Traverses -- Continued

Date Run Relative Rel. Velocity

No. Position Tr. 1 Tr. 2

-- Impact Pressure (psi) -

Transducer 1 Tranducer 2

Mean SD Mean SD

04/16/87 1 0.0000 1.0000 1.0000 6 695 0.0346 6 698 0.0303

04/16/87 2 0.0000 1.0001 1.0000 6 677 0.0269 6 679 0.0223

04/16/87 23 0.0000 1.0006 1.0006 6 445 0.0354 6 448 0.0315

04/16/87 24 0.0000 1.0007 1.0007 6 439 0.0290 6 442 0.0243

04/17/87 39 0.0000 1.0000 1.0000 6 602 0.0334 6 605 0.0279

04/17/87 40 0.0000 0.9988 0.9989 6 599 0.0391 6 603 0.0346

04/17/87 67 0.0000 0.9988 0.9988 6 184 0.0307 6 186 0.0269

04/17/87 68 0.0000 0.9988 0.9988 6 182 0.0402 6 184 0.0368

04/29/87 152 0.0000 1.0000 1.0000 7 380 0.0343 7 383 0.0271

04/29/87 153 0.0000 1.0005 1.0005 7 377 0.0252 7 380 0.0213

04/29/87 170 0.0000 0.9989 0.9988 7 358 0.0362 7 359 0.0341

04/29/87 171 0.0000 0.9999 0.9998 7 362 0.0395 7 363 0.0370

04/29/87 174 0.0000 0.9998 0.9998 7 342 0.0485 7 345 . 0444

04/29/87 175 0.0000 0.9988 0.9988 7 327 0.0270 7 330 0.0236

04/29/87 178 0.0000 0.9995 0.9995 7 325 0.0394 7 329 0.0359

04/29/87 179 0.0000 1.0001 1.0001 7 338 0.0279 7 341 0.0257

04/29/87 182 0.0000 0.9998 0.9998 7 326 0.0321 7 330 0.0282

04/29/87 183 0.0000 0.9992 0.9991 7 307 0.0285 7 309 0.0244

04/29/87 186 0.0000 0.9992 0.9992 7 316 0.0249 7 319 0.0216

04/29/87 187 0.0000 0.9993 0.9993 7 323 0.0493 7 328 . 0442

04/30/87 188 0.0000 1.0000 1.0000 7 364 0.0449 7 369 0.0425

04/30/87 189 0.0000

mean

std. dev.

1.0003

0.9997

0.0006

1.0001 7 357 0.0367 7 359 0.0328

04/16/87 5 0.1995 0.9721 0.9720 6 264 0.0618 6 265 0.0543

04/16/87 6 0.1995 0.9716 0.9714 6 256 0.0357 6 257 0.0297

04/17/87 41 0.1995 0.9714 0.9714 6 162 0.0354 6 164 0.0287

04/17/87 42 0.1995 0.9710 0.9709 6 158 0.0383 6 159 0.0353

04/29/87 154 0.1995 0.9716 0.9715 6 992 0.0387 6 994 0.0339

04/29/87 155 0.1995 0.9723 0.9723 7 001 0.0433 7 004 0.0359

04/29/87 172 0.1995 0.9714 0.9715 6 955 0.0365 6 958 0.0317

04/29/87 173 0.1995 0.9721 0.9722 6 956 0.0410 6 959 0.0352

04/29/87 180 0.1995 0.9705 0.9706 6 911 0.0568 6 916 0.0515

04/29/87 181 0.1995 0.9703 0.9702 6 .896 0.0511 6 898 0.0478

04/30/87 192 0.1995 0.9711 0.9711 6 .942 0.0426 6 946 0.0391

04/30/87 193 0.1995

mean

std. dev.

0.9711

0.9714

0.0006

0.9710 6 .945 0.0517 6 949 0.0462

526-
Table Fl . Summary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Horizontal Traverses - - Continued

Date Run Relative Rel. Velocity

No. Position Tr. 1 Tr. 2

-- Impact Pressure (psi) -

Transducer 1 Tranducer 2 Mean SD Mean SD

04/16/87 7 0.3990 0.9215 9214 5 605 0.0544 5 606 0.0462

04/16/87 8 0.3990 0.9232 9232 5 620 0.0649 5 622 0.0561

04/17/87 43 0.3990 0.9172 9172 5 490 0.0639 5 492 0.0511

04/17/87 44 0.3990 0.9203 9204 5 528 0.0551 5 532 0.0493

04/29/87 160 0.3990 0.9209 9212 6 306 0.0598 6 312 0.0492

04/29/87 161 0.3990 0.9216 9217 6 315 0.0709 6 319 0.0639

04/30/87 194 0.3990 0.9244 9245 6 295 0.0522 6 301 0.0454

04/30/87 195 0.3990

mean

std. dev.

0.9230

0.9215

0.0022

9231 6 279 0.0466 6 284 0.0395

04/16/87 9 0.5986 0.8606 8607 4 866 0.0695 4 869 0.0578

04/16/87 10 0.5986 0.8602 8602 4 867 0.0538 4 869 0.0451

04/17/87 45 0.5986 0.8563 8565 4 718 0.0643 4 721 0.0552

04/17/87 46 0.5986 0.8558 8558 4 716 0.0628 4 718 0.0536

04/29/87 162 0.5986 0.8603 8604 5 503 0.0641 5 507 0.0544

04/29/87 163 0.5986 0.8605 8606 5 511 0.0484 5 514 0.0373

04/30/87 200 0.5986 0.8619 8619 5 483 0.0641 5 487 0.0564

04/30/87 201 0.5986

mean

std, dev.

0.8610

0.8596

0.0022

8610 5 472 0.0714 5 475 0.0625

04/16/87 11 0.7981 0.7824 7824 4 020 0.0668 4 022 0.0599

04/16/87 12 0.7981 0.7840 7842 4 034 0.0522 4 038 0.0491

04/17/87 47 0.7981 0.7813 7813 3 927 0.0693 3 929 0.0571

04/17/87 48 0.7981 0.7807 7805 3 921 0.0604 3 921 0.0530

04/29/87 168 0.7981 0.7862 7864 4 614 0.0624 4 618 0.0573

04/29/87 169 0.7981 0.7859 7860 4 615 0.0726 4 618 0.0658

04/30/87 202 0.7981 0.7838 7839 4 532 0.0621 4 536 0.0538

04/30/87 203 0.7981

mean

std. dev.

0.7842

0.7836

0.0020

7843 4 548 0.0650 4 553 0.0543

527-
Table Fl . Summary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Horizontal Traverses - - Continued

Date Run Relative Rel. Velocity

No. Position Tr. 1 Tr. 2

-- Impact Pressure (psi) -

Transducer 1 Tranducer 2

Mean SD Mean SD

04/16/87 13 0.8380 0.7690 7688 3 857 0.0680 3 857 0.0564

04/16/87 14 0.8380 0.7632 7633 3 804 0.0699 3 807 0.0612

04/17/87 49 0.8380 0.7609 7611 3 726 0.0598 3 729 0.0478

04/17/87 50 0.8380

mean

std, dev.

0.7633

0.7641

0.0035

7638 3 753 0.0634 3 759 0.0477

04/16/87 15 0.8779 0,7434 7437 3 599 0.0675 3 604 0.0584

04/16/87 16 0.8779 0.7431 7431 3 593 0.0616 3 595 0.0502

04/17/87 51 0.8779 0.7431 7430 3 503 0.0728 3 504 0.0619

04/17/87 52 0.8779

mean

std. dev.

0.7404

0.7525

0.0014

7403 3 491 0.0624 3 492 0.0530

04/16/87 17 0.9178 0.7118 7118 3 288 0.0669 3 290 0.0599

04/16/87 18 0.9178 0.7155 7153 3 318 0.0662 3 318 0.0573

04/17/87 53 0.9178 0.7102 7105 3 213 0.0678 3 217 0.0584

04/17/87 54 0.9178

mean

std. dev.

0.7136

0.7128

0.0023

7136 3 244 0.0744 3 245 0.0707

04/16/87 19 0.9577 0.6773 6774 2 961 0.0747 2 964 0.0593

04/16/87 20 0.9577 0.6746 6748 2 938 0.0504 2 940 . 0445

04/17/87 55 0.9577 0.6724 6726 2 856 0.0687 2 859 0.0652

04/17/87 56 0.9577

mean

std. dev.

0.6726

0.6742

0.0023

6730 2 857 0.0678 2 862 0.0623

04/16/87 21 0.9976 0.5974 5975 2 298 0.0640 2 300 0.0590

04/16/87 22 0.9976 0.5976 5979 2 299 0.0473 2 303 0.0423

04/17/87 57 0.9976 0.5967 5970 2 248 0.0626 2 251 0.0566

04/17/87 58 0.9976

mean

std. dev.

0.5955

0.5968

0.0009

5956 2 239 0.0591 2 241 0.0514

-528-
Table F2 . Sioimnary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Vertical Traverses

The relative position, Y/R, is the radial distance from the

meter tube center. Looking downstream Y/R < denotes the

upper left portion of the flow field.

The relative velocity V/Vcl is the velocity non-dimensionalized by the velocity measured on the meter tube

centerline.

Date Run Relative Rel. Velocity

No. Position Tr. 1 Tr. 2

-- Impact Pressure (psi) -

Transducer 1 Tranducer 2 Mean SD Mean SD

04/14/87 92 -.9178 0.7288 7290 3 549 0.0656 3 551 0.0545

04/14/87 93 -.9178 0.7259 7262 3 545 0.0626 3 549 0.0563

04/15/87 120 -.9178 0.7268 7270 3 405 0.0766 3 407 0.0647

04/15/87 121 -.9178

mean

std. dev.

0.7292

0.7277

0.0016

7291 3 441 0.0891 3 442 0.0758

04/14/87 90 -.8779 0.7553 7554 3 830 0.0948 3 832 0.0780

04/14/87 91 -.8779 0.7530 7530 3 789 0.0653 3 790 0.0544

04/15/87 118 -.8779 0.7576 7577 3 678 0.0627 3 679 0.0481

04/15/87 119 -.8779

mean

std. dev.

0.7549

0.7552

0.0019

7546 3 683 0.0633 3 681 0.0527

04/14/87 94 -.8380 0.7797 7800 4 087 0.0719 4 091 0.0617

04/14/87 95 -.8380 0.7790 7797 4 070 0.0753 4 079 0.0608

04/15/87 116 -.8380 0.7820 7820 3 935 0.0663 3 935 0.0576

04/15/87 117 -.8380

mean

std. dev.

0.7797

0.7776

0.0035

7799 3 917 0.0732 3 920 0.0658

04/14/87 86 -.7981 0.8026 8024 4 276 0.0695 4 275 0.0572

04/14/87 87 -.7981 0.8041 8040 4 315 0.0825 4 316 0.0672

04/15/87 110 -.7981 0.8031 8034 4 343 0.0814 4 348 0.0704

04/15/87 111 -.7981 0.8009 8009 4 331 0.0909 4 332 0.0795

04/28/87 148 -.7981 0.8159 8159 5 253 0.1008 5 255 0.0939

04/28/87 149 -.7981

mean

std. dev.

0.8165

0.8072

0.0071

8169 5 265 0.0873 5 271 0.0761

529-
Table F2 . Summary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Vertical Traverses -- Continued

Date Run Relative Rel. Velocity

No. Position Tr. 1 Tr. 2

-- Impact Pressure (psi) -- Transducer 1 Tranducer 2 Mean SD Mean SD

04/14/87 84 -.5986 0.8838 0.8841 5,,168 0.0666 5..173 0.0591

04/14/87 85 -.5986 0.8871 0.8874 5,.207 0.0441 5 .212 0.0385

04/15/87 108 -.5986 0.8883 0.8884 5,.301 0.0632 5,.304 0.0538

04/15/87 109 -.5986 0.8883 0.8883 5,.334 0.0567 5,.336 0.0490

04/28/87 146 -.5986 0.8949 0.8948 6,.446 0.0707 6..447 0.0599

04/28/87 147 -.5986

mean

std. dev.

0.8944

0.8995

0.0044

0.8945 6,.391 0.0580 6..395 0.0498

04/14/87 82 -.3990 0.9498 0.9497 6,.032 0.0374 6 .034 0.0320

04/14/87 83 -.3990 0.9501 0.9501 6,.042 0.0438 6 .043 0.0384

04/15/87 102 -.3990 0.9493 0.9495 6..086 0.0482 6 .090 0.0430

04/15/87 103 -.3990 0.9509 0.9510 6,.101 0.0554 6,.104 0.0465

04/28/87 140 -.3990 0.9556 0.9555 7..454 0.0611 7,.456 0.0531

04/28/87 141 -.3990

mean

std. dev.

0.9556

0.9518

0.0029

0.9556 7,.448 0.0560 7,.451 0.0508

04/14/87 80 -.1995 0.9919 0.9918 6..523 0.0314 6 .525 0.0278

04/14/87 81 -.1995 0.9928 0.9928 6,.532 0.0368 6..533 0.0329

04/15/87 100 -.1995 0.9922 0.9924 6,.695 0.0603 6 .700 0.0524

04/15/87 101 -.1995 0.9930 0.9930 6,.645 0.0419 6,.647 0.0358

04/28/87 138 -.1995 0.9943 0.9944 8,.229 0.0472 8,.232 0.0418

04/28/87 139 -.1995

mean

std. dev.

0.9946

0.9931

0.0011

0.9946 8,.278 0.0429 8,.281 0.0364

04/14/87 58 0.0000 1.0000 1.0000 7,.100 0.0910 7..102 0.0759

04/14/87 59 0.0000 0.9994 0.9995 7,,142 0.0990 7,.145 0.0886

04/14/87 78 0.0000 0.9990 0.9990 6,.678 0.0256 6..680 0.0213

04/14/87 79 0.0000 0.9997 0.9997 6,,634 0.0355 6,.636 0.0319

04/15/87 96 0.0000 1.0000 1.0000 6.,708 0.0398 6..710 0.0355

04/15/87 97 0.0000 1.0000 1.0000 6,,694 0.0366 6,,696 0.0321

04/28/87 134 0.0000 1.0000 1.0000 8,,377 0.0465 8.,379 0.0410

04/28/87 135 0.0000

mean

std. dev.

0.9993

0.9997

0.0004

0.9994 8,,391 0.0382 8,,393 0.0339

530-
Table F2 . Summary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Vertical Traverses -- Continued

Date Run Relative Rel. Velocity -- Impact Pressure (psi) -- No. Position Tr. 1 Tr. 2 Transducer 1 Tranducer 2 Mean SD Mean SD

04/14/87 60 0.1995 0.9738 0.9740 6.935 0.0937 6.940 0.0802

04/14/87 61 0.1995 0.9731 0.9728 6.884 0.1083 6.883 0.0924

04/15/87 98 0.1995 0.9733 0.9735 6.387 0.0575 6.392 0.0472

04/15/87 99 0.1995 0.9710 0.9712 6.443 0.0534 6.448 0.0435

04/28/87 136 0.1995 0.9732 0.9732 7.886 0.0571 7.888 0.0509

04/28/87 137 0.1995

mean

std. dev.

0.9739

0.9731

0.0011

0.9738 7.927 0.0388 7.928 0.0347

04/14/87 62 0.3990 0.9238 0.9240 6.208 0.0938 6.211 0.0811

04/14/87 63 0.3990 0.9237 0.9236 6.236 0.0810 6.236 0.0730

04/15/87 104 0.3990 0.9239 0.9237 5.760 0.0602 5.759 0.0502

04/15/87 105 0.3990 0.9243 0.9246 5.821 0.0592 5.826 0.0536

04/28/87 142 0.3990 0.9290 0.9289 7.042 0.0632 7.043 0.0544

04/28/87 143 0.3990

mean

std. dev.

0.9276

0.9254

0.0023

0.9276 6.999 0.0594 7.001 0.0539

04/14/87 64 0.5986 0.8616 0.8616 5.459 0.0877 5.460 0.0744

04/14/87 65 0.5986 0.8612 0.8608 5.482 0.1065 5.479 0.0938

04/15/87 106 0.5986 0.8651 0.8652 5.094 0.0783 5.097 0.0701

04/15/87 107 0.5986 0.8661 0.8663 5.060 0.0515 5.064 0.0418

04/28/87 144 0.5986 0.8661 0.8662 6.099 0.0639 6.102 0.0528

04/28/87 145 0.5986

mean

std. dev.

0.8687

0.8648

0.0029

0.8689 6.158 0.0768 6.163 0.0630

04/14/87 66 0.7981 0.7914 0.7914 4.541 0.0794 4.543 0.0667

04/14/87 67 0.7981 0.7914 0.7916 4.475 0.0912 4.478 0.0781

04/15/87 112 0.7981 0.7998 0.7997 4.090 0.0740 4.090 0.0607

04/15/87 113 0.7981 0.7951 0.7951 4.015 0.0768 4.016 0.0627

04/28/87 150 0.7981 0.8011 0.8011 5.062 0.0654 5.063 0.0615

04/28/87 151 0.7981

mean

std. dev.

0.7974

0.7960

0.0041

0.7975 4.981 0.0711 4.983 0.0625

04/14/87 68 0.8380 0.7736 0.7736 4.270 0.0943 4.271 0.0770

04/14/87 69 0.8380 0.7714 0.7718 4.181 0.0948 4.186 0.0782

04/15/87 114 0.8380 0.7784 0.7783 3.881 0.0773 3.881 0.0656

04/15/87 115 0.8380

mean

std. dev.

0.7815

0.7837

0.0033

0.7815 3.938 0.0696 3.938 0.0593

-531-
Table F2 . Summary of Relative Velocities and Positions and Observed

Mean Impact Pressures and Standard Deviations of the Mean for

Vertical Traverses - - Continued

Date Run Relative Rel. Velocity

No. Position Tr. 1 Tr. 2

-- Impact Pressure (psi) -• Transducer 1 Tranducer 2

Mean SD Mean SD

04/14/87 70 0.8779 0.7462 7463 3 996 1122 3 998 0.0957

04/14/87 71 0.8779 0.7511 7510 4 014 0841 4 015 0.0673

04/15/87 122 0.8779 0.7575 7571 3 720 0652 3 717 0.0563

04/15/87 123 0.8779

mean

std. dev.

0.7564

0.7528

0.0052

7566 3 688 0675 3 690 0.0545

04/14/87 72 0.9178 0.7183 7185 3 623 0763 3 625 0.0690

04/14/87 73 0.9178 0.7222 7226 3 691 1008 3 696 0.0894

04/15/87 124 0.9178 0.7286 7287 3 416 0566 3 418 0.0492

04/15/87 125 0.9178

mean

std. dev.

0.7282

0.7243

0.0050

7286 3 449 0915 3 454 0.0783

04/14/87 74 0.9577 0.6775 6779 3 261 0765 3 265 0.0656

04/14/87 75 0.9577 0.6751 6748 3 235 0898 3 233 0.0760

04/15/87 126 0.9577 0.6872 6871 3 047 0633 3 047 0.0551

04/15/87 127 0.9577

mean

std. dev.

0.6830

0.6807

0.0055

6830 2 994 0660 2 994 0.0552

04/14/87 76 0.9976 0.6005 6005 2 536 0672 2 537 0.0565

04/14/87 77 0.9976 0.6041 6047 2 .587 0603 2 .592 0.0576

04/15/87 128 0.9976 0.6128 6126 2 .409 0521 2 .408 0.0469

04/15/87 129 0.9976

mean

std. dev.

0.6100

0.6769

0.0056

6104 2 .395 0577 2 .399 0.0502

-532-
References

:

[Fl] Starrett, P. S,, Nottage, H.B. , and Halfpenny, P. F. "Survey of

Information Concerning the Effects of Non- Standard Approach

Conditions Upon Orifice and Venturl Meters," ISA Preprint of ASME

paper 65-WA/FM-5, 1965.

[F2] Mattlngly, G. E. , Fundamental Flow Research- Potential for

Contributing to Orifice Meter Technology, appears in Mattlngly, G. E. , et al.. Workshop on Fundamental Research Issues in Orifice

Metering, GRI Report 84/0140, September 1984.

[F3] Davis, R. and Mattlngly, G. E. , Numerical Modeling of Turbulent

Flow through Thin Orifice Plates, NBS SP484/2, 1977.

[F4] Goldstein, S., Modern Developments in Fluid Dynamics, Dover

Press, New York, NY, 1965.

[F5] Schlichting, H. , Boundary Layer Theory, McGraw-Hill Book Co., New

York, NY, Sixth Edition, 1968.

[F6] Streeter, V. L. , Fluid Mechanics , McGraw-Hill Book Co., New York,

NY, 5th Edition, 1971.

533-

NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

I. PUBLICATION OR

REPORT NO. NIST/TN-1264

2. Performing Organ. Report No. 3. Publication Date

June 1989

4. TITLE AND SUBTITLE

Measurements of Coefficients of Discharge for Concentric Flange-Tapped Square-Edged

Orifice Meters in Water Over the Reynolds Number Range 600 to 2,700,000

5. AuTHOR(S)janies R. Whetstone, William G. Cleveland, George P. Baumgarten,

Samuel Woo, and M. Carroll Croarkin

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

KATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

(formerly NATIONAL BUREAU OF STANDARDS)

U.S. DEPARTMENT OF COMMERCE

QAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

American Petroleum Institute

122C L Street, NW

Washington, DC 20005

10. SUPPLEMENTARY NOTES

[3J Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here) Presented here is a descripcion of Che measuremenc procedures and

standards, data acquisition systems, and data bases developed in the American Petroleum Institute (API) -sponsored orifice discharge coefficient data base project performed at the National Bureau of Standards

(NBS) primary water flow rate measurement facility. Measurements were performed on five orifice meter sizes, 2, 3, 4, 6, and 10 inches, over

the beta ratio range of 0.08 to 0.75. The measurement systems and

procedures were designed to provide full documentation of the relation between the observations comprising the data base developed and U.S. national measurement standards.

Data acquisition procedures were automated to minimize human error in data recording, particularly for differential pressure observation. Laboratory-quality transducers and pressure standards were used and data acquisition was automated for observation of differential pressure,

flowing fluid temperature, collected mass of water, and time of

collection. Only a few parameter observations were made manually and entered into the data base. A large data base stored in computeraccessible form has resulted. This data base consists of the recorded

raw data and the results calculated from them.

To realize the full potential of the transduction equipment used in the project, appropriate working standards were incorporated into the measurement systems to allow calibration of differential pressure

transducers, thermometers, length-measuring devices, and weigh scales. These working standards were, in turn, calibrated against U.S. national working standards over the course of the project and are described in detail. Gravimetric measurement of the mass flow rate through the orifice meters utilized the NBS primary water mass flow rate measurement

system. Documentation of the measurements, standards, and procedures

utilized in this project is given in an NBS report to be published

shortly. The data base will be available from NBS and API.

12. KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

discharge coefficient database; orifice metering; Pipe Reynolds Number;

water flowrate measurement

13. AVAILABILITY

[X~| Unlimited

I I For Official Distribution. Do Not Release to NTIS nn Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[^31 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

546

15. Price

fr U.S. GOVERNMENT PRINTING OFFICE: 1989— 21*2-200' 05031* USCOMM-DC 6043-P80

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