Pi P2

Nutating Disc Nozzle

NBS BUILDING SCIENCE SERIES 159

On-Site Calibration of Flow

Metering Systems Installed

in Buildings

U.S. DEPARTMENT OF COMMERCE • NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

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

and facilitate their effective application lor public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engmeering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATION.\L MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities- — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering^ — Manufacturing

Engineering — Building Technology — Fire Research — Chemical Engineering^

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
WATIOMAL EUREAl OF ETAHD/'JtDS LIBRARY NBS BUILDING SCIENCE SERIES 159

On-Site Calibration of Flow Metering Systems^

Installed in Buildings o

,

David W. Baker

C. Warren Hurley

Building Equipment Division

Center for Building Technology

National Bureau of Standards

Washington, D.C. 20234

Prepared for: U.S. Navy

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued January 1984

r

o

til

CO Q
Library of Congress Catalog Card Number: 83-600626

National Bureau of Standards Building Science Series 159

Natl. Bur. Stand. (U.S.], Bldg. Sci. Ser. 159, 154 pages (Jan. 1984]

CODEN: BSSNBV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1984

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
ABSTRACT

The measurement of flow of the various fluids (air, water, steam) lised in

building service systems is usually the most difficult parameter to obtain and

maintain. Consequently, in energy management and control systems (KMCS), the

flowrate or the total quantity of flow is often the least accurate measurement.

However, in most systems the energy consumed depends directly on this

parameter.

Since the majority of fluid flow measuring techniques require the sensing

element to be located in the stream of the fluid being monitored, flow measuring devices often are the most difficult instruments to calibrate initially and

to maintain in calibration within the required accuracy. This report summarizes

the various types of flowmetering devices used in EMCS , various methods for their

initial calibration and, when practical, techniques for maintaining their calibration while they are in service. Emphasis is placed on the use of transfer

reference meter systems, where the working meter is calibrated on site by

connecting it in series with a calibrated transfer meter of any variety.

Other methods of calibration are also described.

Reference tables and the necessary equations for flow calculations are presented throughout the text and in the appendicies. Illustrative examples

are given in detail for the calculation of flow using each type of metering

device described. These examples are extremely helpful in field calibration

when the metering being calibrated is of a different type than the meter being

used as a reference. Because of this, the reader is encouraged to review

these examples.

Key words: calibration methods; flowmetering devices; flow nozzle meters;

multiple pitot-static tube assemblies; orifice meters; positive

displacement meters; reverse-pitot tube assemblies; target meters;

turbine meters; ultrasonic flowmeters; venturi meters; vortex

shedding meters.

iii
TABLE OF CONTENTS

Page

ABSTRACT iii

LIST OF FIGURES vi

LIST OF TABLES viii

NOMENCLATURE ix

SI CONVERSIONS xii

DISCLAIMER xiv

1. INTRODUCTION 1

2. ORIFICE, FLOW NOZZLE AND VENTURI METERS 4

2.1 PHYSICAL CHARACTERISTICS 4

2.2 HYDRAULIC EQUATION 4

3. CALIBRATION METHODS FOR DIFFERENTIAL PRESSURE AND OTHER TYPES OF

METERS 11 3.1 TRANSFER REFERENCE FLOWMETER SYSTEM U

3.2 DIRECT G^LIBRATEON METHtiD 15

3.3 PERFORMANCb: EVALU\r'ON "^ROM niRECT CALIBRATION OF AP

I KANSnrCF.R SYS TKM' ] 9

3.^ ADDITIONAL FACTOR!^ :0 BK CONSIDERED IN THE ON-SITE CALIBRATION

OF DIFFERENTIAL PRESSURE METERS USING TRANSFER REFERENCE

METERS 21

4. ON-SITE CALIBRATION OF OTHER FLOW METERING SYSTEMS 29

4.1 POSITIVE DISPLACEMENT FLOWMETER 29

4.2 VORTEX SHEDDING FLOWMETER 34

4.3 TURBINE METER 38

4 .4 TARGET METER , 43

4.5 MULTIPLE PITOT-STATIC AND REVERSE-PITOT TUBE ASSEMBLIES 48

4.6 ULTRASONIC FLOWMETER 51

4.7 INSERTION TYPE TURBINE METER 54

REFERENCES 57

ACKNOWLEDGMENTS 59

APPENDIX A. COEFFICIENT OF DISCHARGE C AND FLUID EXPANSION FACTOR Y

FOR ORIFICES, FLOW NOZZLES AND VENTURI METERS A-1

APPENDIX B. FLUID PROPERTIES AND FLOW QUANTITY CONVERSION FACTORS B-1

APPENDIX C. TEMPERATURE AND PRESSURE RELATIONS C-1

APPENIOIX D. RELATION BETWEEN MASS AND VOLUME RATE OF FLOW D-1

iv
TABLE OF CONTENTS (Continued)

Page

APPENDIX E. ILLUSTRATIVE EXAMPLES E-1

E.l MASS AND VOLUME RATES OF FLOW, SUPERHEATED STEAM E-1

E.2 MASS AND VOLUME RATES OF FLOW, WET STEAM E-2

E.3 MASS AND VOLUME RATES OF FLOW, DRY AIR E-3

E.4 DENSITY OF MOIST AIR E-5

E.5 DIRECT CALIBRATION OF AN ORIFICE METER ON SITE WITH A

GRAVIMETRIC CALIBRATOR E-7

E.6 CALIBRATION OF AN ORIFICE METER ON SITE USING THE TRANSFER

METER METHOD . J E-1

1

E.7 ON-SITE CALIBRATION OF A POSITIVE DISPLACEMENT METER USING

THE TRANSFER METER METHOD E-1

4

E.8 ON-SITE CALIBRATION OF A VORTEX SHEDDING METER USING THE

TRANSFER METER METHOD E-1

8

E.9 ON-SITE CALIBRATION OF A TURBINE METER E-22

E.IO ON-SITE CALIBRATION OF A TARGET METER E-25

V
LIST OF FIGURES

Page

Figure L. Thin plate, square edge orifice meter 5

Figure 2. Flow nozzles 6

Figure 3. Nozzle venturi meter 7

Figure 4. Classical venturi meter 8

Figure 5. On-site calibration, transfer meter system downstream 12

Figure 6. On-site calibration, transfer meter system upstream 12

Figure 7. Transfer and working meter systems 14

Figure 8. Gravimetric calibration system 16

Figure 9. Calibration system for steam 20

Figure 10. Systematic error in flowrate M 22

Figure 11. Orifice plate sensing line and valve schematic 24

Figure 12. Tubular flow straightener design 26

Figure 13. Perforated plate flow straightener 27

Figure 14. Cross plate flow straightener 28

Figure 15. Cross section of a positive displacement meter 30

Figure 16. Positive displacement meter performance 33

Figure 17. Mechanical design of a vortex shedding flowmeter 35

Figure 18. Vortex shedding flowmeter performance 37

Figure 19. Axial flow turbine meter 39

Figure 20. Performance of a turbine meter 41

Figure 21. Sketch of a target meter 44

Figure 22. Drag coefficient for two target meters 45

Figure 23. Target meter flowrate outputs 47

Figure 24. Pitot-static rake assembly 49

vi
LIST OF FIGURES (Continued)

Page

Figure 25. Reversed pitot tube assembly 50

Figure 26. Single path, transit time ultrasonic flowmeter 53

Figure 27. Insertion type turbine meter 55

Figure 28. Velocity profiles for fully developed turbulent flow 56

Figure A.l. Fluid expansion factor Y for orifice plates A-20

Figure A. 2. Fluid expansion factor Y for flow nozzles and yenturi

meters, Y = 1.3 A-21

Figure A. 3. Fluid expansion factor Y for flow nozzles and venturi

meters, Y = 1.4 A-22

Figure B.l. Compressibility factor for air B-7

Figure B.2. Area factor F^ B-8

Figure B.3. Dynamic viscosity of water y, and kinematic viscosity v .... B-9

Figure B.4. Dynamic viscosity of saturated and superheated steam B-10

Figure B.5. Kinematic viscosity of steam and of water B-11

Figure B.6. Dynamic viscosity of air B-12

Figure C. 1 . Conversion factor F^^ water columns C-8

Figure C.2. Conversion factor F^i for mercury columns C-9

Figure C.3. Water manometer correction factor F„2 ^'^^ column

density C-10

Figure C.4. Mercury manometer correction factor Fn,2 ^or air column

density C-11

Figure E.l. Coefficient of discharge for an orifice meter E-15

Figure E.2. Calibration factor for a turbine meter E-26

Figure E.3. Performance of a target meter E-30

vii
LIST OF TABLES

Page

Table 1. Pressure Loss through Differential Pressure Primary

Elements 9

Table A.l Coefficient of Discharge C, Orifice Plates A-2

thru A. 10 A-11

Table A.ll. Coefficient of Discharge C, 1932 ISA Flow Nozzle A-12

Table A. 12. Coefficient of Discharge C, Long Radius Flow Nozzle A-13

Table A. 13. Coefficient of Discharge C, Nozzle Venturi Meter A-14

Table A. 14. Coefficient of Discharge C, Classical Venturi Meter A-15

Table A. 15. References, Equations for Coefficient of Discharge A-16

Table A. 16. Fluid Expansion Factor Y for Flow Nozzles and Venturi

Tubes A-17

Table A. 17. Uncertainty of Discharge Coefficients A-18

Table A. 18. Uncertainty of Expansion Factors A-19

Table B.l. Density of Saturated and Compressed Water B-2

Table B.2. Density of Mercury B-4

Table B.3. Conversion Factors for Mass, Volume, and Mass and Volume

Flowrates B-'S

Table C. 1 . Conversion Factors for Pressure C-12

Table E.l. Moist Air Data E-6

Table E.2. Sample Data for Calibration of an Orifice Meter E-8

Table E.3. Turbine Meter Calibration Data E-24

Table E.4. Target Meter Calibration Data E-29

viii
NOMENCLATURE

Units

CF

d

Acceleration ft/s^

Coefficient of discharge for an orifice, flow nozzle none

or venturi meter

Meter calibration factor *

Diameter of an orifice, flow nozzle throat, or in.

ventari throat

D

F

F=

Pipe inside diameter

Force

Area factor for thermal expansion of an orifice,

nozzle or venturi

in

.

none

Ftii2

Fw2

Correction factor for local acceleration due to

gravity

Combined conversion factor for mercury to convert

inches of mercury at a known temperature to psi

Correction factor for density of air in the high

pressure leg of a mercury manometer

Correction factor for density of water in the

high pressure leg of a mercury manometer

Combined conversion factor for water to convert

inches of water at a known temperature to psi

Correction factor for density of air in the

high pressure leg of a water manometer

Frequency

Dimensional and proportional constant relating

force, mass and acceleration (= 32.1740)

Local acceleration due to gravity

none

psi/in. Hg

none

none

psi/in. H2O

none

Hz

(Ib'f t)/(lb

ft/s^

* As designated

ix
NOMENCLATURE (Continued)

Units

h Differential pressure at manometer temperature In. H2O , or

in. Hg

Differential pressure at reference conditions, 68 °F in. H2O

and standard gravity

I Transmitter current ma DC

K Meter calibration factor *

m Mass _ lb

M Mass rate of flow Ib/hr

p Pressure relative to existing atmospheric pressure psig

P Absolute pressure psia

P]3 Barometric pressure psia

in. Hg at 32 °F

Pg - Saturation pressure psia

Ap Differential pressure between points in a flow * system; flowmeter differential pressure

Q Volumetric rate of flow ft-^/min

r Pressure ratio P2/P1 where P^ - P2 = AP none

R Gas constant ^ (psia) ft /lb °R

Rq Pipe Reynolds number DVp/y none

t Temperature °F

T Absolute temperature °R

V Specific volume ' ft^/lb

V Velocity ft/s

V Expansion factor for air or steam none

* As designated

X
NOMENCLATURE (Continued)

Z Gas compressibility factor

3 Ratio d/D

Y Specific heat ratio Cp/c^

p Density

y Dynamic viscosity

V Kinematic viscosity

0 Denotes "function of"

Units

none

none

none

lb/ft3

lb/gallon

lb/(ffs)

ft2/s

none

Note: This list comprises principal symbols; additional symbols are defined as needed

xi
SI CONVERSIONS

In view of the presently accepted practice of the building industry in the

United States and the status of engineering references and tables used by

Engineering Management Control Systems (EMCS) personnel, common U.S. units of

measurements have been used in this report. In recognition of the United States

as a signatory to the General Conference of Weights and Measures, which gave

official status to the SI system of units in 1960, appropriate conversion factors

have been provided in the table below. The reader interested in making further

use of the coherent system of SI units is referred to: NBS SP330, 1972 Edition,

"The International System of Units;" E830-72, ASTM Metric Practice Guide

(American National Standards 2210.1); or 1976 Edition of ASHRAE SI Metric Guide

for Heating, Refrigerating, Ventilating and Air-Conditioning . Additional SI

conversions are given in appendices B and C of this report.

Metric Conversion Factors

To convert from To Multiply by'"

Acceleration

2 2 2 ft/s metre per second (m/s ) 3.048000E-01

Area ' -

ft^^ metre^ (m^) 9.290304E-02

in.

2 >..^^.^2

metre (m2) 6.451600E-04

Energy

British thermal unit joule (J) 1.055056E+03

Force

pound-force (Ibf) newton (N) 4.448222E+00

Length

ft metre (m) 3.048000E-01

in. metre (m) 2 . 540000E-02

Mass

lb kilogram (kg) 4.535924E-01

"The notation "xE+y," where x and y are numbers, is a standard form for

indicating multiplication of the number x by the number 10 raised to the

power + y.

xii
Metric Conversion Factors (cont. )

To convert from To Multiply hy*

Mass per unit time

ib/h

ib/min

ib/s

Mass per unit volume

lb/ft\

Ib/ln.

lb/gal (U.S. liquid)

Pressure or stress

atmosphere (standard)

in. of mercury (32°F)

in. of mercury (60°F)

in. of water (39.2°F)

in. of water (60°F)

lbf/ft2

Ibf/in^ (psi)

Temperature

degree Fahrenheit

degree Celsius

degree Fahrenheit

degree Celsius

kelvin

degree Rankine

kilogram per second (kg/s)

kilogram per second (kg/s)

kilogram per second (kg/s)

3 3 kilogram per metre^ (kg/m ) kilogram per metre (kg/m^)

kilogram per metre^ (kg/m^)

pascal (Pa)

pascal (Pa)

pascal (Pa)

pascal (Pa)

pascal (Pa)

pascal (Pa)

pascal (Pa)

degree Celsius (°C)

degree Fahrenheit (°F)

kelvin (K)

kelvin (K)

degree Celsius (°C)

kelvin (K)

Velocity (includes speed )

ft/h

f t/min

ft/ sec

in. /s

metre per second (m/s)

metre per second (m/s)

metre per second (m/s)

metre per second (m/s)

1.259979E-0^

7.559873E-03

4.535924E-01

1.601846E+01

2.767990E+04

1.198264E+02

013250E+05

,38638E+03

37685E+03

49082E+02

4884E+02

788026E+01

6.894757E+03

subtract 32 and

divide by 1.8

multiply by 1.8

and add 32

add 459.67 and

divide by 1.8

add 273.15

subtract 273.15

divide by 1.8

8.466667E-05

5.080000E-03

3.048000E-01

2.540000E-02

"(see preceding page)

xill
Metric Conversion Factors (cont .

)

To convert from To Multiply by'"

Viscosity (dynamic)

lb/(ffs) pascal-second (Pa-s) 1.488164E+00

Viscosity (kinematic )

ft Is

2 2 metre per second (m /s) 9.290304E-02

Volume

ft

gallon (U.S. liquid)

in . ^

3 3 metre^ (m ) 3 'X metre (m-')

metre^ (m-^)

2.831685E-02

3.785412E-03

1.638706E-05

Volume per unit time

c 3/ • ft /mm

gal (U.S. liquid)/min

3 3 metre^ per second (m^/s)

metre^ per second (m^/s)

metre per second (m Is)

4.719474E-04

2.831685E-02

6.309020E-05

*(see preceding page)

xiv
DISCLAIMER

Certain commercial equipment and instrumentation are identified by name in this

report in order to adequately describe the types, capabilities, and technical

features of hardware available for flow metering and the on-site calibration of

flow metering instrumentation. In no case does such identification imply recom- mendation or endorsement by the National Bureau of Standards, nor does it imply

that the material or equipment identified is necessarily the best available for

the purpose.

XV

1 . INTRODUCTION

In monitoring the performance of building service systems, one of the most

difficult parameters to measure is the flow of the various fluids (air, water,

steam). As a consequence, in Energy Management and Control Systems (EMCS), the

flowrate or the total quantity of flow is often the least accurate measurement.

The energy consumed, however, normally depends directly on this parameter.

This document is intended as an aid or guide to building services personnel

(service managers, engineers, technicians) who have a basic understanding of

fluid flow and who may be faced with the task of making flow measurements in

building systems. The main purpose of this document is to summarize calibration methods for flowmeter systems installed in buildings and to present under

one cover essentially all Aecessary data and equations needed, with the

exception of steam tables, for the calculation of meter performance. Flowmeter

types and their characteristics as they relate to calibration are also discussed.

Fluids covered are air, water, and dry or super-heated steam. Emphasis is

placed on the use of transfer reference meter systems where the working meter

is calibrated on site by connecting it in series with a transfer meter, which

need not be the same type as the working meter. Design characteristics of

various types of flowmeters are listed in chapter 13 of reference 1.

While the transfer meter method is usually considered the most desirable choice,

a second method used is the direct calibration method. In this case, either

the working meter is removed from the building system and calibrated directly

at a primary calibration facility employing a volumetric or weighing-type fluid

collection and measurement system, or the working meter is calibrated on site

against a volumetric or weighing system.

A third method, employed with differential pressure (AP) meter systems of

orifice, nozzle or venturi types, is to perform a direct calibration of the AP

transducer. Then, using published data for discharge coefficients and fluid

expansion factors for the meter primary element, the system accuracy can be

estimated and the flow characteristics for the complete metering system can be

determined

.

For best accuracy, all flowmeters need to be calibrated using the working or service fluid under typical operating conditions including flowrates, temperatures, and pressures. Accuracies approaching those of primary calibration

facilities (tenths of a percent) may be obtained with an on-site calibration

using a volumetric or weighing-type collection aad measurement system. However,

this approach is usually too costly, requiring excessive time, space and/or

labor. Also, this degree of accuracy is not often needed in EMCS. The transfer meter method is considered most feasible since the on-site installation and

operational efforts are generally less demanding and good accuracy is possible.

Reliable, accurate flow measurements depend on certain factors or conditions

which often receive too little attention. Two of these factors are: (1) improper meter installation causing a distorted, asymmetrical flow pattern at the

meter entrance, and (2) lack of sufficient follow-up or continuing calibration

effort to assess the system performance for its entire service period.

Admittedly, an adequate installation in existing EMCS lines of the transfer

1
reference meter system and/or the working meter is often difficult, impractical,

or virtually impossible. In any new construction, facilities for a transfer

reference meter should be considered along with the design of the building

mechanical systems.

The types of meters to he discussed include differential pressure types

(orifice, flow nozzle, venturi, pitot-static tube, and reversed- type pitot);

volumetric types (positive displacement, turbine and vortex); target (impact)

and the ultrasonic meter (transit time). Each type will be discussed for use

on water, air and steam as appropriate. A brief description of each meter is

given, followed by the basic hydraulic or performance equation, installation

notes, and sample calculations. Emphasis is placed on the orifice, nozzle, and

venturi meters since they are used extensively as both transfer and working

meters

In an effort to make this publication most helpful to the intended user,

supplementary data and information are included in the appendix sections as follows: Discharge coefficients and fluid expansion factors for orifice plates,

flow nozzles, and venturi meters along with corresponding tolerance (uncertainty,

accuracy) data for these quantities are given in appendix A. The sources for

these data are references 2, 10, and 11. Properties of air, water, and steam

along with mass/volume conversion factors needed for calculation of flow

quantities are presented in appendix B. Temperature and pressure relations are given in appendix C. In particular, conversion factors for mechanical pressure

gauges, pressure transducers, and liquid manometers are discussed. The relations

between mass and volume rate of flow for gases are discussed in appendix D.

Appendix E is a compilation of several example calculations given in detail.

Those readers already familiar with the flow measurement techniques discussed

here may prefer to read these examples first, before reviewing the main body of

this report.

Many flow measurements involve the quantities force and mass. In the English

system, the same word "pound" refers to both and therefore it becomes necessary

to distinguish between the two quantities. In this report, "lb" refers to pound

mass, and "Ibf" refers to pound force. These two quantities are related through

Newton's second law, force = mass x acceleration. The pound mass is defined in

terms of the kilogram and the pound force is defined as the force exerted on a pound mass when it is subjected to the standard acceleration of gravity of

32.1740 ft/s^. When Newton's second law is used in equation form, a conversion

factor designated is necessary to maintain both numerical and dimensional

equality, i.e., F = ma/g^.. In the English system when the unit of force is

designated Ib^ and the unit of mass is lb, g^ = 32.1740 (lb'ft)/(lb^'s2).

Throughout this report, the reader will find references to scheduled maintenance

calibration of the various types of metering methods described. Scheduled on- site calibration is recommended for all types of flow meters and their transmitting systems. The extent and type of on-site calibration varies from one type of meter to another. However, one major factor applicable to all types of

flow metering calibration must be called to the attention of the reader in the

introduction of this report to avoid repeating it throughout the text and to

emphasize its importance when carrying out the actual on-site calibration and

2
when setting up maintenance schedules for routine calibration: the deterioration

of primar}' elements of the meter (the parts which interact with the flowing

fluid) by abrasion and chemical and/or electrolytic reactions has been found

to be a major problem in the continuous monitoring of fluids. This is especially true in monitoring the flow of liquids. The designer of a flow system is

not always aware of the characteristics of the components in a metering device

nor is he always aware of possible changes in the characteristics of the fluid

which is to be monitored. In general, the deterioration of a metering system

by abrasion and chemical and/or electrolytic reactions is a continuing problem

that is hidden in the initial design and is often founci to be the basis of on- site meter calibration problems. When continous deterioration of any metering

system becomes apparent from previous calibration records or from an erratic

response of a metering system which cannot be readily diagnosed, one should

always examine the primary parts of the meter for evidence of abrasion and

chemical and/or electrolytic reaction with other components in the system. The

transducer (i.e., a device which converts one form of energy into another) is

also subject to deterioration from environmental conditions. In the case of

the metering devices utilizing differential pressure (A?) measurements, the

calibration of the transducers often is more critical than that of the

primary elements.

3
2. ORIFICE, FLOW NOZZLE AND VENTURI METERS

Since differential pressure meters of the orifice, flow nozzle, and venturi

types are used extensively as both transfer and working meters, a brief description of them and the hydraulic equation from which the performance is calculated

will be given here. These meters have been used for flow measurements in closed

conduits dating back to the past century. Their characteristics have been

investigated extensively and are well known. Bernoulli's theorem (1738) is the

basis for the hydraulic equation.

2.1 PHYSICAL CHARACTERISTICS

Figures 1, 2, 3, and 4 indicate the shapes and pressure tap locations for

orifice, flow nozzle, and venturi meters. When the meter is to receive a direct

calibration, the choice of faeter type is largely a matter of allowable building

system pressure loss versus meter cost. Orifice meters are simple in design.

They are manufactured from flat plates and therefore are relatively inexpensive,

but they produce the largest pressure losses. The design of nozzle and venturi

meters is more complex, with manufacture necessary from machined castings or welded sections, but these meters offer lower pressure losses. Table 1 gives

pressure loss data for these types as a function of the beta ratio, 3 = d/D,

where d is the meter orifice or throat diameter and D is the inside diameter

of the pipe.

The primary element is known as that part of the meter system which interacts

with the flowing fluid. In these meters, this is the orifice plate, flow

nozzle, or venturi. The interaction causes fluid acceleration and pressure

change. The secondary element is the instrument system which senses and measures this interaction; in these cases, the secondary element is a AP transducer

system or a differential manometer including the pressure sensing lines.

2.2 HYDRAULIC EQUATION

Two forms of the hydraulic equation from which the flowrate is calculated are:

M = 358.93 (C Y d^ F^)[p hj(l - 3^)]^/^ (2_i)

Q = 5.982 (C Y d^ F^)[hyp(l- d>^)]^'^ (2-2)

where 358.93 (lbl/2/hi-)( f ^3/2 /in. ) 5.982 (ft3/2/min)(lbl/2/in.5/2)

M = mass flowrate, Ib/hr

Q = volume flowrate, ft3/ mm

C = coefficient of discharge, dimensionless

Y = fluid expansion factor, dimensionless

d = diameter of orifice, nozzle throat, or venturi throat, in.

p = density of fluid entering primary element, Ib/f t3

h^^ = differential pressure P]^ - P2, inches of water at 68 °F

3 = ratio d/D, dimensionless, where D is the pipe inside diameter

Fa = area factor for thermal expansion of a primary element, dimensionless

4
i-l •• 0 po J=

01 oj 3

craw

ra

w -a

1-1 c

(u ra co - O CL,

ra

w

M-i o. e •H

ra ra

C q;

0) ra

cb a» c 4-1 4J

S-i

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0)

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ra

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ra

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6
7

Table 1. Pressure Loss Through Differential

Pressure Primary Elements

Pressure Loss in Percent of Actual Differential Pressure

Ratio

3 Orifice* Flow Nozzle* Nozzle Venturi** Classical Venturi*

0.3 88 86 26 13

.4 82 75 22 12

.5 73 64 17 11

.6 63 53 15 10

.7 52 41 13 11

Classical venturi meters, 7° outlet cone

* Reference 2

** BARCO (Aeroquip) catalog 866

9
The theory of flow of fluids In terras of pressure differences and a derivation

of these equations may be found in reference 2, pages 47-56. Equations (2-1)

and (2-2) apply for subsonic flow.

When calibrating a working meter on site, the flowrate M or 0 is measured either

by the transfer reference meter system or by a direct calibration system. The

quantity h^ is the working meter output. The fluid expansion factor is con- sidered a known quantity; for liquids, Y = 1.000 and for gases, Y is calculated

from gas relations. Thus, with d, F^, p, and 3 known, common practice is to

determine the discharge coefficient, C, for the particular working meter.

The coefficient of discharge is defined as

Q - Actual rate df flow

Theoretical rate of flow

In turbulent flow, this coefficient must be measured experimentally. It depends

on the shape of the primary element (orifice, nozzle, venturi), the pressure

tap locations (flange; ID, 1/2D; corner), the 3 ratio, and the Reynolds Number,

Rq = D V p/m, where V is the fluid average velocity and \i is the dynamic viscosity. Its dependence on flowrate is through V, and on fluid properties

through p and y . It is important to note that once a AP meter is calibrated

using one fluid, its performance with other fluids can be predicted through

this C vs Rq relationship. Data for this relationship are given in appendix A

for reference purposes.

The fluid expansion factor, Y, accounts for any change in density as the fluid

flows through the primary element. For flow through nozzle and venturi meters,

a correction based on ideal flow is used. This correction is dependent on the

pressure ratio P]^/P2, on the 3 ratio, and on the gas specific heat ratio

Y = Cp/Cy. For flow through orifices, an empirical relation is used. For

liquids, Y = 1. Appendix A gives equations and tabular data for Y.

The factor F^ accounts for any expansion or contraction in the meter throat or orifice area due to temperature increase or decrease from the (ambient) temperature which existed when diameter d was determined. For operating temperatures within 50 °F of ambient, this effect can usually be ignored. Figure B-8

in appendix B includes graphical data for F^ as a function of temperature for

several materials used in primary elements.

10
3. CALIBRATION METHODS FOR DIFFERENTIAL PRESSURES AND OTHER TYPES OF METERS

3 . 1 TRANSFER REFERENCE FLOWMETER SYS TEM

A transfer reference flowmeter system consists of one or more flowmeters with

upstream and downstream piping sections along with flow straightening vanes

and (usually) all necessary transducer and readout equipment. This system is

calibrated at a primary calibration facility such as NBS or a qualified independent laboratory and then installed and used on site as the reference meter

to calibrate the working meter(s). For AP reference systems, the pressure

transducers and their sensing lines must be included in all primary and rou- tine calibrations since they may be influenced by the system performance. For

maximum accuracy, the transfer flowmeter should be calibrated using the same fluid at test conditions (pressure, temperature, flowrates) which can be

expected to occur during later use on site. In this way, the performance of

the working meter can be "traceable" to a primary calibration facility.

Periodic recalibration of the transfer reference flowmeter system is imperative.

Maintenance of a reference file on each meter will help the user determine the

frequency of a recalibration schedule.

Use of transfer reference systems is often the most practical method for

calibrating building-systems working flowmeters. Direct calibration may be

too expensive, particularly where large numbers of on-site meters are involved.

While there is some loss of accuracy over that achievable by direct calibration

of the working meter at a primary calibration facility, perhaps of order 2:1,

there is a compensating gain in efficiency since one transfer meter may be used

to calibrate many working meters. On-site calibration may tend to mask errors

in meter performance due to local piping system characteristics such as distorted flow patterns downstream of pipe bends, or temperature gradient

effects in Ap meter sensing lines. Although such effects may be unknown, every

effort should be made to eliminate distorted flow patterns through use of good

meter installation practices. For example, the configuration shown in figure

5 is preferred over that shown in figure 6.

An ideal fluid flowmeter responds only to flowrate or fluid quantity collected

and, for a given flow, it will always produce the same output. In the real

world, however, many factors can affect the flowmeter performance. To serve

as a suitable transfer (or working) meter, all parameters or factors which

affect performance must be known and must remain under adequate control. For

example, many types of meters are influenced by fluid viscosity. Furthermore,

the AP meter calibration factor or discharge coefficient often varies with flowrate. In addition, swirling flow or transverse flow components such as those

immediately downstream from elbows and valves influence the accuracy of many

meters. Many meters fail to operate satisfactorily in dirty fluids containing

foreign particles such as rust or pipe scale which have detrimental effects on meter repeatability. All such factors need adequate attention and control.

Figure 5 shows a flow schematic for on-site calibration of a working meter

system with the transfer meter system downstream, and figure 6 gives a similar

schematic with the transfer meter system upstream. In each, valve functions

are as follows:

11
12
Valve Calibration Normal Notes

VI Closed Open Blocking valve, positively no leakage

allowed, low AP , suggest ball valve

V2 , V3 Open Closed Isolation valves, full open during

calibration, low AP , suggest gate

valves

V4 Control Open Flowrate control valve, must be

downstream of both systems, fine control necessary, low A? when open,

suggest ball valve

Note: Valves VI - V4 should be permanent in the working system to permit

periodic re-calibration.

Since all fluid must pass through both meters, the need for a high quality,

non-leaking blocking valve VI, can not be overemphasized. An alternative would

be the use of three valves in lieu of VI in a Tee arrangement with the leg valve

vented to the atmosphere during calibration. Any leakage would be apparent

through this vent valve. Likewise, there should be no leakage through the

branch circuits between the two meter systems. Valves V2 and V3 allow the

transfer meter system to be deactivated or used elsewhere during normal operation. With the transfer meter system downstream (figure 5), V4 could be eliminated, with flow control accomplished through V3 . However, V2 should never be

used for flow control in either case because this could disturb the flow pattern

in the transfer meter system. For the same reason (flow pattern control), the

transfer meter system downstream configuration is preferred.

Figure 7 gives minimum straight pipe requirements for each part of the transfer

and working meter systems. Each metering system requires a minimum of about 20D

of straight pipe. Flow straightening vanes or tube bundles are necessary in

both cases, unless very long straight pipe lengths (estimated greater than lOOD

to 150D minimum) exist upstream. It is noted that most standards, including

reference 2, recommended shorter lengths when no straightening vanes are used.

However, more recent research indicates that these lengths are too short to

eliminate the predicted effects on accuracy. See reference 4 for experiments

conducted with elbows upstream of orifice plates and reference 5 for experimental results which show that swirling flow decays at quite low rates in pipes at

Reynolds numbers comparable to those existing in building systems (turbulent

flow). Also, it must be realized that tubular type flow straighteners only

eliminate swirling or transverse velocity components; they will not completely

reshape the axial velocity profile to a fully developed or even a symmetrical

one. Therefore, a meter which requires a fully developed velocity profile such

as the transit time ultrasonic type may not perform to best accuracy unless some other flow conditioning device such as a perforated plate type flow

straightener or very long straight runs are used to aid in development of a fully developed profile. However, positive displacement (PD) meters are not

normally affected by swirling flow and flow straighteners may often be

13
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14
eliminated. Consequently, PD meters are often recommended for sitiiatlons

where adequate straight piping runs are unavailable.

3 . 2 DIRECT CAL IBRATION METHOD

The calibration of the working meter system against a volumetric f)r weighing

type fluid measurement system is known as a direct calibration. The working

meter system is either removed from the building system and calibrated at the

primary calibration facility, or the working meter is calibrated using on-site

volumetric or weighing facilities. When it is to be calibrated at the primary

facility, it is important that the entire working meter system (figure 7) be

removed and calibrated at this facility. During on-site calibration, the fluid

is directed into the volumetric or weighing system downstream of the working

meter with precautions taken to ensure that no leakage or branch circuits cause

fluid to be lost before entering the calibration equipment. The following

comments pertain to direct calibration on site.

For building systems involving flowing water , a direct on-site calibration may

be more satisfactory than the transfer method for differential pressure (AP)

meters of sizes accommodating less than 2-inch pipe for the following reasons:

the uncertainties of the discharge coefficients are large and sometimes unavailable; and, flow measurements in these smaller sizes can usually be made with

satisfactory accuracy using commercially available equipment of reasonable size

and cost. (For example, commercially available scales offer good accuracy at

reasonable cost.)

The calibration of a volumetric metering system by use of smaller reference

volumes or by physical measurement is often considered less convenient. Therefore, volumetric-type meters are often calibrated using a volumetric-type meter

which has been calibrated using the gravimetric calibration method with the

water in the same temperature range.

A gravimetric- type calibrator system for water is shown in figure 8. The basic

equipment are the scales and weigh tank, a timer, a thermometer, valves, and a timer switch. Gravimetric systems are classified into two types according to

the method used in collecting the water: the static-weigh and the dynamic-weigh

methods

.

Static-Weigh

Operation consists of:

1. Set flowrate.

2. Determine tare weight (mass) while water is diverted to drain or storage

3. Divert flow to weigh tank, starting timer (or working meter counter

for totalizing operation).

4. After collection of desired amount of water, divert flow to drain or storage, stopping timer or counter.

15
o

16
5. Determine gross weight (mass).

6. Drain weigh tank through dump valve (or pump out).

Flowrate = Net Weight (mass)/Time Interval

Meter Output/Pulse = Net Weight (mass)/Total Count (pulse type output).

Weighing is performed with water stationary in the tank and the net weight

(mass) can be determined quite accurately. The weighing, liowever, requires two

operations and thus becomes time consuming. A critical component is the diverter

valve. Its function is to direct the flow as desired to drain or storage, or

to the weigh tank without disturbing the rate of flow through the working

meter. The timer switch is connected directly to the diverter valve and should

be adjusted to activate at the midpoint of the diverter operation. This switching is often performed using a suitable photocell and light source to develop a sharp on/off relationship at the midpoint. When the desired uncertainty is one percent or more, manual timing will usually be satisfactory if the diverter

valve and timer are operated with the required care.

Dynamic-Weigh

Operation consists of:

1. Set flowrate with dump valve open and tare weight on the weigh beam.

2. Close dump valve. Tank begins to fill.

3. l^fhen tare weight is balanced, beam rises, starting timer or counter.

4. Place weights on scale beam pan corresponding to the desired amount

of water being collected, lowering beam.

5. When total counterpose weights are balanced, beam rises again,

stopping timer or counter.

Thus, the time interval or total count for a preselected amount of water to

enter the weigh tank is determined, and the weighing operation is completed "on

the run" while the water enters the tank. This method has the advantage of con- suming less time and offers greater convenience compared to the static method.

The timer switch activated by the weigh beam may be a direct contact, magnetic,

capacitance, or optical type. When load cells are used for weighing, the timer

start/stop circuitry must, of course, sense the load cell system output. Possible errors due to the change in inertia of the water and added weights should

be considered. This inertia error is discussed in reference 22. When the

desired uncertainty is one percent or more, manual timer actuation may be used.

Pertinent features of both of these systems include:

The weigh tank capacity should be sufficient for a minimum collection time

of 30 seconds at the maximum flowrate plus tare weight collection time.

For faanual timing, a minimum collection time of 1 minute is recommended.

17
« It is important thiit ao part of the system touches or rubs against the

weigh tank. If it is mandatory that the system be connected to the

weigh tank, then the construction should be such that no vertical force

components are exerted on the scale from the system.

•9 It is essential that all of the flow and only that flow passing through

the working meter be collected in the weigh tank. There must be no leakage through the blocking valve or through any branch circuits. kr\y air

or vapor must be vented at the high points. Keep all meter discharge

lines as short as possible.

^ Commercially available scales of conventional design with weigh beam and

counterpoise weights are recommended for high accuracy at reasonable cost.

For a calibration accuracy of 0.5 percent, a desirable scale accuracy

would be 0.05 to O.l percent of reading. The scale should be calibrated

in place with static weights, Commercial Class C, before the weigh tank

is installed, and after the installation of the tank connections is complete. This procedure checks on possible interference from any connections. In selecting a scale, the scale sensitivity (weight necessary for

shifting the weigh beam from an equilibrium position at the midpoint to an equilibrium position at either extremity) should be sufficient for the

desired accuracy. However, more sensitivity than necessary should be

avoided because scale "settling time" usually increases with sensitivity

which increases the static weighing time unnecessarily. During dynamic

weighing, increasing beam oscillations may generate unnecessary problems.

WVien weighing to an accuracy of 0.5 percent or better, the air buoyancy

effect should be considered. This effect is about 0.12 percent when water

is weighed in air.

No leakage is allowed through the dump valve during the weighing or collection operations.

3 The minimum net weight (mass) of water collected should be at least 10

percent of the scale capacity. When totalizing pulse-type meter outputs,

the minimum net weight (mass) should correspond to at least 1000 pulses,

preferably 5000.

'3 Water density is determined from the temperature and pressure, table B-1

Linear interpolation may be used if necessary. A mercury-in-glass thermometer is preferred, and it should be graduated in single degrees, accurate

to one degree Fahrenheit or better.

o Water temperature should not exceed about 150 °F due to liquid volatility

and possible evaporation losses. At this temperature level, the weigh tank

should be provided with a cover to reduce this loss. Safety precautions

should be taken to avoid personnel injury when handling water at these

temperatures in a system open to the atmosphere.

An example calibration of an orifice meter with a gravimetric calibrator system,

including sample data and calculations, is included in appendix E, example E.5.

18
Direct calibration of meters used to measure the flow of a gas such as air

requires a closed weigh tank or a volumetric tank. Such approaches are used in

primary calibration facilities, but because of their complexity and costs they are considered generally impractical for calibrating working meters on-site.

Flowmeters in building systems monitoring steam flow may receive a direct

calibration by measuring condensate flow provided all steam flowing through

the working meter is condensed and flows through a single pipe at a convenient

location. Great care must be exercised to trace all lines to assure that no loss through branch lines and that no leakage occurs. The major advantage to

the steam-condensate method is that liquid flow is easier to measure accurately

than is gas flow. Figure 9 shows a flow schematic for a calibration for steam

flowmeters. Long pipe lines and service equipment such as heaters will nor- mally be located between the working meter and the calibrator. Thus, calibration should be attempted only during periods of steady steam load. Even then,

long periods may be required to obtain a steady flowrate in -the meter and at

the calibrator. The system should be vented as necessary to expel all air.

The calibrator may be a gravimetric type as discussed above, or a positive

displacement meter properly calibrated at a primary facility.

Procedures and equipment which can result in accurate measurements of the mass flowrate, M, have been described above. Such measurements require the services

of personnel who are knowledgeable and experienced in measurement techniques

and have access to the required equipment, space and labor. The level of accu- racy thus attained may not be needed nor economical. Alternatives include the

use-of a transfer reference meter system as discussed previously. For a AP

meter, a differential-pressure performance evaluation of the flow measurement

system based on the direct calibration of the AP transducer only is required.

3 . 3 PERFORMANCE EVALUATION FROM DIRECT CALIBRATION OF AP TRANSDUCER SYSTEMS

ONLY

In some situations, an on-site calibration of the working meter using a direct

calibration or a transfer reference meter may not be feasible. However, with

differential pressure (AP) transducers used on meters of the orifice, venturi,

or flow nozzle types, their performance can be evaluated by performing direct

calibration of the AP , pressure, P, and temperature, T, monitoring systems

only. By using published data to obtain discharge coefficients and fluid

expansion factors for the meter primary element, the flow characteristics or performance of the complete working meter system can then be determined. This

approach requires relatively little straight pipe run since no transfer meter

system is involved. However, the AP , P, and T systems need to be calibrated.

Appendix A is a compilation of available data and equations for discharge

coefficients and fluid expansion factors for orifice, flow nozzle, and venturi

type primary elements. Equations which may be used to assign uncertainties to

the discharge coefficient and expansion factor are also included.

The disadvantages of this method include loss of accuracy due to the

uncertainties assigned to the discharge coefficient and the expansion factor.

In addition, when the AP transducer is required to perform only within a narrow

band corresponding to its full scale output, the loss of accuracy at the low or

19
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20
part scale AP values can become quite large. For example, a transducer rated

at 0.5 percent full scale would need only produce a differential pressure mea- surement accurate to within 5 percent at a AP value of 10 percent full scale to

still comply with its rated performance. This indicates the importance of

using a transducer which has excellent repeatability characteristics and the

need for periodic calibration over the operating range. Transducers are available which specify accuracy of the actual reading plus a small portion of the

full scale reading (e.g., +0.15 percent of reading + 0.005 percent f.s.).

Regardless of the specified accuracy, when a transducer is first put into ser- vice, 3 or 4 calibrations might be performed over a period of 6 months to a year and the results used to establish a performance curve from which linearity

and hysteresis corrections can be made if necessary. Once the transducer performance has been established, intervals between the periodic calibrations may

be increased. It should b^e noted that the AP transducers often require a specified "warm-up" period and respond to changes in the ambient conditions by loss

of accuracy.

When a system's flow rate more than doubles (range 4:1 in AP) , the use of two

AP transducers may be preferred; one for HIGH AP and one for LOW AP. Significant improvements in the uncertainty are possible through the use of this technique. For example, figure 10 shows the actual systematic error e^^/H, percent

of rate, as a function of flowrate, M, for a HVAC system installed at NBS which

uses two such transducers. For a flow range of 500 to 2000 Ib/hr, the systematic error ranged from about 2 to 5 percent with two transducers, whereas with

one transducer (HIGH), the error would have ranged from about 2 to 15 percent.

While efv|g depended on the combined effects of several errors in this case, the error in AP dominated at low AP values. In this example, the AP transducer

error was expressed on a full scale basis and no linearity corrections were

made.

Reference 23 is a detailed analysis of the performance of an energy monitoring

system for steam flow at NBS using the above approach of direct calibration of

the AP , P, and T systems only. An appropriate method and sample calculation is

given for estimating the uncertainty in the total energy consumed over a one-year period.

3.4 ADDITIONAL FACTORS TO BE CONSIDERED IN THE ON-SITE CALIBRATION OF

DIFFERENTIAL PRESSURE METERS USING TRANSFER REFERENCE METERS

This section deals with on-site calibration of AP meters of the orifice, flow

nozzle, and venturi types using transfer meter systems as the reference. The

transfer reference meter is calibrated off site and its flow characteristics or performance including an estimated uncertainty, are known. The transfer reference meter is not necessarily a AP meter. Reasons for calibrating a AP meter on site include the situations when a direct f lowmeter-system calibration using a gravimetric calibrator approach is not practical; when the assignable accuracy

would be too low with calibration of the AP transducer only; or, when the

performance must be verified.
1.0

100 200 500 1000 2000 5000

FLOWRATE M, Ib/hr

Figure 10. Systematic error in flowrate M

22
Pertinent features of AP meters include:

o Flowrate varies vjith the square root of the pressure differential (AP)^/^^

as indicated in equations (2-1) and (2-2).

^ Primary elements (the parts which interact with the flowing fluid) may be

used in air, water, or dry (superheated) steam. For wet steam, consult

reference 1

.

® Discharge coefficients and fluid expansion factors for these primary

elements are well established and used extensively. However, the on-site

calibration determines the discharge coefficient which may vary with

conditions at the particular installation.

<* Accurate measurement of the output of a AP metering system is relatively

difficult (particularly at AP values of a few inches of water) compared

with meters producing a pulse type output (e.g., vortex shedding, positive

displacement, turbine).

® Since flowrate varies with (AP)l/2, the practical flow range is often

limited to about 3:1 for a single AP transducer because many transducers

are rated on a full scale AP basis.

® For best accuracy of an on-site calibration, the transfer reference meter

should be calibrated using the working fluid under test conditions which

incbjde temperatures and flowrates that duplicate those of the working

me t e r

.

o The detailed calculations necessary to obtain the flowrate or total flow

through equations (2-1) or (2-2) make a strong case for an automatic data

processing approach when measurements are to be made over a long period

or when many flows are to be monitored.

Meter system design, construction, and installation should receive careful

attention regardless of whether or not the meter is to be directly calibrated.

Common trouble areas include the pressure taps and the pressure sensing lines.

The pressure differential sensed by the transducer should be exactly the same

as that existing at the meter taps. The pressure tap hole at the inner surface

of the pipe or meter section should contain no burrs or roughness or other

irregularities. Special precautions should be taken when installing the sensing lines, keeping these lines short and close together, and including adequate

provisions for flushing, venting, and drainage. Figure 11 shows a recommended

sensing line schematic. The bypass valves facilitate transducer zero AP checks.

To ensure a positive check on bypass valve leakage (liquids) during normal

operation, the leg valve in the Tee network remains open to the atmosphere.

The likelihood of accumulation of rust, scale, and other solids in the lines

and in the AP cell make periodic flushing of the lines imperative.

Another common trouble area is the lack of sufficient straight pipe lengths

upstream and downstream. As discussed previously, it is important that the

flow field posseses no swirling components. According to recent research

23
Figure 11. Orifice plate sensing line and valve schematic.

Applies to flow nozzles and venturi meters as well.

24
(references 4 and 5) most standards are simply too optimistic about the lengths

of straight pipe needed to dampen the swirling components. This fact alone can often justify calibration on site when specific accuracy requirements are to

be met. For best accuracy, the straight length upstream should be 100 to 150

pipe diameters minimum. If this is not feasible, a flow straightener section

or vane assembly should be located a minimum of lOD upstream of the meter as indicated in figure 7. Suitable flow straightener designs are shown in figures

12, 13, and 14. The diameter of the straightener tubes in the tubular design

should be D/4 maximum. Wh^n thin wall tubes are used, the pressure losses will

be small. The perforated plate design will cause relatively large pressure

loss but it will tend to reshape and improve the symmetry of the axial velocity

profile. For more detailed discussions of design and construction, consult

references 2 and 3.

An example calculation of the calibration of an orifice meter system using a transfer meter system is given in appendix E, example E.6.

25
26
27
28
4. ON-SITE CALIBRATION OF OTHER FLOW METERING SYSTEMS

The types of flowmeters discussed in this "other" category are indicated in the

table below. Depending upon the application and accuracy requirements, they

all require calibration. The fluids indicated are those considered most likely

to be encountered in building service and do not necessarily encompass all possible fluid applications. Included in this section are meter descriptions and

summaries of operating principles, graphs showing typical performance, installation and use notes, basic equations for calculating the flow, and sample

calculations for on-site calibration.

Flowmeter Type

Positive Displacement

Vortex Shedding

Turbine

Water Air Steam

Pitot-Static Types

Reverse Pitot x x x

Multiple Pitot Static ^

Target x

Ultrasonic x

Insertion Type Turbine x x x

4.1 POSITIVE DISPLACEMENT (PD) FLOWMETER

This is a quantity-type meter in which a chamber is completely filled with

fluid and then emptied. Counting each filling indicates the flow. The counter

may be a mechanical, totalizing type with disc or wheel type readout; or an electromagnetic pulse or optical type readout may be used. This will allow the

meter to be used for either flowrate or totalizing applications. In some cases

the primary element is magnetically coupled to the counter, eliminating shaft

sealing. The PD meter may be considered a special type of fluid motor with a high volumetric efficiency and operating under light load.

The PD meter is widely used in commercial, industrial and domestic applications

metering both gases and liquids, including water. For liquids, the types of

primary elements used include the nutating disc; reciprocating piston; oscillat

ing or rotary piston; rotating gear, lobed impeller; and sliding and rotating

vanes. Figure 15 is a cross-section view of a nutating disc type.

The advantages of the PD meter include the ability to measure flow despite a wide range of fluid viscosities, a digital type output, and accuracy which is

29
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30
relatively insensitive to upstream flow patterns. Thus, long straight pipes

or flow straighteners upstream may not be necessary. Disadvantages include the

presence of significant loading due to the mechanical and fluid friction of the

metering element as well as that arising from the torque required to drive the

readout or registering mechanism. Because of this loading, a pressure differential is required to drive the meter; as a result there is a small amount of

fluid leakage past the "sealing" surfaces. This leakage is known as "slip" or "slippage". The accuracy of the meter is largely determined by this leakage or "slip". No two meters, even of the same design, will have identical proportions

of leakage. Therefore it is important, for applications requiring accuracies

better than about one half percent, that each meter be calibrated individually,

and that all parameters or factors which affect the performance be known and

adequately controlled.

Factors associated with leakage which are known to affect the meter performance

include: liquid properties, viscosity and lubricity, meter design, meter temperature, and readout loading. Other factors influencing rae.ter performance

include flowrate; pressure level in the meter; contamination in the fluid; and,

possibly, meter operating position.

Thus, in the selection of a PD meter either as a working meter or as a transfer

reference meter, the flowing fluid properties (viscosity, lubricity, and temperature) should be considered. The pressure level and allowable pressure loss

also need consideration. For water, typical pressure losses at the rated flow

may range from 2-5 psi for capillary or film seal meters (example: nutating

disc, oscillating piston) and from 10-15 psi for packed seal (reciprocating

piston) meters. For most applications, an absolute pressure level (psia) equivalent to the vapor pressure plus 3 or 4 times the meter pressure loss at the

rated flow is probably sufficient for proper operation. The user should refer

to the manufacturer's specifications for details on each meter. In calibration,

the pressure drop across the meter should be noted.

The meter should be treated as a precision instrument. Filtering of the fluid

so that solid particle size is much smaller than the meter clearances is necessary. Although optimum conditions are not known, filtration in the range of 25

to 50 microns appears adequate to ensure normal meter operation without excessive wear. No meter, including the nutating-disc type widely used in domestic

and industrial water applications, should operate continuously in fluids

containing solid particles.

Before use as a transfer reference meter, a PD meter should first be calibrated

using the same fluid at or near the temperatures and pressures which will exist

during field usage. Thus fluid viscosity and lubricity, meter dimensions, and

seal leakage are duplicated during calibration and use as a transfer reference

device. In this manner, meter performance is duplicated. Meter performance is

affected by meter orientation (vertical vs. horizontal, if permitted by the

manufacturers). Positional changes vary the mechanical friction in the metering element and in the readout mechanism, and modify the lubricant level in the

gear reduction mechanism of the readout. A safe approach is to calibrate and use the meter in the same position. Magnetic and optical readouts may not

impose the same positional operating restriction. The user should always refer

to the manufacturer's specifications regarding the positioning of the meter.

31
Several points should be noted with regard to the meter readout, when the PD

meter is used as a transfer reference. Although the mechanical readout has

long been the "work horse" for domestic, commercial and industrial applications,

other types such as the magnetic or optical types are available. A small change

in the loading of the metering element by a mechanical readout may have a significant effect on the slip characteristics of the meter, especially those of

the film seal type. Piston-type meters with packed seals are said to be less

affected by small changes in readout loading. Because wear or the presence of

dirt or corrosion can change readout loading, recalibration of the meter on a regular schedule, with more frequent intervals at the beginning of the program,

should be considered for long term measurement programs.

Also, with regard to readouts, the meter should not be calibrated with one readout and used with anOjther because of the influence of readout loading on

the meter accuracy. The readout and metering element should be connected by a positive drive, without cams, clutches or the like which may cause relative

motion between the readout and the metering element; the sole exception is the case where the meter and readout have been designed to be coupled magnetically.

In this type, the rotary motion of the metering element is magnetically coupled

to a mechanical readout or else it drives a pulse generator, producing an AC

voltage which varies with a frequency exactly proportional to the speed of the

metering element. Such a system, by proper design, should result in decreased

loading on the metering element and increased resolution in the readout. The

meter is also more readily adaptable to both rate and totalization applications.

Suitable external Instrumentation such as an electronic counter is used to count

the pulses received from the meter.

Air and vapor in the PD meter should be avoided because of effects on meter

operation and accuracy. Thus, during installation, meter layout should be

planned to avoid locations where air could accumulate and valves should be

provided for venting the system during use, usually at points of high elevation.

Throttling upstream of the meter should be avoided whenever possible.

Pulsed-readout meter performance can be expressed conveniently in terms of a "calibration factor" plotted as a function of meter output frequency when the

fluid, viscosity, and meter temperature are known, i.e., when a given meter is

operated on a single fluid at a known temperature. Figure 16 shows such a plot

of meter performance. While the sample calibration factor, pulses/gallon, is

shown to vary with frequency (flowrate), the calibration factor may be essentially constant over considerable flow ranges such as 10:1 or larger for a typical

meter operating on a single fluid. Also, large changes in kinematic viscosity

such as 1 X 10~5 to 20 x 10"^ ft^/s may have a rather small influence on the

meter factor, tyically + 0.5 percent for a five or ten-fold increase in flow.

Denoting the calibration factor by the symbol K, the volume flowrate Q, is

Q = 60(f/K) GPM (4-1)

and the mass flowrate M, is

M = 3600 (p)(f/K) Ib/hr (4-2)

32
33
where, t, is the'' pulse frequeacy in Hz, K has units pulses/gal Lon , and p is

the density, lb/gallon.

The actual totalized flow (ATF) where the meter register reads directly in

volume units, is

ATF = [(Kq/K) (net meter registration)], (4-3)

where Kq is the calibration factor corresponding to the current setting of the

meter register. The quantity Kq/K. is defined as the meter factor (MF) , a diraensionless number, ideally equal to 1.000.

An example calculation for on-site calibration of a positive displacement meter

is given in appendix E, example E.7.

In summary, the PD meter is considered quite suitable for building system

applications. Advantages include: (1) a digital output, (2) frequent calibrations are usually not needed once a meter element is calibrated and used with

clean fluids, (3) elimination of periodic and long term calibration programs

for output signal transducer systems, and (4) a calibration factor essentially

independent of flowrate.

4 . 2 VORTEX SHEDDING FLOWMETER

This meter, part of the industrial scene for about 10 years, operates on the

principle that the frequency of vortex shedding for fluid flow around a submerged object is proportional to the fluid stream velocity. Flowrate is mea- sured by detecting the frequency. Figure 17 shows design details of one meter.

The vortices are shed behind the bluff body.

Advantages include lack, of moving parts in the primary element* and a digital

output. Accurate measurem'ent of the probe output is a much simpler measurement

task than accurate measurement of, for example, the AP from a differential pres- sure meter. Meter configurations are available for both gases and liquids in

pipes one inch or more in diameter, and at temperatures up to about 400 °F or 500 °F. The meter output is usually expressed in dimensionless terms according

to the following equation:

f D/V = C5(D V p/u) = 0(D V/v) (4-4)

w^'.are f D/V = Strouhal number, dimensionless

D V p/m = Reynolds number, dimensionless

V = fluid velocity

D = characteristic linear dimension of the meter

f = frequency of vortex shedding

p = fluid density

* Some models do employ moving parts in the secondary element that detects the

vortex frequency.

34

U - fluid dynamic viscosity

V = fluid kinematic viscosity (v = p/p).

The function 0 is determined by calibration for each geometrical shape of meter

in the same sense that the coefficient of discharge C for an orifice is determined experimentally for each geometry (such as concentric orifice, beta ratio,

pressure tap configuration). la principle, the performance of a meter calibrated on one fluid is predictable when used with another fluid provided that

each fluid is incompressible and that its properties p and p are known. The

meter is a volumetric type as indicated by use of the Strouhal number f D/V,

where V is proportional to Q, the volumetric flowrate.

When a vortex shedding meter is calibrated using a single fluid at a specific

temperature, its performance can be conveniently expressed in terms of a calibration factor K, such as pulses/ft^ plotted as a function of frequency f,

rather than the dimensionless parameters of equation (4-4). -When a meter is to

be used for several fluids, a function f/v may be used instead of DV/v since D

is constant for a given meter and f varies nearly directly with V. Verification

of the meter's accuracy requires calibrating the meter with several fluids to

encompass the range of interest for v. Note that the function 0 accounts for

changes in meter performance with fluid kinematic viscosity, v, only. Any

changes in performance due to changes in dimensions with temperature are uncorrected. In both of these cases, the volume and mass flowrates are computed from:

_Q = (60)(f/K) GPM (4-1)

M = (3600)(p)(f/K) Ib/hr (4-2)

where f is the frequency in Hz, K has units ft-^/gallon, and p is the liquid

density, Ib/ft^. Figure 18 is a sample plot of meter performance on different

fluids

At Reynolds numbers greater than about 15,000, the vortex shedding flowmeter

calibration factor K, in units such as gallon/ pulse , is essentially constant

within 0.5 to 2 percent for flowrates varying from about 10:1 to 100:1, according to the manufacturers' specifications. Pressure losses at the rated flow

can vary from a few inches of water to a few psi depending upon the fluid.

Pulse output frequencies are relatively low. For example, a particular 2-inch

diameter meter in water flowing at a rate of 100 GPM produced an output pulse

frequency of about 50 Hz. Thus, for adequate resolution, sampling times of

several seconds or more may be needed for frequency measurements, or interval

measurement techniques can be used (time to count, say, 10 pulses).

The vortex shedding meter should not be considered a "cure-all" for meter

installation troubles encountered in building systems. The same requirements

exist for vortex meters as for orifice meters in terms of straightening vanes

and straight runs of pipe upstream and downstream. Such conditions are needed

to minimize the effects of transverse velocity components and (abnormal)

upstream turbulence on the steady formation of vortices behind the meter

obstruction body. The meter system design of figure 7 is considered adequate,

36
U> 51- CO CM O 0)

U> 10 U) 10 U> 10 ^

u/sesind '>i ao±ovd NOiivaanvo

37
although some manufacturers may recommend longer straight pipe lengths between

the meter and the flow straightener

No effect on the performance of the meter due to the position or orientation of

the section of pipe enclosing the meter should be expected. The pressure level

should be high enough to ensure that no vapor formation (in the case of liquid

flow) occurs in the meter. An absolute pressure, psia, equal to the fluid

vapor pressure plus 3 on 4 times the pressure loss at the rated flow should be

sufficient. Since this meter element has no moving parts, fluid filtration or straining is usually not required. However, changes in internal dimensions

caused by excessive scale build up or abrasion could influence the calibration

factor. Internal passages to the vortex sensing transducers must remain clear

and open. With each meter design, there will be a minimum fluid flow necessary

to create a steady vortex flow.

An example calculation for on-site calibration of a vortex shedding meter is

given in appendix E, example E.8.

4.3 TURBINE METER

Figure 19 shows a typical turbine meter. This meter contains a bladed rotor

which rotates at a velocity proportional to the volume rate of flow. Most

models employ a magnetic pickup, as shown, in which passing rotor blades vary

the reluctance of a magnetic circuit, and generate an AC voltage in the pickup

coil. The pulse frequency is directly proportional to rotor speed . This

signal is sensed as an indication of flow. It can be counted by an electronic

counter, or converted to an analog signal using circuits converting frequency

to voltage.

The calibration factor is expressed in electrical pulses generated per unit

volume of throughput, e.g., pulses/gallon. This factor is sensitive to flowrate, fluid density, and viscosity, the fluid flow pattern at the meter entrance,

and sometimes the meter orientation. For a meter of a specified shape, meter

performance can be expressed in terms of dimensionless parameters as

Q/(n d3) = 4) (n d2 p/y) = ^ (n d2/v) (4-5)

where Q = volume flowrate

n = speed of rotor

D = a characteristic linear dimension of the meter

p = fluid density

U = dynamic viscosity

V = kinematic viscosity (v = y/p)

The function (j) , determined by calibration, describes the performance provided

retarding forces acting on the rotor (bearing friction and electromagnetic

forces) are insignificant and the fluid is incompressible. When considering

one particular meter of fixed size and shape, the quantity D is constant and

the above dimensionless quantities may be reduced to the form

38
M

•H3

cr •HO CM

U-l ' 1

0) -H U O

0)

O

01C ^

•H

O

-Q -H U U

•H 3 4-1 O QJ

--H

C

M-t bO

cq o

•H ^ X 4-J CO O C rH

<; 0)

0^

0)3

GO •H

39
f/Q = i>{f/\>) (4-6)

where f is the pulse frequency and f/Q has dimensions pulses/unit volume.

Unfortunately no single performance curve (function rp) exists for all turbine

meters such as the corresponding coefficient of discharge data which exists,

for example, for orifice meters. Therefore, e ach meter must be calibrated to

obtain its performance or function i|) given above. When used as a transfer

reference meter and for best accuracy, each meter should be calibrated using

the same liquid to be used during the application. This applies in particular

to a liquid such as water which has a different lubricity characteristic as compared to, say, liquid hydrocarbons. Meter performance on water may be different from that obtained using liquid hydrocarbons of similar viscosity as noted in reference 14. The difference is apparently due to changes in

retarding forces and bearing friction. Also, the temperature during calibration and application should not differ appreciably since the function does

not account for change in meter dimensions with temperature.

The frequency output of a typical turbine meter can be linear, (i.e., f/Q = constant) within 0.5 percent at its higher rates of flow when operating with

low viscosity fluids, such as water. This range of linear operation may extend

over a flow range of 10:1 or higher, depending on meter design and size, and

on liquid viscosity. For example, with water in the range 40 - 450° F, the kinematic viscosity v, varies from 1.66 x 10"^ to 0.16 x 10~^ ft^/s. Thus, the temperature range needs consideration for each application, and f/v remains the

controlling variable when temperature varies significantly. At the lower rates

of flow for each meter, frequency output becomes very nonlinear presumably

resulting from the combined effects of retarding forces due to electromagnetic

and mechanical loading on the turbine. There is always some minimum flowrate

below which retarding forces are greater than the fluid forces causing rotation

and the rotor ceases to turn. Figure 20 shows performance characteristics of a turbine meter in which the calibration factor K = f/Q is plotted as a function

of f/v. When the meter is calibrated and the operator is using a single fluid

at a known temperature , the usual case in building system applications, a convenient graph, as with the vortex shedding meter, is a plot of f/Q vs f.

With both plots, the volume flowrate is once again:

Q = 60(f/K) GPM (4-1)

where f is the pulse frequency in Hz and K has units pulses/gallon. Similarly,

the mass flowrate is

M = 3600(p)(f/K) Ib/hr (4-2)

where p is the density, lb/gallon.

The pressure drop through the meter depends on its design and varies with pq2.

Typically, this may be 5 to 10 psi at the rated flow. The pressure level in the

meter should be high enough so that cavitation or formation of vapor does not occur. An entrance pressure of 50 psia plus the vapor pressure of the water is

40
o

<0 cm O 00 o

<0 <0 (D <0 10

uoiiB6/sesind '>i aoiovd Noiivaanvo

41
usually adequate to overcome pressure losses in the meter and connecting piping,

and to prevent cavitation in the meter.

Long terra, satisfactory turbine meter operation requires a clean fluid. When

dirt or particulate matter are entrained in the fluid, meter performance may be

adversely affected due to increased bearing friction. Therefore, a suitable

filter upstream is needed. The dirt problem is one of the common difficulties

in using turbine meters in the water lines of building systems because these

systems easily may become contaminated. The level of contamination tolerable

for heating, ventilating and air-conditioning (HVAC) equipment may very likely

be intolerable for turbine meters. The required level of filtration depends on both the meter size and the bearing design. For smaller meters such as the one- inch size, filtration to 50 microns is typical. Meter bearing material and

design should be compatible with operation in water.

Calibration should be performed periodically and may be performed either on a flowmeter calibration facility or on site using suitable transfer reference

flowmeters as shown in figure 5 or 6. In either case, for best accuracy, it

is important that the flow straightener , the meter, and the necessary lengths

of upstream and downstream piping, as shown in figure 7 for example, be calibrated as a unit. For best accuracy, both the meter and the pickup unit should

be installed in the same positions as that used during calibration.

Maintenance procedures should include servicing the filter equipment, including

changing filters as necessary to avoid excessive flow blockage and/or pressure

loss. Also, the meter should be removed from the line periodically and examined

for possible deterioration of its components or for solids deposited on them.

Recalibration should be conducted during these maintenance activities.

Severe overspeeding of the meter should be avoided. Such a problem may occur when venting air from a piping system or by subjecting the meter to very high

flowrates above the rated value. High rotor speeds when the meter is dry, in

particular, can hasten bearing wear and failure. Subjecting the meter to

intense pressure or flow pulsations or to mechanical vibration may hasten

bearing failure. Exposure to excessive dirt and solid particles may cause bearing seizure.

In summary, the turbine meter has advantages of small size, excellent

repeatability, and a digital output. Also, the calibration factor is often

essentially constant when the meter is operated within specified ranges of

flowrate and viscosity; this fact simplifies flow calculations. Installation

as part of a meter system using a flow straightener and calibration in water

at the required temperature are essential for best accuracy. However, the

amount of dirt often encountered in building systems raises a question as to

its general suitability for this application. Clean liquids are required for

satisfactory long term operation.

An example calculation for calibration in water is given in appendix E, example

E.9.

42
4.4 TARGET METER

A sketch of a target meter for closed channel flow is shown in figure 21. Other names used for this type meter include vane, force, and drag force. The change

in momentum of the fluid as it accelerates past the target causes a drag force

which deflects the target. This deflection is measured by a force transducer

such as a strain gauge system or linear differential transformer. With incompressible flow past the target, this drag force depends on the size and shape

of the target and the proportion of the pipe cross section it occupies, the

fluid velocity, and the fluid properties of density and viscosity. The drag

coefficient is dimensionless and is defined as:

Cd =

2 g,

p a V' (4-7)

where F = drag force, Ibf

p = fluid density, Ib/f t3

g^ = 32.1740 (fflb)/(lbf -s^)

a = target area, ft^

V fluid velocity upstream, ft/s.

While the drag coefficient has been studied for such shapes as the flat plate,

the sphere, and the circular cylinder in a free stream, expressing C^i as a function of target Reynolds number, drag coefficients for the various shapes

of target meters used in closed channel flow are not well known. Each meter,

therefore, needs an individual calibration covering the Reynolds number ranges

of interest. Figure 22 is a plot of versus Reynolds number for two target

meters, where Rq = D V p/y.

When C(j is known, the volumetric flowrate Q and the mass flowrate M are calculated from the following equations:

1/2

and

1/2

M = cJ-^-:i-^-l ^/ 2g^ F p = C, (H -J^.] I

- I (4-9)

where d = target diameter.

Although the theory for the target meter is "old", these meters have been on

the industrial scene only about 25 years. Their principal advantages include

their ability to handle fluids with suspended particles, their lack of moving

parts, and their absence of pressure sensing lines.

43
44
XI O

UJO

UJO

o

o

<

Q

0.75

0.70

0.65

0.60

0.55

0.50

0.45

1 1 1

1

—— ^

Bore

——

— diaipeter D: 2.067 in. (52.50 mm) —

Target

diameter d: 1.3610 in. (34.57 mm) ~

_ ^rd/D = 0 .658 _

T 1 1 1 10 10 10 104 10

PIPE REYNOLDS NUMBER Rq

0.75

73

o

UJ5

UJo

o

o

<

QC

o

0.70 -

0.65 -

0.60

0.55

0.50

0.45

0.40

Bore

diameter D: 2.067 in. (52.50 mm)

Target

diameter d: 1.6679 in. (42.36 mm)

/3= d/D= 0.807

I I I 10 10 10 10' 10

PIPE REYNOLDS NUMBER Rp

Figure 22. Drag coefficient for two 2-inch target meters,

d/D = 0.658 and 0.807 [15]
The output is usually an analog signal, nonlinear with flowrate. Additional

electronics are needed to convert it to a digital signal, linearize it with

flowrate and/or totalize the flow. Accurate measureraent of the meter output is

deemed comparable to accurate measurement of pressure or differential pressure,

except that a problem in limiting the noise in the electrical lines to

acceptable limits may exist.

Since no study has been published to date on the effects of installation

conditions, it is recommended that each meter be mounted in a metering section

with straight lengths of pipe upstream and downstream together with a flow

straightener , as shown in figure 7. Some manufacturers may recommend more than

lOD of straight pipe upstream between the meter and the flow straightener.

Target meter systems are available for water in pipe sizes 1/2 inch to 8 inches

and larger, flowrates to 2000 GPM and larger, with full scale pressure drops as low as a few tenths of a psi for the larger-size meters. Nominal flow range

ratio is 10:1 (transmitter output 100:1). Available transmitter output signals

include 0-10 volts DC and 4-20 mA DC. These outputs vary directly with force

input as in equations (4-8) and (4-9). Outputs which vary linearly with flowrate , i.e., with (F)l/2 are also available. These two outputs are illustrated

in figure 23. While the linear Q output is generally more useful, accuracy

suffers because of the added electronics.

For best accuracy, the target meter should be calibrated with the fluid to be

used on site using the transmitter. Thus, for on-site calibration using

flowing water at a known temperature, the meter performance can be given through

a plot of a calibration factor CF as a function of transmitter output, volts or mA, where

^ CF = GPM/(volts)l/2 or GPM/(mA)l/2 (4-10)

Then flowrates can be calculated directly from an expression, for example:

Q = (CF)(I - Iq)^/^ = [GPM/(mA)^/2](mA)^/2 = gp^ (4-11)

where Iq = current at zero flow

I = current at flowrate Q \

The calibration factor CF will then account for variation in C^j with flowrate

and for the nonlinear characteristics of the transmitter electronics. Corresponding expressions can be written for mass flowrate M. Example E.IO in

appendix E includes sample calculations and a plot of meter performance for the

calibration of a target meter in water.

The target meter is attractive for building services because of its ability to

handle particulate matter and the absence of pressure sensing lines. For best

accuracy, the meter should be calibrated with the fluid to be used. As with

the AP meter, the output signal varies with which may limit its useful operating flow rate as compared to a PD meter. For calculating flowrates, the

nonlinearity characteristic can be accomodated by using a calibration factor

having the dimensions of f lowrate/(output) -^^^^

46
(0 1%

o o

T- CM

_ U) CM

0)

lU

(0

z

<

OC

o ^ o

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00

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CM

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uc

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c

XIc

cd cyu

CO

QJ

CDD QJ

4-J CD aO CD

cu

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r-l

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QJ

3

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-U CD

0) 5-1 tC 4-1

CdCN

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CM

47
4.5 MULTIPLE PITOT-STATIC AND REVERSE-PITOT TUBE ASSEMBLIES

Several designs of flowmeters of these types are available. Figure 24 shows

the schematic diagrams of an assembly designed for mounting in an air duct system. It contains 16 pitot-tubes spaced on an equal area traverse basis and

connected to a common impact pressure line, and four static legs connected to

a common static pressure line. Since the velocity profile varies in the duct cross section, an average value of impact pressure and a average value of

static pressure are obtained. The AP is measured by means of a manometer or pressure t-ransducer system. An advantage of this assembly is that a single AP

measurement is used instead of 16 measurements, or instead of the traversing

approach with a single tube. Because of the variation in impact pressure (velocity) from tube to tube and to account for the blockage effect of the assembly,

reliable measurement of flowrates require that the assembly be calibrated on site over the range of velocities to be encountered. A flow straightener

(honeycomb) is installed upstream of the assembly to eliminate transverse or swirling velocity components.

Figure 25 shows a commercially available reversed type of pitot tube assembly.

This consists of a probe which extends completely across the diameter of a pipe and which senses impact pressure at four specific openings along the

upstream side of the probe. The resulting impact pressure is some average

value which connects to a manometer or AP transducer system. A single reversed

pressure tube senses the pressure on the downstream side of the probe. Advantages include increased differential pressure for a given fluid velocity compared

to a conventional pitot-static tube, and ease of probe installation.

In fully developed turbulent flow, the velocity profile (velocity V as a function of radius r) changes with Reynolds number Rq becoming more uniform as

Rj) increases; or with a single fluid, as flowrate increases. For a detailed

analytical analysis of the influence of the velocity profile on the coefficient

of discharge, see reference 16. A significant influence on the coefficient of

discharge by an increase in velocity can be expected. Also, when the flow is

asymmetrical, such as the case downstream of elbows and valves, significant

errors on the impact pressure will result. The static hole is located in the

probe wake region; a region of higher turbulence and fluctuating pressures.

For all these reasons, it is strongly recommended that the probe be mounted in

a metering section such as shown on figure 7 and calibrated on site with the

working fluid over the range of flowrates to be encountered. If necessary, to

aid in producing a symmetrical velocity profile, the flow straightener should

be of the perforated plate design rather than the tubular design (at the expense

of a larger pressure loss). (See figures 12 and 13.)

The reversed pitot-tube sensing probes are suitable for flowing air, water or steam. However, flowing hot water at pressure levels approaching the vapor

pressure should be avoided to eliminate possible cavitation at the static hole.

Building system pressures of 50 to 100 psig should present no problem. To

illustrate this point, consider the static pressure behind a circular cylinder

where the static pressure has an approximate value corresponding to Cp = -1.3.

The dimensionless pressure coefficient Cp is defined by the following

relationship:

48
T 1 r

J I L

• Velocity taps at centers of 1 6 equal areas

o Static pressure taps at centers of 4 equal areas

Flow straightener

Flow

Velocity manifold

Static pressure manifold

Inclined differential manometer

or aP meter

Figure 24. Pltot-static rake assembly for measuring air flow in a duct. The ends of the velocity taps are open to receive

the impact pressure. The ends of the static pressure

taps are closed and a ring of radial perforations receive

the static pressure

49

For example, with water flowing at V = 20 ft/s

P - Pq = (Cp p v2)/(2 g^)

= (-1.3)(62.4 lb/ft'^)(20 ft/s)-

(2)(32.174)[(lb-ft)/(s2.1bp](l44 in.^/ft^)

'

P - Pq = -3.5 psi

This means the pressure P at the static hole is 3.5 psi less than system

pressure Pq. Thus, if the water temperature is 212°F, system pressure ?^ must

be at least 14.7 + 3.5 = 18.2 psia (or 3.5 psig) to avoid flashing of the water

at the static hole. A pressure Pq of 7 to 10 psig would probably i)rovide an adequate degree of safety from flashing.

The pressure differential, AP , for both of these probe systems is nonlinear

with flowrate, where AP « or AP ^ M^. When used with a AP transmitter where

the current or voltage output varies directly with AP , or when used with a manometer system, a calibration factor of the following form must be used:

CF = flowrate/(output) 1/-^ .

This will allow direct calculation of flowrate Q (or M) from an expression such

as

Q = (CF)(I - 1^)1/2 (^_^3)

Q = (CF)(inches of manometer fluid)-'-/^ (4-14)

Refer to figure 23 and the discussion in section 4.4 which discusses a similar

situation for the target meter. In these mutliple assemblies, with an on-line

calibration, the calibration factor CF will then account for any effects of

changing velocity profiles on the probe performance.

Multiple pressure probe assemblies offer the advantage of a single AP output

resulting from sensing impact pressure (velocity) and static pressure at multiple

points. For reliable flow measurement, calibration is required. For a large

flow range such as 10:1, HIGH and LOW AP transmitter systems such as discussed

in section 3.3 may be necessary. The nonlinearity in the AP can be accommodated

by using a calibration factor of the form: flowrate/ ( output ) 1/2 . Electronic

noise from a AP transducer generated by small changes in the velocity profiles

can also be a problem which is usually solved with little effort.

4 . 6 ULTRASONIC FLOIMETER

Ultrasonic flowmeters can be readily attached to the outside of existing liquidfilled pipes without shutdown, diversion, special sections, or isolation valves.

The economic advantage of ultrasonic flowmeters over conventional flowmeters

increases with pipe size.

51
The primary elements are nonintrusive and are sensitive over a wide range of

velocities of the liquid flowing within the pipe without inducing a pressure

drop or other disturbance to the medium being monitored.

Several ultrasonic techniques are used in the measurement of flow. The

majority of instruments of this type use various configurations of acoustic

sources (transmitters) and detectors (receivers). The velocity of the fluid

flowing in the pipe is detected from the effect of the moving liquid on the

sound waves. In general, this effect is determined by comparing the signals

transmitted with those received. The two techniques most commonly used to

detect the effect of the flowing liquid on the sound waves are known as the

transit-time meters and the Doppler meters.

The transit-time flowmeters utilize the fact that fluid flow along the acoustic

path affects the time it takes for the acoustical signal to travel from the

transmitter to the receiver. Transit-time meters transmit bursts of ultrasonic

energy across the pipe as sho\^ in figure 26. The transit times in the downstream (t+) and upstream (t-) directions are given by;

_ distance _ L ^ _ L

conduction velocity c+ u cos 6 ' ' c- 'u cos 0

where t = time in seconds

L = distance between the two transceivers

c = velocity of sound in the liquid being monitored

u = velocity of the liquid averaged along the path of the ultrasound,

u" = 1.33 u for laminar flow, and, for turbulent flow, u" = 1 . 07 u where u - the average velocity of the flow over the cross-sectional

area

9 = angle between the direction of travel of the acoustical signals and

direction of fluid flow

Note that u^ dif f er s from u because the ultrasonic path is along a single line

rather than averaged over the cross-sectional area.

The downstream transit time is shorter than the upstream transit time by

At =

2L u" cos

c2

and thus the average fluid velocity along the acoustical path, u, is proportional

to At. A short acoustic pulse is transmitted alternately in the upstream and

downstream directions. Unfortunately, the resulting At is in the nanosecond

range and higher quality electronics are required to achieve adequate stability.

It should be noted that this type of meter requires relatively clean liquids

since minute particles can absorb or disperse sound energy.

Ultrasonic flowmeter utilizing the Doppler effect function on the shift in

frequency produced when the sound waves are reflected from moving bodies. In

this type of ultrasonic flowmeter, a single transmitter projects a continuous

ultrasonic beam at about 0.. 5 MHz through the pipe wall to the liquid flow being

52
53
monitored. The particles carried by the liquid have velocity components in

the direction of the ultrasonic beam since the beam makes an angle which is

less than 90 ° to the direction of flow. The reflected ultrasonic waves detected at the receiver (which can be located adjacent to the transmitter or on the opposite side of the pipe) are shifted in frequency in proportion to the

velocity of the liquid. The shift in frequency is determined and used to

measure the flow rate. Doppler meters are suitable for liquids containing a consistent density of acoustically reflective particles.

Since the transmit-time meters require relatively clean liquids and the

Doppler type meters require relatively small acoustically reflective particles,

and these conditions are rarely met in typical EMCS applications, frequent

periodic calibrations of these meters are required.

The vast differences in the designs of currently available ultrasonic flowmeters requires that the reader consult a particular manufacturer's literature

for further information on calibration procedures [17,18,19].

4.7 INSERTION TYPE TURBINE METER

This is another type of turbine meter In which a meter assembly is mounted on

the end of a stem or strut and positioned as desired in a large pipe, duct, or open channel. Figure 27 shows a typical installation sketch. Advantages

include low cost compared to the "full bore" turbine meter for large pipe

installations; easy installation including no disruption to the fluid flow when

an isolation valve is used, insuring essentially no pressure loss; and a digital

autput. Other characteristics, including the influence of fluid properties,

density and viscosity, fluid lubricity, the effects of retarding forces due to

bearing friction and electromagnetic loading, and the effects of flow patterns

have all been discussed above for full bore turbine meters (section 4.3).

These characteristics apply generally to the insertion meter. Again, a clean

fluid is imperative for satisfactory, long-term operation.

Insertion turbine meters are available for use in water, air, and steam.

Typical velocities range from 50 or 60 feet/second raaximum for liquids to

300 feet/second maximum for gases. Manufacturers typically claim a linearity

of 1 percent full scale for 10:1 flow range.

The insertion turbine meter, like the target meter, senses local fluid velocity

only and thus, for measuring flow in closed conduits (pipes and ducts), the

performance is dependent on the velocity profile. Figure 28 shows velocity

profiles for fully developed turbulent flow as a function of Reynolds number

Rq . Such profiles normally occur only in very long, straight pipes. Furthermore, it should be noted that the conversion factor betweea measured velocity

and flowrate will be flow dependent. An iteration is recommended for each mea- surement. Note also that velocity gradients are lowest near the pipe center,

indicating a preferred probe position.

The insertion type turbine meter is attractive because of its relatively low

cost for large pipe sizes and its ease of installation. For best accuracy,

the meter should be calibrated on site with the operating fluid over the

operating flow and temperature ranges.

54
55
o

TO

O o o

rX X X X X

CO o CM

r- CO 1 1 1 1 DQ O o UJ

00ooo

CMo

0>o

00a o o o o o

COo

CMa O

•H 4-1 dJ •H U

Pi

a n3 o

>-i 0)

0) > 3 o

•H

01 -U

•H X3 3o

4-1

C 'X)

C CU <U O OJ

4J

u in

u

•H

oj ^ :d O

iH

C CO

Q)

O i~> > -H

0) 4-1 -a -H

Cfi >^ o

iH CX 4J

.-4 -H 3 rH O

14-1 03

O

•H .-I

O cfl >

M-l S-i

Cfi Cfi 03

CU -H -H H X

—

S-i CT3 -H

Cxi •HMHOa 3

>, T3 Cfi 4-1 CI3 -H •H 5-1 CJ 3 O Q) rH T3

<D -H

C > CX CT3

CO

CM

-a

0)N

CU

S-I d

•H

56
REFERENCES

1. "Handbook of Fundamentals, 1981," Chapter 13, ASHRAR, 1971 Tuilie Circle,

N.E., Atlanta, GA 30329.

2. Fluid Meters, Their Theory and Application, ASME, 6th ed., 1971.

3. Standard Methods for Measurement of Flow of Fluids - Liquids, ASHRAE

Standard 41.8-78, 1978; and. Procedure for Fluid Flow Measurement of

Gases, ASHRAE Standard 41.7-78, 1978.

4. S.J. Irwin, The Effect of Bends on the Discharge Coefficient of Orifice

Plates, Flow Measurement of Fluids, Proceedings of FLOMEKO 1978, International Measurement Confederation, IMEK.0 Conference, pp. 247-252.

5. D.W. Baker and C.C. Sayre, Jr., Decay of Swirling Flow of Incompressible

Fluids in Long Pipes, Proceedings of ISA/ ASME Symposium on Flow, Its

Measurement and Control in Industry, Vol. 1, Part 1, 1971, pp. 301-312.

6. Thermodynamic and Transport Properties of Steam, ASME, 3rd Ed., 1977.

7. Manometer Tables, Recommended Practice 2.1, Instrument Society of America,

Pittsburgh, PA, 1962.

8. Units and Systems of Weights and Measures - Their Origin, Development, and

"Present Status, Letter Circular LC-1035 , National Bureau of Standards,

Washington, DC, January 1960.

9. M.R. Shafer, Jr. and D.W. Baker, Practical Considerations for Gas Flow

Measurement, Proceedings of the Third Annual PMA Metrology Conference,

Precision Measurements Association, Volume 1, pp. 187-227, 1970.

10. Measurement of Fluid Flow by Means of Orifice Plates, Nozzles, and Venturi

Tubes Inserted in Circular Cross-Section Ducts Running Full, International

Standard 5167, International Organization for Standardization, First

Edition, 1980, American National Standards Institute, New York, N.Y.

11. The ISO-ASME Orifice Coefficient Equation, Research Committee on Fluid

Meters, ASME, Mechanical Engineering, Volume 103, No. 7, July 1981,

pp. 44-45.

12. Tables of Thermodynamic and Transport Properties of Air, Argon, CO2 , CO,

H2, N2 , O2 and Steam, Joseph Hilsenrath et. al., Pergammon Press, New

York, 1960.

13. D.F. White, A.E. Rodely, and C.L. Murtrie, The Vortex Shedding Flowmeter,

Proceedings of ISA/ASME Symposium on Flow, Its Measurement and Control,

Vol. 1, Part 2, 1971, pp. 967-974.

57
14. H.R. Shafer, Performance Characteristics of Turbine Flow Meters, Journal

of Basic Engineering, Transactions of the ASME, Vol. 84, Series D, 1962,

pp. 471-481.

15. David E. Curran, Laboratory Determination of Flow Coefficient Values for

the Target Type Flowmeter at Low Reynolds Number Flow, Proceedings of the

Second International Symposium on Flow: Its Measurement and Control in

Industry, ISA/ASME, 1981, pp. 263-276.

16. N.Q. Thoi and W.K. Soh, On the Averaging Technique and the Discharge

Coefficient of the Annular-Averaging Flow Sensor, ISA Transactions, Volume

18, No. 1, January 1979, pp. 41-48.

17. Thomas R. Schmidt, What You Should Know About Clamp-On Ultrasonic

Flowmeters, ISA, InTech, May 1981, pp. 59-62.

18. Ronald E. Burner, Theoretical and Experimental Assessment of Uncertanlties

in Non-Intrusive, Ultrasonic Flow Measurement, Symposium on Flow Measurement in Opens Channels and Closed Circuits; Proceedings, NBS Special

Publication 484, National Bureau of Standards, 1977.

19. Lawrence C. Lynnworth, Industrial Applications of Ultrasound - A Review

II. Measurements, Tests, and Process Control Using Low-Intensity Ultrasonics, IEEE Transactions on Sonics and Ultrasonics, March 1975, Volume

SO-22, Number 2, pp. 71-101.

20. P. .4. Bigg, The Density of Mercury, British Jol. of Applied Physics,

Volume 15, 1964, pp. 1111.

21. Hermann Schlichting, Boundary Layer Theory, 4th Edition, 1960.

22. M.R. Shafer and F.W. Ruegg , Liquid-Flowmeter Calibration Techniques,

Transactions of the ASME, October 1958, pp. 1369-1379.

23. David W. Baker, James Y. Kao, and David A. Didion, "Performance Evaluation

of a Typical Energy Monitoring System for Steam Flow in Buildings," National

Bureau of Standards Report NBSIR 81-2313, January 1981.

58
ACKNOWLEDGMENTS

Discussions with Mr. Kenneth Benson of the Fluid Engineering Division at NBS on flowmeter characteristics and calibration techniques have been especially helpful. The authors also wish to acknowledge the excellent work of Dr. James F. Schooley of the NBS Center for Absolute Physical Quantities in editing this

report and contributing many technical improvements. Also, long past discussions on similar subjects with Mr. Montgomery R. Shafer Jr. (retired, deceased)

of the former Fluid Meters Section at NBS are recalled. Mr. Shafer's very

significant contributions through his work on flowmeter characteristics and

calibration techniques are remembered by many, and his paper (reference lA) on turbine meter characteristics is still a classic.

i

59

APPENDIX A

Coefficient of Discharge C and Fluid Expansion

Factor Y for Orifices, Flow Nozzles and Venturi Meters

(The data in this appendix were taken from references 2, 10, or 11)

A-1
Table CoefELcient of Discharge C

Orifice Plate with Corner Taps

3

5

1 , i3 X 10-^ ll) 1 X 10 3 X 10 ' 1 m4

J X 10' 7 X iu 10-^ 1 n5 3 X 10^ 1 rib 10" 1 ,7 10

U.2 j 0 .6U12 0 . 5997 0 . 5987 0 . 5983 0 . 5980 0.5979 0. 5977 0. 59 7 5 0 . 5974 0. 59 73

U . 24 u .0018 u . 6iJon rj. 5990 0 . 5986 0 . 5982 0 . 5981 0.9579 0. 5977 0. 5975 0 .9575

0 . 2 0 0 .6031 0.6009 0 . 5996 0 . 5990 . 5987 0 . 5985 0 . 5983 0 . 5980 0 . 59 78 0. 5978

U.2ij u .6044 0.6019 0.6003 0.5997 0. 5992 0.5989 0.5987 0.5983 0.5982 0.5981

' 0.30 0 . 6060 0 . 6029 0.6011 0.6004 0 . 5997 0 . 5994 0 . 5992 0 . 5987 0 . 5983 0. 5984

0 . j 2 0 .6077 0.6040 0.6019 0.601

0 . 6003 ij . 6000 0 . 5997 0. 5991 0 . 5989 0.5988

0. 34 0 . 6095 0 . 6U53 0.6028 0.6018 0.6010 0.6005 0.6002 0. 5996 0.5993 0. 5991

0 . 35 0 .6115 0.6066 0 . 6037 0 ,6026 0.6016 0.6012 0.6003 0.6001 0 . 5997 0.5995

0.3« 0 .6136 0.6081 0.6048 0.6035 0.6024 0.6018 0.6014 0.6005 0.6002 0.6000

0.4U 0 .6159 0 .6096 0 . 6059 0 . 6044 0.6031 0 . 6025 0.6020 0 . 601

0.6006 0.6004

0.42 0 . 6184 0.6113 0 . 6070 0 . 6054 0.6039 0 . 6032 0 .6026 0.6016 0.6011 0 . 6008

0.44 0 .6210 0 . 6 1 30 0 . 6082 0 .6064 0 .6047 0 . 6039 0 .6033 0.6021 0.6016 0.6013

0 .46 0 .6238 0.6148 0 . 609 5 0 . 6074 0 . 6056 0 . 6047 0 . 6040 0 . 6027 0.6021 0.6017

0 . 4o 0.6167 0 . 6 108 0 . 6085 0 .6064 0 . 6055 0 . 6047 0.6032 0 .6025 0.6021

U . 5 U 0.6187 0.6121 0 . 6096 0.6073 0 . 6062 0.6053 0.6037 0 . 6030 0 . 6026

0.52 0.6027 0.6135 0.6107 0.6082 0.6070 0.6060 0.6042 0.6034 0.6029

U.54 — 0.6228 0.6148 0.6117 0.6090 0.6077 0.6066 0.6047 0.6037 0.6032

U . 30 0 .6249 0.6162 0.6128 0 . 6098 0 . 6084 0 . 6072 0.6050 0 . 6040 0 . 6035

0 . 5y O.o270 0.6175 0.6138 0.6105 0 .6089 0.6077 0 .6053 0 .6042 0.6036

U . bO 0.6291 0.6187 0.6147 0.6111 0 . 6094 0 . 6080 0 .6055 0 . 6043 0 . 6036

0.62 0.6311 0.6198 0.6155 0.6116 0.6098 0.6083 0.6055 0 .6042 0.6035

0.64 0.633U 0 .6208 0.6161 0.6119 0.6099 0.6083 0 . 6053 0.6039 0 . 6031

0.65 0 .6339 0.6212 0.6164 0.6120 0 .6099 0 . 6082 0.6051 0.6037 0.6028

0.66 0.6348 0.6210 0.6165 0.6120 0.6099 0.6081 0.6048 0.6033 0.6025

0.67

II 0.6356 0.6219 0.6167 0.6120 0.6097 0.6079 0.6045 0.6029 0.6021

U.68 U.6363 0.6222 0.O167 0.6118 0.6095 0.6076 0.6041 0.6025 0.6016

0.69 — 0.6370 0.6223 0.6167 0.6116 0.6092 0.6072 0.6036 0.6019 0.6010

0.70 0 . 6 J / 6 0.6224 0.6165 0 . 6 1 1

0 . 6088 0 . 6U6

0 . 60 JO 0.6012 0 . 6003

0.71 0.6382 0.6224 0.6163 0.6109 0.6083 0.6061 0.6023 0.6004 0.5994

0.72 0.6386 0.6222 0.6160 0.6103 0.6076 0.6054 0.6014 0.5995 0.5985

0.73 0.6389 0.6220 0.6155 0.6097 0.6069 0.6046 0.6004 0.5985 0.5974

0.74 0.6391 0.6216 0.6149 0.6089 0.6060 0.6036 0.5993 0.5973 0.5962

0.75 0.6392 0.6211 0.6141 0.6079 0.6049 0.6025 0.5980 0.5959 0.5948

0.76 0.6391 0.6204 0.6132 0.6068 0.6037 0.6012 0.5966 0.5944 0.5932

0.77 0.638-. 0.6196 0.6121 0.6055 0.6023 0.5997 0.5949 0.5927 0.5915

0.7c; 0.6185 0.6108 0.6039 0.6007 0.5980 0.5931 0.5908 0.5895

0.79 0.6173 0.6093 0.6022 0.5988 0.5960 0.5910 0.5886 0.5873

0.80 0.6158 0.6076 0.6003 0.5968 0.5939 0.5887 0.5862 0.5849

ATabLe A. 2. Coefficient of Discliarf;e C

Orifice Plate witii Taps at II) and 1/2IJ \N.

3

5 X 10-^ , ^4 10^ 2 X 10"* 3 X

10-* 5 X Kr 1 X ur 10^ s 3 X 10^ 10° 7 lo'

U . 20 0 . 5997 0 . 5985 0 . 5979 0.5976 0.5974 0.5973 0.5972 0.5970 0.5969 0 . 5969

0.22 0.6006 0 . 5992 0 . 5984 0.5980 0.5977 0. 5976 0.5975 0.5973 0. 5972 0.59 71 0 . 24 0.6017 0 . oOOO 0 . 5989 0 . 5985 0.5981 0 . 5980 0.5978 0 . 5976 0 . 5974 0. 5974

0 .26 0.6030 0.6008 0. 5995 0.5990 0. 5986 0. 5984 0.5982 0.5979 0.5977 0.5977

0.28 U.6043 0.6017 0.6002 0.5996 0.5991 0.5988 0.5986 0.5932 0.5981 0.5980

0 . Jo 0 . b028 0 . 60 10 0 . 6003 0 . 5996 0 . 5993 0.5991 0 . 5986 0.5984 0 . 5983

0 . 32 0 . 6039 0 . 6018 0 .6010 0.6002 0 . 5999 0 . 5996 0 . 5990 0 . 5988 0 . 5987

0 . 34 0 . 6052 0 . 6027 0.6017 0 . 6009 0 . 6004 0.6001 0 . 5995 0 . 5992 0 . 5990

0 . 36 II 0.6066 0 .6037 0.6026 0.601b 0.6011 0.6007 0.6000 0 . 5997 0. 5995

0. 3d 0.6080 O.b047 0.6035 O.b02 3 O.bOlo 0.6013 0.b005 0.6001 0.5999

0 . 40 0 . 6096 0.6059 0 . 6044 0.b031 0 . 6025 0.6020 0.6011 0.6006 0.6004

0.42 0.6071 0.6054 0 . 6040 0 .6033 0.6027 0.6017 0 .6012 0.6009

0.44 0.6084 0.6065 0.6049 0.6041 0.6035 0.6023 0.6017 0 . 6014

0 . 4b II II0 . b09b 0.6077 0 . b059 0.6050 0.6043 0.6030 0 .6023 0.6020

0.48 0.6112 0.6089 0.60b9 0.6059 0.6051 0.6036 0.6030 0.6026

0. 50 0.6127 0 . 6102 0 .6079 0.6068 0.6060 0.6043 0.6036 0.6032

0. 52 0.6143 0.6115 0.6090 0.6078 0.6063 0.6051 0.6042 0.6038

0. 54 0.6159 0 . 61 29 0.6101 0.6088 0.6077 0.6058 0.6049 0.6044

0 . 56 0.6176 0.6143 0.6113 0.6098 0.6087 0.6065 0.6055 0.6049

0.58 0.6157 0.6124 0.6108 0.6095 0.6072 0.6061 0.6055

u . o u U . O J. J J U . O i i o n An7Q 0U • AnA7 DUD

/

U . DUDU 0.02 0.6185 0.6146 0.6128 0.6112 0.6085 0.6072 0.6065

0.64 0.6198 0.6156 0.6136 0.6120 0.6090 0.6076 0.6068

0.66 0.6211 0.6166 0.6144 0.6127 0.6094 0.6079 0.6071

0.68 0.6223 0.6175 0.6151 0.6132 0.6097 0.6081 0.6072

0.70 0.6182 0.6157 0.6136 0.6099 0.6081 0.6071

0.71 0.6185 0.6159 0.6138 0.6099 0.6081 0.6071

0.72 0.6187 0.6161 0.6139 0.6098 0.6080 0.6069

0.73 0.6190 0.6162 0.6139 0.6097 0.6078 0.6067

0.74 0.6191 0.6163 0.6139 0.6096 0.6076 0.6065

0.75 0.6193 0.6163 0.6138 0.6094 0.6073 0.6062

A-3
Table A. 3. Coefficient of Discharge C

Orifice Plate with Flange Taps

D = 2 in.

B \^

5 X 103 10^ 2 X 10^ 3 X 10^ 5 X 10^ 7 X 10^ 105 3 X 105 106 107

0.25 0.6023 0.6003 0.5992 0.5987 0.5983 0.5981 0.5980 0.5977 0.5976 0.5975

0.26 0.6029 0.6008 0.5995 0.5990 0. 5986 0.5984 0.5982 0.5979 0.5977 0.5975

0.28 0.60^3 0.6017 0.6002 0.5996 0.5990 0.5988 0.5986 0.5982 0.5980 0.5979

0.30 0 .6028 0 .6009 0 .6002 0 . 5996 0.5993 0.5990 0 . 5986 0.5984 0.5983

0.32 0.6039 0 .6017 0 .6009 0 .6002 0.5998 0 . 5995 0.5990 0.5988 0.5986

0.34 0 .6051 0.6026 0 .6017 0 .6008 0 .6004 0.6001 0.5994 0.5992 0.5990

0.36 0.6065 0.6038 0.6025 0.6015 0.6010 0.6006 0.5999 0.5996 0.5994

0.38 — 0.6080 0.6047 0.6034 0.6022 0.6017 0.6013 0.6004 0.6001 0.5998

0.40 0 .6058 0 .6043 0 .6030 0 .6024 0 .6019 0 .6010 0 .6006 0.6003

0.42 0 .6070 0 . 6054 0 .6039 0.6032 0 .6026 0.6016 0 .601

0.6008

0.44 0.6083 0 .6064 0 .6048 0.6040 0 .6034 0 .6022 0 .6016 0.6013

0 . 46 0 .6096 0 .6076 0 .6057 0 .6049 0.6041 0 .6028 0 .6022 0.6019

0 .48 0.6111 0 . 6088 0 .6067 0 .6058 0 .6050 0.6035 0.6028 0 .6024

0.50 0.6126 0.6100 0.6078 0.6067 0.6058 0.6042 0.6034 0.6030

0.52 — — 0.6141 0.6113 0.6088 0.6076 0.6067 0.5049 0.6041 0.6036

0 . 54 0.6157 0 .6127 0 .6099 0.6086 0.6075 0 .6056 0 .6047 0 .6042

0 . 56 0.6174 0 .6140 0.6110 0 .6096 0.6084 0 .6063 0 .6053 0 .6047

0 . 58 0 .61 54 0.6121 0 .6106 0 .6093 0 .6070 0 .6059 0 .6053

0 . 60 0.6168 0.6132 0.6115 0.6101 0 .6076 0 .6064 0 .6057 0.62 — — — 0.6182 0.6143 0.6124 0.6109 0.6082 0.6069 0.6062

0 . 64 0.6195 0.6153 0.6133 0.6117 0 .6087 0 .6073 0 .6065

0.65 0.620L 0.6158 - 0.6137 0.6120 0.6089 0.6074 0.6066

0.66 0.6208 0.6162 0.6141 0.6123 0.6091 0.6076 0.6067

0.67 0.6214 0.6167 0.6144 0.6126 0.6092 0.6076 0.6068

0.68 0.6219 0.6171 0.6147 0.6128 0.6093 0.6077 0.6068

0.69 0.6225 0.6174 0.6150 0.6130 0.6094 0.6077 0.6068

0.70 0.6177 0.6152 0.6132 0.6094 0.6077 0.6067

0.71 0.6180 0.6154 0.6133 0.6094 0.6076 0.6066

0.72 0.6183 0.6156 0.6134 0.6094 0.6075 0.6064

0.73 0.6185 0.6157 0.6134 0.6092 0.6073 0.6062

0.74 0.6186 0.6157 0.6134 0.6091 0.6071 0.6059

0.75 0.6187 0.6157 0.6133 0.6088 0.6068 0,6056

A-4
Table A. 4. Coefficient of Discharj^e C

Orifice Plate with Flange Taps

D = 3 in.

... , \^ Rd

3

5 X 103

. . .

10^ 2 X 10^ 3 X

10^-*

-

5 X 10^ 7 X 10^ 105

. _

3 X 105 106 107

0.20 —0 .5997

1 0.5986 0.5979 0.5976 0.5974 0.59 7 3 0.5972 0.59 70 0.5970 0.5969

0.22 0 .6006 0.5992 0.5984 0.5981 0.5978 0.5976 0. 597.5 0.5973 0.5972 0.59 72 0.24 — 0.6000 0.5989 0.5985 0.5982 0.5980 0.5979 0.5976 0.5975 0.597 4 0.26 — 0.6008 0.5996 0.5991 0.5986 0.5984 0.5982 0.59 79 0.5973 0.59 7 7 0.28 — 0.6018 0.6002 0.5997 0.5991 0.5989 0.5987 0.5983 0.5981 0.5980

0.30 — 0.6028 0.6010 0.6003 0.5997 0.5994 0.5991 0.5987 0.5985 0.5983

0.32 — 0.6040 0.6018 0.6010 0.6003 0.5999 0.5996 0.5991 0.5988 0.5987

0.34 — — 0.6027 0.6018 0.6009 0.6005 0.6002 0.5996 0.5993 0.5991

0.36 — — 0.6037 0.6026 0.6016 0.601

1

0.6008 0.6000 0.5997 0.5995

0.38 0,6048 0.6035 0.6024 0.6018 0.6014 0.6006 0.6002 0.6000

0.40 — — 0.6059 0.6045 0.6032 0.6026 0.6021 0.6011 0.6007 0.6005

0.42 — — 0.6071 0.6055 0.6040 0.6033 0.6028 0.6017 0.6012 0.6010

0.44 — — 0.6084 0.6066 0.6049 0.6042 0.6035 0.6023 0.6018 0.6015

0.46 — — 0.6098 0.6077 0.6059 0.6050 0.6043 0.6030 0.6024 0.6020

0.48 — — — 0.6089 0.6069 0.6059 0.6051 0.6036 0.6030 0.6026

0.50 — — — 0.6102 0.6079 0.6068 0.6059 0.6043 0.6036 0.6032

0.52 0.61 15 0.6090 ^.0.6078 0.6068 0.6050 0.6042 0.6037

0. 54 0 .6128 0 .6100 0.6087 0.6077 0 .6057 0.6048 0 .6043

0.56 — — — 0.6141 0.6111 0.6097 0.6085 0.6064 0.6054 0.6048

0.58 — — — — 0.6122 0.6106 0.6093 0.6070 0.6059 0.6053

0.60 — — — — 0.6132 0.6115 0.6101 0.6076 0.6064 0.6057

0.62 — — — — 0.6142 0.6123 0.6108 0.6080 0.6068 0.6060

0.64 0.6151 0.6131 0.6114 0.6084 0.6070 0.6063

0.65 — — — — 0.6155 0.6134 0.6117 0.6086 0.6071 0.6063

0.66 0.6159 0.6137 0.6119 0.6087 0.6072 0.6064

0.67 0.6162 0.6140 0.6121 0.6088 0.6072 0.6063

0.68 0.6165 0.6142 0.6123 0.6088 0.6072 0.6063

0.69 0.6168 0.6144 0.6124 0.6088 0.6071 0.6061

0.70 0.6170 0.6145 0.6124 0.6087 0.6069 0.6060

0.71 0.6172 0.6146 0.6124 0.6086 0.6067 0.6057

0.72 0.6173 0.6146 0.6124 0.6084 0.6065 0.6054

0.73 0.6145 0.6122 0.6081 0.6061 0.6051

0.74 0.6144 0.6120 0.6077 0.6057 0.6046

0.75 0.6142 0.6118 0.6073 0.6052 0.6041

A-5
Table /^.S. Coeirt icienC uf Di3caart;e C

OrlEice Plate with Flaa^e Taps

13 = 4 ia.

e

10^ 2 X 11)'+ 3 X 10'^ 5 X 10'+ 7 X 10^ 10 5 3 X 105 10^ 107 ^

0 .20 0.5986 n .5979 0.59 76 0 .5974 0 . 5973 0 .5972

. , ,

0.5971

....

0 . 5970 0.5969

(J .22 1). 5992 0 , 5984 0.5981 0 .5973 0 . 5976 0 . 5975 0. 5973 0 . 5972 0.5972

0 .24 0.6000 0 .5990 0.5985 0 .5982 0 . 5980 0 . 5979 0.5976 0 . 5975 0.5974

0 . 2h 0.6009 0 . 5996 0.5991 0 .5986 (') .5984 0 . 5983 0.5979 0 . 5978 0.5977

0 .28 0 .60 18 0 .6003 0.5997 0 .599 1 0 . 5989 0 . 5987 0.5983 0 . 5981 0.5980

0 .30 0 .6011) 0.6003 () .5997 0 . 5994 0 . 5991 0.5987 0 . 5985 0. 5984

(J . 32 — 0 .6019 0.6011) 0 .6003 0 .5999 0 .5996 0.5991 0 . 5989 0.5987

0 , 34 0 .6028 0.6018 0 .6009 0 .6005 0 .6002 0.5996 0 . 5993 0,5991

(J .3b — 0 .h037 0,6026 0 .6016 0 .6010 .6008 0,6000 0 . 5997 0,5995

0 .38 — 0 .6048 0,6035 0 .6024 0 .6018 0 .6014 0,6006 0 .6002 0,6000

0 .40 — 0.6045 0 .6032 0 .6025 (J .6020 0.601 1 0 .6007 0.6004

0 .42 — — 0.6055 0 .6040 0 .6033 0 .6027 0,6017 0 .6012 0.6009

(J . 4<4 0 . 606 5 0 . 6049 0 . 6040 .6035 0 ,6023 0 . bO 17 0.6014

0 .46 0.6077 0 .6058 0 .6049 0 .6042 0.6029 0 .6023 0,6020

0 .48 — — 0.6088 0 .6068 0 .60 58 0 .6050 0.6035 0 .6029 0.6025

0 .50 — 0 .6078 0 .6067 0 .6058 0,6042 0 .6034 0.6030

0 .52 -- — — 0 .6088 0 .6076 0 ,6066 0,6048 0 .6040 0.6035

0 .54 — — — 0 .6098 0 .6085 0 .6074 0.6054 0 .6045 0.6040

(J .56 0 .6108 0 .6093 0 ,6082 0,6060 0 .6050 0.6045

0 .58 0 .6118 0 .6102 0 ,6089 0,6066 0 .6055 0.6049

0 ,60 0 .6127 0 .6110 0 ,6096 0.6070 0 .6058 0.6052

0 .62 0 .6135 0 .6117 0 ,6102 0.6074 0 .6061 0.6054

0 .64 0 .6123 0 .6107 0.6077 0 .6063 0.6055

0 .65 0 .6125 0 .6108 0.6077 0 ,6063 0.6055

0 .66 0 .6127 0 .6110 0.6077 0 ,6062 0.6054

0 .67 0 .6129 0 .6111 0.6077 0 .6061 0.6053

0 .68 0 .6130 0 .611

0.6076 0 ,6060 0,6051

0 .69 0 .6131 0 .61 10.6075 0 .6058 0.6049

0 .70 0 .6131 0 .6110 0.6073 0 .6055 0,6045

0 .71 0 .6130 0 .6109 0.6070 0 .6052 0.6042

0 .72 0 .6128 0 .6106 0.6066 0 .6047 0.6037

u .73 0 .6126 0 .6103 0.6062 0 .6042 0.6031

0 .74 0 .6123 0 ,6099 0.6056 0 .6036 0.6025

0 .75 0 .6094 0.6050 0 .6029 0.6018

A-6
Table k.h. Coefficient of Discharge C

Orifice Plate with Flange Taps

D = 6 in.

.

2 _ .

X in4 3 X kV* 5 X 10^-^ 7 X 10^ 105 3 X 105 10^ 107

0.20 0 . 5986 0 .5979 0.597 7 0. 5974

_ _ _ 0.5973 0. 59 7 2 0.5971 0.5970 0.5969

0.22 0 . 5993 0 . 5984 0.5981 0.5978 0.59 7 7 0.5975 0.59 7 3 0.5972 0.5972

0.24 0 .5990 0.5986 0.5982 0.5980 0,5979 0.5976 0.5975 0.5974

0.26 — 0 .5996 0.5991 0.5987 0.5984 0.5983 0.5980 0.5973 0.5977

0.28 0 .6003 0 . 5997 0.5992 0.5989 0.5987 0.5983 0.5981 0.5980

0. 30 0 .6010 0.6003 0 . 5997 0. 5994 0.599 2 0.5987 0 . 5985 0 . 5984

0.32 (J .60 19 0 .60 10 0 .6003 0 . 5999 0 . 5996 0.5991 0 . 5989 0.5987

0.34 0.6018 0.6009 0.6005 0.6002 0.5996 0.5993 0.5991

0.36 — — 0.6026 0.6016 0.6012 0.6008 0.6000 0.5997 0.5945

0 . 38 0 .6035 0 .6024 0 .6013 0.6014 0 .6006 0 .6002 0 .6000

U.'tO 0 .6031 0 . 6025 0 .6020 0.601

1

0 .6007 0.6004

0 .6040 0 .6033 0.6027 0.6017 0 .60 1

2

0 . 6009

n ^ n A o 0 .oOhU 0.6034 0 . 6022 0.6017 0.6014

U .'to - 0 .6057 0 . 6049 0 . 604

1

0 .6028 0 .6022 0 .6019

f\ AO 0.48 0 .6067 0 . 6057 0 .6049 0 .6034 0 .6027 0 .6024

0.50 — — 0.6076 0.6065 0.6056 0.6040 0.6033 0.6029

0 .6074 0 . 6064 0 .6046 0 .6038 0 .6033

0.54 0 .6082 0 .607

1

0 .6052 0.6043 0 .6038

0.56 0 .6090 0 .6078 0 .6057 0.6047 0 .6041 0.58 0 .6098 0 .6085 0.6061 0.6051 0 .6044

0.60 — — — — 0.6105 0.6091 0.6065 0.6053 0.6047

U.oZ 0 .6095 0 .6068 0.6055 0 . 6048

0.64 0.6099 0.6069 0.605 5 0.6047

0.65 0.6100 0.6068 0.6054 0.6046

0.66 0.6100 0.6068 0.6053 0.6044

0.67 0.6100 0.6066 0.6051 0.6042

0.68 0.6099 0.6064 0.6048 0.6039

0.69 0.6098 0.6062 0.6045 0.6036

0.70 0.6096 0.6058 0.6041 0.6031

0.71 0.6093 0.6054 0.6036 0.6026

0.72 0.6089 0.6049 0.6030 0.6020

0.73 0.6043 0.6023 0.6012

0.74 0.6035 0.6015 0.6004

0.75 0.6027 0.6006 0.5994

A-7
Table A. 7. Coefficient of Oischar^^e C

OrLfi-ce Plate with Flange Taps

D = 8 in.

ii \^

Z X I'

1 V I (1^ X i ' ' J) V 1 n4 7 I05 A V 1 n 5 11 n6u

0.20 0.59 79 0 .5977 0 . 5974 0 .59 73 0 . 5972 0.59 71 0.5970 0 .5970

0.22 0.5984 0 .5981 0 .5973 0 .5977 0 . 5975 0.9573 0.5972 0 .5972

nu nu . J ? o n . 5980 Q . 5979 0 . 59 76 0 . 59 7 5 n . 59 74 0.26 0.5996 0 . 5991 0 .598 7 0 .5985 0 .5983 0.5980 0.59 78 0 .5977 0.28 0.6003 0 .5997 0 . 5992 0 .5989 0 .598 7 0.5983 0.5981 0 .5980

0.30 — 0 .6003 0 .5997 0 .5994 0 . 5992 0.5987 0.5985 0 .5984

0.32 — 0 .6010 0 .6003 0 .5999 0 .5997 0.5991 0.5989 0 .5987

U • JH f 1 U AO 1 9. u . 0 U U 7 nu . Ann O U U 3 Ann? ny I ^UQ 1 • }y 7 1 0.36 — 0 .6016 0 .6012 0 .6008 0.6001 0.5597 0 . 5995

0.38 — 0 .6024 0 .6018 0 .6014 0.6006 0.6002 0 .6000

0.40 — — 0 .6031 0 .6025 0 .6020 0.601

0.6007 0 .6004

0.42 — — 0 .6040 0 .6033 0 .6027 0.6016 0.6011 0 .6009 0.44 — — 0 .6048 0 .6040 0 .6034 0.6022 0.6017 0 .6014

0.46 — — 0 .6048 0 .6041 0.6028 0.6022 0 .6018

0.48 — — — 0 .6056 0 .6048 0.6034 0.6027 0 .6023

0.50 — — — 0 .6065 0 .6056 0.6040 0.6032 0 .6028

0.52 — — 0 .6073 0 .6063 0.6045 0.6037 0 .6032

0.54 — — — — 0 .6070 0.6050 0.6041 0 .6036

0.56 — — — — 0 .6077 0.6055 0.6045 0 .6040

0.58 — — — — 0 .6083 0.6059 0.6048 0 .6042

0.60 0 .6088 0.6063 0.6051 0 .6044

0.62 0 .6092 0.606i 0.6052 0 .6044

0.64 0.6065 0.6051 0 .6043

0.65 0.6064 0.6050 0 .6041 0.66 0.6063 0.6048 0 .6039

0.67 0.6061 0.6045 0 .6037 0.68 0.6059 0.6042 0 .6033

0.69 0.6055 0.6039 0 .6029

0.70 0.6051 0.6034 0 .6024

0.71 0.6046 0.6028 0 .6018

0.72 0.6040 0.6021 0 .6011 0.73 0.6033 0.6014 0 .6003

0.74 0.6025 0.6005 0 .5993

0.75 0.6015 0.5994 0 .5983

A-8
Table A. 8. Coe f t" Ic Lent of Oischar,;<e C

fjrifice Plate with Flange Taps

D = 10 in.

\^ 2

1 ^/l X lO'* 3 X lo '-t 5 X 10^ 7 105 3 X lip 10^ n 1 10'

0.20 0 .59 79 0 5977

^_

0 . 5974 0 .5973 0 . 5972 0.5971 0.59 70 0.59 70 0.22 0 .5984 0 5981 0 .5978 0 .5977 0 .5976 0.59 7 3 0.5972 0.59 72 0.24 0 .5990 0 598b 0 . 5982 0 .5980 0 .5979 0.5976 0.59 75 0. 5975

0.26 — 0 5991 0 . 5987 0 .5985 0 .5983 0.5980 0.5978 0. 59 7 7 U.28 0 5997 0 . 5992 0 . 5989 0 .5987 0.5983 0.5981 0.5980

0.30 0 6003 0 .5997 0 . 5994 0 . 5992 0. 5987 0.5985 0.5984

0.32 — 0 .6003 0 . 5999 0 .5997 0.5991 0.5989 0.5987

0.34 — — 0 .6009 0 .6005 0 .6002 0.5996 0.5993 0.5991

0.36 — — 0 .6016 0 .6012 0 .6008 0.6001 0.5997 0.5995

0.38 — — 0 .6024 0 .6018 0 . 60 14 0.6006 0.6002 0.6000

0.40 — — — 0 .6025 0 .6020 0.601

1

0.6006 0.6004

0.42 — — — 0 .6032 0 .6027 0.6016 0.6011 0.6009

0.44 0 .6040 0 .6034 0.6022 0.6016 0.6013

0.46 0 .6048 0 .6041 0 .6028 0 .6022 0.6018

0.48 — — — 0 .6048 0.6033 0.6027 0.6023

0.50 — — — — 0 .6055 0.6039 0.6032 0.6027

0.52 — — -- — 0 .6062 0.6045 0.6036 0.6032

0.54 — — — 0 .6069 0.6050 0.6041 0.6035

0.56 0 .6076 0.6054 0.6044 0.6039

0.58 — — — — 0.6058 0.6047 0.6041

0.60 0.6061 0.6049 0.6042

0.62 0.6063 0.6050 0.6042

0.64 0.6062 0.6048 0.6041

0.65 0.6061 0.6047 0.6039

0.66 0.6060 0.6045 0.6037

0.67 0.6058 0.6042 0.6034

0.68 0.6055 0.6039 0.6030

0.69 0.6051 0.6035 0.6025

0.70 0.6047 0.6029 0.6020

0.71 0.6041 0.6023 0.6013

0.72 0.6035 0.6016 0.6006

0.73 0.6027 0.6008 0.5997

0.74 0.6018 0.5998 0.5987

0.75 0.6008 0.5987 0.5976

A-9
T'.hle A. 9, Coefficient of Discharge C

Orifice Plate with Flange Taps

D = IS in.

•V V 1 n4

1

•3J V 1 n4

1

J V 1 n4

1

7 X 10^

1

J X. i 1,^ io6 1 U

0.20 —

0 .5979 0 .5977 0 . 5974 0 .5973 0.5972 0.5971 0 .5970 0.5970

(J SQt^ 1 . J 7 O 1 () n\j . 59 77 0 . 5976 0U . SJ 47 7/ -J 0 .5973 U

jy 1 L O . _ H

(

C\U . J -/ o ^ nu S Q S 0 f) SQ7Q nU . J7SQ7/ A0 U U . J7 / J n ?(-. ("1 • J J O 1 u « J 7 O J nU . J70v^ SQRd U

7 W • 3 7 / O U . J 7 / / Q _ 9 1

u . JyOy (1\j w SQX7 jy O t U . J 7 O J u . 370 Z dU 8 1 . J 7 o i

0.30 -- — 0 .5997 0 . 5994 0.5992 0.5987 u .3703 0.5984

J • J z . 0 U U J> U . ouuu \j a jy y 1 U • 3 7 7 J. U U . J700

n "XL . OUU J n Add? U • 3 " 7 O U . 3y y J dU Q 1 . J 7 7 i U • J 0 A n 1 ? i\u . Ados 0 u u o U • OUU

0 . 5997 U . jyy J W • JO . OU i O U . 0 U i H U > D U L' O 0 .6002 dU • Addd OUUU

U • 4U o Anon U • DU 1 1 0 .6006 d A n d /i

/~1 /. 0 vJ , Z n A no 7 n A ri 1 A U . o U L o 0 .6011 d AndO

0.44 0.6033 0.6022 0 .6016 0.6013

Q.46 — — — 0.6040 0.6027 0 .6021 0.6018

() . 4o 0 .ou3j 0 .6026 0 .6022

0.50 0.6038 0 .6031 0.6027

0.52 0 .6044 0 .6035 0.6031

0 . 54 0 .6049 0 .6040 0 .6034

0.56 — — — — — 0.6053 0 .6043 0.6037

U . JO 0 . 605o 0 .6046 0.6039

0.60 0.6059 0 .6047 0.6040

0.62 0.6060 0 .6047 0.6040

0.64 0.6059 0 .6045 0.6037

0.65 0.6058 0 .6043 0.6035

0.66 0.6056 0 .6041 0.6033

0.67 0.6054 0 .6038 0.6029

0.68 0.6050 0 .6034 0.6025

0.69 0.6046 0 .6029 0.6020

0.70 0.6041 0 .6024 0.6014

0.71 0.6035 0 .6017 0.6007

0.72 0.6028 0.6009 0.5999

0.73 0.6020 0 .6000 0.5989

0.74 0.6010 0 .5990 0.5979

0.75 0.5999 0 .5978 0.5966

A-10
Table A. 10. Coefficient of Discharge C

Orifice Plate with Flange Taps

D = 30 in.

5 X 10^ 7 X 10^ 105

3 \. ——

0 S9 74 n S9 7 ^ 0 . 22 0 . 5978 0 . 597 7 0.5976

0.24 0.5981 0.5979

0.26 — 0.5985 0.5983

0 98 0 . 5987

0 . 30 0 . 5992

0.32 0 . 5997

0.34 — —

0.36 —

0 . 38

0.40

0.42

0 .44

0 46

0 48

0.50 —

n 57

n S8

0.60 — — —

0.62

0.64

0.65

0.66

0.67

0.68

0.69

0.70

0.71

0.72

0.73

0.74

0.7 5

3 X 105 106 107 —

SQ 7 1 (1 0 . 5970

n sq 7Zi. 0 0 .5972

0 .5977 0 .5975 0 .5975

0 .5980 0 .5978 0 .5978

n S982 n S98 1

0 .5987 . 5985 0 .5984

0 599 1 0 5989 0 .5988

0 .5996 0 .5993 0 .5991

0 .6001 0 .5997 0 .5995

n n • 600? vJ Z. 0 .6000

60 1 1 6006 0 .6004

0 n 60 1 1 u . A008 u u u o

\) . 'J L' Z, 1 nV ^ AO 1 A 0 .6013

AD?? 0 AO? 1 0 .6017

. DU J Z .ouzo AO 7 A 0 .6022

0 .6038 0 .6030 0 .6026

nU ADA 7 AO"^ S 0 .6030

u ADA ft. O U 4 O u Afl R 0 .6033

(

)

0 .6036

u

A n /, A . 0 1^1 H 4 0 .6038

0 .6045 0 .6038

vJ A n A A 0 .6037

0 .6042 0 .6034

0 .6040 0 .6032

0 .6037 0 .6029

0 .6034 0 .6025

0 .6029 0 .6020

0 .6024 0 .6015

0 .6018 0 .6008

0 .6011 0 .6001

0 .6002 0 .5992

0 .5992 0 .5982

0 .5981 0 . 5970

0 . 5969 0 .5957
Table A. 11. Coefficient of Discharge C

ISA 1932 Flow Nozzle

2" < D < 2(1"

2 X 10^ 3 X 10^ 4

3 X 10^ 7 -vr 1 l"^ / X lU^ in5 1 r^6 -1 1 A 0 Z X iU"

u . 30 u . y o 0 u u • y 0 D 0

n O Q 7 o A O Q J J A Q U Q O U . y o £5 J u U . 70 jU n Q ^ 7 /i i') U W 7 *-i U •70/

ilu Q « 7 X . y o / o u . 3h u . y o J i M OU 7 1 U • y o / i n Q >i 7 7 u . y o / z u • JO u . y o'4

U . y o J 7 A Q Q A ^ 0 .38 — — 0.9818 0.9831 0.9850 0.9855 0.9856

u

/i n u • y oUh c\ Oft 1 Q J • y 0 i y u . yo jy A Q Q /, A Q Q A A u

A 9 • 4-Z n Q 7 Q r 1 u . y / y u u . y o u J u . y o z / A Q Q T 1 u . yo J

A Q Q T A u . y o J t

/. /. . 44 u . y 0 y 'I n Q 7 c: I n Q 7 7 "3 u . y / / J n Q 7 U M A Q Q 1 'J u . y o i J A Q O 7 A

u . y o z u

A Q Q T 1 u . y o z i u .40 0.9 59 3 0 . 9 6 / Z 0 . y / 3 z

i"l Q 7 Q ^ u . y / 5 6 n Q 7 7 u . y / 1 i A Q 7 O 7 1^ Q Q A /. 0 .48 0.9567 0.9650 0.9711 0.9736 0.9754 0.9779 0.9786 0.9737

U . 30 0 .9542 0 .9626 0 .9689 0.9/15 A n 7 i o 0 .9/33 A n 7 c o 0.9/38 A l1 7 £^ 0.9/66 A O 7 7 0.9/6/

0 . D2 0 . 9 5 10 .9601 0.9665 IJ .969 1 A (1 7 A n 0 .9/09 A n 7 o c 0.9/35 A O 7 /. Q 0.9/43 A Q 7 A /. 0 .9 /44

0 . 54 0 .9490 0.9575 0 .9639 0 .9665 0.9683 0 . 9709 0.9717 0.9718

u . DO 0 .9464 0 .9548 0.9611 0.9636 0.9655 A ri O A

0 .9680 A a /I o o 0 .9688 A n /I o n 0 .9689

0 .58 0.9437 0.9519 0.9581 0.9605 0.9623 0.9648 0.9655 0.9656

0 .60 0.9411 0.9489 0.9548 0.9572 0.9588 0.9612 0.9619 0.9620

u • uZ n Q 7 ft A U . 3 J O U • y ^Do u . y J i J u . y J J J u . y J J u U • 7 D / J A QS7Q U • -7 JOU

0 .64 0.9358 0.9425 0.9475 0.9495 0.9509 0.9529 0.9535 0.9536

u .66 0.9332 0.9390 0.9434 0.9451 0.9464 0.9481 0.9437 0.9487

u .68 0.930D 0.9354 0.9390 0.9404 0.9414 0.9429 0.9433 0.9434

u .70 0.9280 0.9316 0.9342 0.9353 0.9361 0.9372 0.9375 0.9375

0 .72 0.9255 0.9276 0.9292 0.9298 q.9303 0.9309 0.9311 0.9311

u .74 0.9230 0.9235 0.9238 0.9239 0.9240 0.9241 0.9242 0.9242

0 .76 0.9207 0.9191 0.9180 0.9175 0.9172 0.9168 0.9166 0.9166

0 .78 0.9184 0.9146 0.9118 0.9107 0.9099 0.9088 0.9084 0.9084

0 .80 0.9162 0.9100 0.9053 0.9034 0.9020 0.9001 0.8996 0.8995

A-12
Table \.\2, Coefficient: of Dlscharj^e C

Long riadius Flow iiozzie

2" < j) < 24"

3

10^ 2 X 10^ 3 X

10'^ io5 2 X 10^ 3 X 10^ 10^ 5 X 10^

U

.

i~l O <J '1 /. 0 . y o j4 0.98/3 0 . 9900 11 fi ( 1 o / 0 .9924 0.99 36 0.9952 0 .9556

0.22 0.9659 0.9748 0.9828 0.9868 0.9897 0.9922 0.9934 0.9951 0.9955

0.24 0.9645 0.9739 0.9822 0.9864 0.9893 0.9920 0.9933 0.9951 0.9955

0.26 0.9632 0.9730 0.9816 0.9860 0.9891 0.9918 0.9932 0.9950 0.9954

' 0.28 0.9619 0.9721 0.9810 0.9856 0.9888 0.9916 0.9930 0.9950 0.9954

0.30 0

.

^bU

/

0 . y / 1

2

0 . 9805 0.9852 0 . 9885 0.9914 0 . 9929 0.9949 0.9954

0.32 0.9596 0.9704 0.9800 0.9848 0.9882 0.9913 0.9928 0.9948 0.9953

0.34 0.9584 0.9696 0.9795 0.9845 0.9880 0.9911 0.9927 0.9948 0.9953

0.36 0.9573 0.9688 0.9790 0.9841 0.9877 0.9910 0.9926 0.9947 0.9953

0.38 0.9562 0.9680 0.9785 0.9838 0.9875 0.9908 0.9925 0.9947 0.9952

0.40 0.9552 1 n £1 7 o U . 96 / 3 0 .9780 0 . 9834 0.987 3 U .9907 0 . 9924 0 . 9947 0.9952

0.42 0.9542 0.9666 0.9776 0.9831 0.9870 0.9905 0.9923 0.9946 0.9952

0.44 0.9532 0.9659 0.9771 0.9828 0.9868 0.9904 0.9922 0.9946 0.9951

0.46 0.9522 0.9652 0.9767 0.9825 0.9866 0.9902 0.9921 0.9945 0.9951

0.48 0.9513 0.9645 0.9763 0.9822 0.9864 0.9901 0.9920 0.9945 0.9951

U . 3U <j . y ju J u . y 0 jy n Q 7 c Q u . y / jy u . y o 1 y

i~l Q Q ^ 0 u . y yuu 0 . yy ly 0

.

yy^H 0 . yy 50

0.52 0.9494 0.9632 0.9754 0.9816 0.9860 0.9898 0.9918 0.9944 0.9950

0.54 0.9485 0.9626 0.9750 0.9813 0.9858 0.9897 0.9917 0.9944 0.9950

0.56 0.9476 0.9619 0.9746 0.9810 0.9856 0.9896 0.9916 0.9943 0.9950

0.58 0.9468 0.9613 0.9743 0.9808 0.9854 0.9895 0.9915 0.9943 0.9949

It n O A fi 7 u . y ou

/

-\ 0 7 0 0 u . y oU

J

11 Q y Q 0 u . y y i 4Ci Q Q /, 0 0.62 0.9451 0.9601 0.9735 0.9802 0.9850 0.9892 0.9914 0.9942 0.9949

0.b4 0.9443 0.9596 0.9731 0.9800 0.9848 0.9891 0.9913 0.9942 0.9948

0.66 0.9435 0.9590 0.9728 0.9797 0.9846 0.9890 0.9912 0.9941 0.9948

0.68 0.9427 0.9584 0.9724 0.9795 0.9845 0.988y 0.9911 0.9941 0.9948

0.70 0.9419 0.9579 0.9721 0.9792 0.9843 0.9888 0.9910 0.9941 0.9948

0.72 0.9411 0.9573 0.9717 0.9790 0.9841 0.9887 0.9910 0.9940 0.9947

0.74 0.9403 0.9568 0.9714 0.9787 0.9839 0.9886 0.9909 0.9940 0.9947

0.76 0.9396 0.9562 0.9710 0.9785 0.9838 0.9884 0.9908 0.9940 0.9947

0.78 0.9388 0.9557 0.9707 0.9783 0.9836 0.9883 0.9907 0.9939 0.9947

0.80 0.9381 0.9552 0.9704 0.9780 0.9834 0.9882 0.9907 0.9939 0.9947

A-13
Table A. 13. Coefficient of Discharge C

Nozzle Venturi Meter

2.5" 1 D 5 20"

d >^ 2"

1.5 X 10^ < Rn < 2 X 10^

e C

0.316 0.9847

0.320 0.9846

0.340 0.9843

0.360 0.9838

0.380 0.9833

0.400 0.9826

0.420 0.9818

0.440 0.9809

0.460 0.9798

0.480 0.9786

0.500 0.97 71

0.520 0.9755

0.540 0.9736

0.560 0.9714

0.580 0.9689

0.600 0.9661

0.620 0.9630

0.640 0.9595

0.660 0.9556

0.680 0.9512

0.700 0.9464

0.720 0.9411

0.740 0.9352

0.760 0.9288

0.775 0.9236

A- 14

V
Table A. 14. Coefficient of Discharge, C

Classical Venturi Meter

Rough-cast

Entrance Cone

Machined

Entrance Cone

Rough Welded

Sheet-Metal

Entrance Cone

Coefficient C 0.984 0.995 0.985

Tolerance on

C, % 0.70 1 .00 1 .50

0.30 to 0.75 0.40 to 0.75 0.40 to 0.70

D, in. 4 to 32 2 to 10 8 to 48

2 X 10^ to 2 X 10*' 2 X 10^ to 1 X 10^ 2 X 10^ to 2 X 10^

A-15
Table A. 15. References for Equations for Coefficient of Discharge C

Primary Element

Thin-plate, square-edge orifice

for corner, flange, and D, D/

taps

ISA 1932 flow nozzle

Long radius flow nozzle

Nozzle venturl meter

i Classical venturi meter

Source

Reference 11 or Reference 10

Reference 10

Reference 10

Reference 10

No known references

A-16
Table A. 16. Fluid Expansion Factor Y for Flow Nozzles and Vendiri Meters

Y = 1 . 3 ( steam)

\ r

3 34 , 0.95 0 . 90 u . 0 J u • ou n 7 s n 70 w • 0 J W . J J —

0.20 0.0016

—

0.9707 0.9407 0.9099

-—

0.8781 0.8454 0.8117

.

0.7768 0.7406 0.7030

* J\J J\JO L .9402 «7 7 .0 1 wO . f 1 JO . 7/ jyAQTJ 70 1 6 AH . U Z JD Q n 7 A 8 7 sri 807 11 ")1 7 7 .07AQ7a/ 0

U . J U . 7 DO J .y\jJH • 0 / u u . 0 J J 0 . 0 U U 0 7 9 7H .0070

DQ 1 S Qh7 1 • yu^iL .Ou JO . 0 J U

" 7Q s 7 • 7' SHR J 0 0 7 9 1 A . 0 0 Z 7 .60 .1296 .9654 .9 305 .8954 .8599 .8 240 .7876 .7505 .7126 .6738

.1785 .9629 .92 59 .8889 .8519 .8 146 7 7 7 1 . 7t ^Qjy 9^ .7007 .2401 .9594 .9193 ,8798 .8406 .80 16 .7627 .I'lyi .6844 .6447 .725 .2763 .9570 .9150 .8739 .8333 .7933 .7535 .7139 .6742 .6343

0.75 .3164 .9542 .9098 .8667 .8246 .7833 .7426 .7023 .6622 .6221 .775 .3608 .9507 .9034 .8580 .8141 .7714 .7297 .6886 .6481 .6077

.80 .4096 .9462 .8955 .8473 .8013 .7570 .7141 .6723 .6313 .5908

0.82 .4521 .9418 .8876 .8368 .7888 .7431 .6992 .6568 .6155 .5750

.84 .4979 .9362 .8779 .8241 .7739 .7266 .6817 .6387 .597 1 .5567

.86 .5470

1

.9292 .8658 .8084 .7557 .7067 .6608 .6172 .5756 .5353 — —

Y = 1.4

-

(air)

——

3 0.95 0.90 —

0.85 0.80 0.75 0.70 0.65 0.60

—

0.55

0.20 0.0016 0 .9728 0 .9448 0.9160 0 .8863 0 .8556 0 .8238 0 .7908 0 .7565 0 .7207 .30 .008

1

.9726 .9444 .9 1 54 .8855 .8546 .8227 .7896 .7 552 .7193

.40 .0256 .9719 .9432 .9137 .8833 .852Q .8198 .7864 .7517 .7156

0 . 50 .0625 .9706 .9405 .9099 .8785 .8464 .8133 .7793 .7441 7076

ss . 0915 .9694 .9383 .9067 .8745 .84 16 .8080 .7 378 .7010 .60 .1296 .9678 .9352 .9023 .8690 .8351 .8006 .7292 .6920

0.65 . 1785 .9655 .9309 .8962 .8613 .8261 .7905 .7543 .7175 .6798

.70 . 2401 .9622 .9247 .8876 .8506 .8136 .7765 .7392 .7016 .6633

.725 .2763 .9600 .9207 .8819 .8436 .8056 .7676 .7297 .6915 .6530

0.75 .3164 .9573 .9158 .8751 .8353 .7960 .757 1 .7184 .6797 .6409 .775 .3608 .9540 .9097 .8669 .8252 .7845 .7445 .7050 .6657 .6266

.80 .4096 .9498 .9022 .8566 .8128 .7705 .7292 .6889 .6491 .6097

0.82 .4521 .9457 .8947 .8466 .8009 .7570 .7147 .6736 .6334 .5939

.84 .4979 .9405 .8856 .8344 .7864 .7409 .6975 .6557 .6152 .5755

.86 .5470 .9338 .8740 .8194 .7688 .7215 .6769 .6344 .5936 .5541

Y= (r2/^ Y 1 _ ^(y-D/y 1 -

Y - 1 1 - r

1 - [ T)]/

where r is the pressure ratio Fy/^i and y is the specific heat ratio Cp/

Limits of use are given in reference 10 and are the same as those for discharge coefficient C. See

tables A-11 through A. 14. P2/Pi < 0.75.

A-17
Table A. 17. Uncertainty of Discharge Coefficients

Orifice Meters

Corner Taps Flange Taps D and D/2 taps

3 <_ 0.6 0,6% 0.6% 0.6%

0.6 <_ B < 0.8 3%

0.6 < 3 <_ 0.75 3% 3%

Flow Nozzles

ISA 1983 Long Radius

.3^0.6 0.8%

3 > 0.6 (23 - 0.4)%

0.2 < 6 < 0.8 2%

Classical Venturi

Rough cast entrance 0.7%

Machined entrance 1.0%

Rough-welded sheet iron entrance 1.5%

Nozzle Venturi Meter

The uncertainty in a is (1.2 + 1.5 3^)% where a = C/ ( 1- 3^ )-''^^

Source: "Reference 10

Notes: Quantities 3, Rp and D are assumed known withour error.

The above uncertainties are given for reference purposes.

They would be useful in estimating the uncertainty in

flowrate when the primary element is used uncalibrated

and the secondary element (AP transducer) only receives

calibration.

A-18
Table A. 18. Uncertainty of Expansion Factors [10]

Orifice Meters

3 < 0.75 4(AP/Pi)%

0.75 < 3 < 0.8 8(AP/P]^)% (corner taps only)

Flow Nozzles

ISA 1932 and Long Radius 2(AP/Pi)%

Venturi Meters

Nozzle venturi and Classical vetituri meters (4+1003 )(AP/P,)%

Notes: Quantities 3> AP and ?i are assuraed known without error.

The above uncertainties are given for reference purposes.

They would be useful in estimating the uncertainty in

flowrate when the primary element is used uncalibrated

and the secondary element (AP transducer) only receives

calibration, or when the primary element has been

calibrated with a liquid and is to be used to monitor gas

(air or steam)

.

A-19
0.85 '

'

^ ^ — ^ • 0 0.05 0.10 0.15 0.20 0.25

AP/P^ 7

Y= 1.00 - (0.41 + 0.35 /34)(AP/P^7), where 7 is

the specific heat ratio Cp/Cy

Figure A.l. Fluid expansion factor Y for thin-plate, square-edged orifice

plates with corner taps, flange taps, and ID and 1/2D taps.

Pressure ratio P]^/P2 ^ 0.75. Limits of use for 6 and Rq are

the same as those for C. See tables A-1 through A-10. [2,10]

A-20
in CM ^ U) (O (O

7^ /

/

J

7=1.3

o

o

o Q.\

<M

Q.

II

i O

o

o

00 < 1 o

LU

OC 10

00 0)

i o liJ oc0.

o

0)

to

0)

o

o 0>

o

0> 00

o

00

o

10 o 10

o

o1 o

(0

QJ

4_) CI

•H

1 <5

CD "CJ ,—

1

c

nJ 4J

Cfl d) QJ

(—

1

N w

N

O

CD

o

,—

1

Q

CO o 4-1 •Hg

,—1 o

4-1 o

u

CO

i-i-i co

9"

-H CO

(/] dJ c 4-1 TO CO a

X

dJ IDH

D 11 rH

>-

<

d)

J-i

•H

A 'd013Vd NOISNVdXB Qinid

A-21
A 'UOlOVd NOlSNVdXB Qinid
APPENDIX B

FLUID PROPERTIES AND FLOW QUANTITY CONVERSION FACTORS

B-1
Table B.l. Density of Saturated and Compressed Liquid Water (lb/ft ) [6]

Temperature Pressure, psia Temperature Pressure, Psia

(°F) Saturated 500 1000 (°F) Saturated 500 1000

32 62.4140 62.5217 62.6288 75 62.2654 62.3618 62.4575

33 .4167 .5240 .6308 76 .2568 .3530 .4486

34 .4191 .5260 .6324 77 .2479 .3440 .4395

78 .2389 .3349 .4302

35 62.4212 62.5277 62.6336 79 .2297 .3255 .4207

36 .4229 .5289 .6345

37 • D J J L 80 A9 "^1 An 38 .4252 .5305 .6353 81 .2107 .3063 .4013

39 .4258 .5308 .6352 82 .2009 .2964 .3913

83 .1910 .2864 .3811

40 62.4261 62.5307 62.6348 84 .1809 .2762 .3708

41 .4261 .5304 .6341

42 .4257 .5297 .6330 85 62.1706 62.2658 62.3603

43 .4251 .5287 .6317 90 .1166 .2113 .3055

44 .4241 . 5274 .6301 95 .0585 .1529 .2467

45 62.4229 62.5258 62.6282 100 61.9964 .0906 .1841

46 .4213 .5239 .6260 105 .9307 .0246 .1180

47 .4194 .5218 .6235

48 .4173 .5193 .6208 110 61.8612 61.9551 62.0483

49 .4149 .5166 .6178 115 .7884 .8821 61.9754

120 .7121 .8059 .8992

50 62.4122 62.5136 62.6145 125 .6326 .7265 .8198

51 .4092 .5104 .6110 130 .5500 .6440 .7375

52 .4059 .5068 .6072

53 .4024 .5031 .6031 135 61 .4643 61 .5584 61.6521

54 .3986 .4990 .5988 140 .3757 .4700 .5640

145 .2842 .3787 .4730

55 62.3946 62.4947 62.5943 150 .1899 .2847 .3793

56 .3903 .4902 .5895 155 .0928 .1880 .2830

57 .3858 .4854 .5845

58 .3810 .4804 .5793 160 60.9932 61.0887 61 .1841

59 .3760 .4752 . 5738 165 .8909 60.9868 .0827

170 .7862 .8824 60.9789

60 62.3707 62.4697 62.5681 175 .6789 .7756 .8726

61 .3652 .4640 .5622 180 .5693 .6665 .7640

62 .3595 .4581 .5560

63 .3535 .4519 .5497 185 60.4573 60.5549 60.6531

64 .3474 .4455 .5431 190 .3430 .4411 .5400

195 .2265 .3250 .4246

65 62.3410 62.4390 62.5363 200 .1076 .2068 .3070

66 .3344 .4322 . 5293 205 59.9866 .0863 .1873

67 .3275 .4251 .5221

68 .3205 .4179 .5147 210 59.8635 59.9636 60.0655

69 .3132 .4105 .5071 215 .7382 .8389 59.9416

220 .6108 .7120 .8156

70 62.3058 62.4029 62.4993 225 .4813 .5830 .6875

71 .2981 .3950 .4914 230 .3497 .4520 .5574

72 .2902 .3870 .4832

73 .2822 .3788 .4748 235 59.2161 59.3189 59.4253

74 .2739 .3704 .4663 240 .0804 .1838 .2912

B-2
Table B.l. Density of Saturated and Compressed Liquid Water (lb/ft ) [6]

Temperature Pressure, psia Temperature Pressure, Psia

(°F) Saturated 500 1000 (°F) Saturated 500 1000

245 58.9428 0.0467 .1551 385 54.2597 54.3546 54 .5140

250 .8031 58.9075 .0171 390 .0606 .1531 .3155

255 .6614 .7663 58.8770 395 53.8590 53.9489 .1144

400 .6548 .7418 53 .9105

260 58.5177 58.6231 58.7350 405 .4481 .5318 .7039

265 .3720 .4779 .5910

270 .2244 .3306 .4450 410 53.2387 53.3187 53 .4944

275 .0747 .1814 .2970 415 .0267 .1026 .2819

280 57.9231 .0301 .1471 420 52.8119 52.8833 .0665

425 .5942 .6607 52 .8480

285 57.7695 57.8768 57.9952 430 .3737 .4348 .6262

290 .6139 .7215 .8413

295 .4563 .5641 .6854 435 52.1503 52.2053 52 .4012

300 .2966 .4046 .5275 440 51.9238 51.9723 .1728

305 .1350 .2431 .3675 445 .6942 .7354 51 .9409

450 .4615 .4948 .7054

310 56.9713 57.0795 57.2056 455 .2255 .2501 .4661

315 .8056 56.9137 .0415

320 .6378 .7459 56.8754 460 50.9862 51.0012 51 .2229

325 .4680 .5758 .7072 465 .7434 50.7479 50 .9757

330 .2960 .4036 .5369 470 .4971 .4971 .7243

475 .2472 .2472 .4686

335 56.1220 56.2291 56.3644 480 49.9935 49.9935 .2082

340 55.9458 .0524 .1897

345 .7674 55.8735 .0128 485 49.7359 49.7359 49 .9431

350 .5869 .6922 55.8337 490 .4744 .4744 .6731

355 .4042 .5085 .6523 495 .2087 .2087 .3973

500 48.9387 48.9387 .1170

360 55.2192 55.3225 55.4687

365 .0320 .1340 .2826

370 54.8424 54.9430 .0942

375 .6506 .7495 54.9033

380 .4563 .5534 .7099

B-3
Table B.2. Density of Mercury (Ib/ff^) [20]

Temperature

(°F) p Temperature

C'F) p Temperature

(°F) p Temperature

(°F) p

- 5 851.88814 35 848 .45654 75 845.04735 115 841.65689

- 4 .80205 36 .37101 76 844.96245 116 .57198

- 3 .71598 37 .2861

77 .87692 117 .48771

- 2 .62992 38 .20059 78 .79202 118 .40343

- 1 .54388 39 .11506 79 .70712 119 .31853

0 .45785 40 .02953 80 .62221 120 .23425

1 .37184 41 847 .94401 81 .53731 121 .14997

2 .28584 42 .85848 82 .45241 122 .06507

3 .19963 43 .77295 83 .36751 123 840.98079

\ .11390 44 .68805 84 .28261 124 .89651

S .02795 45 .60253 85 .19770 125 .81161

% 850.94201 46 .51700 86 .11280 126 .72733

.85609 47 .43210 87 .02790 127 .64306

.77019 48 .34657 88 843.94300 128 .55815

9

- .68430 49 .26104 89 .85810 129 .47388

m .59843 50 .17552 90 .77319 130 .38960

ii .51257 51 .08999 91 .68829 131 .30532

IS .42673 52 .00509 92 .60401 132 .22104

13 .34090 53 846 .91956 93 .51911 133 .13677

Vk .25509 54 .83466 94 .43421 134 .05249

IS .16956 55 .74913 95 .34931 135 839.96821

US .08404 56 .66423 96 .26441 136 .88393

It yl 849 .99851 57 .57871 97 .17950 137 .79965

.91236 58 .49380 98 .09523 138 .71538

1'9 .82683 59 .40828 99 .01032 139 .63110

2!0 .74068 60 .32338 100 842.92542 140 .54682

21 .65516 61 .23847 101 .84114 145 .12543

22 . 56963 62 .15295 102 .75624 150 838.70467

S'3 .48348 63 .06805 103 .67196 155 .28390

24 .39795 64 845 .98314 104 .58706 160 837.86376

25 .31243 65 .89762 105 .50216 165 .44362

26 .22690 66 .81272 106 .41788 170 .02348

27 .14137 67 .72719 107 .33298 175 836.60397

28 ,05522 68 .64229 108 .24870 180 .18445

29 848.96970 69 .55739 109 .16380 185 835.76556

3?@ .88417 70 .47248 110 .07952 190 .34667

3i .79864 71 .38758 111 841.99462 195 834.92778

32 .71312 72 .30268 112 .91034 200 .50888

33 .62759 73 .21715 113 .82544 205 .09062

34 .54207 74 .13225 114 .74116 210 883.67297

212 833.50567

B-4
Table B.3. Con\'ersion Factors for Mass, Volam<>, and Mass and Volune Rate of Flow

VOLIJt-IE

Multiply

Numbe r of

By

•J! U

a;

4-1 o

a,o

c

i_t c

<D

<u

1' o To Obtain O

Ou

u

V X

oX

CJ

—

-X

v.

Cubic centimeters 1 1.0000

X 103 16.387 2.8317X 10"^

. 3785.4

Liters 1.0000

X 10-3

1 1.6387

X 10-2 28.316 3.7853

Cubic inches 6. 1024

X li)"2 61 .025 1 1728 231

Cubic feet 3.5315

X 10^

3.531b

X JO 2 5.7870X 10

1 0. 13368

US gallons 2.6417

X 10-^ 0.26418 4.3290

X 10-3 7.4805 1

All underlined figures are exact

VOLUME RATE OF FLOW

Multiply

Number of

By

To Obtain \

\ Cubic

centimeters

per

minute

Liters

per

minute

Cubic

inches

per

minute

Cubic

feet

per

minute

US

gallons

per

minute

Cubic centimeters

per minute

1 1.0000

X 103 16.387 2.8317X IC^ 3785.4

Liters per minute

1.0000

X 10-3

1 1.6387

X 10-2 28.316 3.7853

Cubic inches

per minute

6.1024

X 10-2

61.025 1 1728 231

Cubic feet per minute

3.531

5

X 10-5

3.5316

X 10-2

5.7870 X 10-^

1 0.13368

US gallons per minute

0.26417

X 10-3

0.26418 4.3290

X 10-3

7.4805 1
Table B.3. Conversion Factors for Ilass, Volur.ie, and riass and Volume Rate of Flow [8] (Continued)

llultipl'y

Number of

ny

To Obtain

Grams

Kilograms

Ounces* Pounds*

Tons

(short)

G ITSlilS 1 1000 28.350 453.59 0 . 90718

X 10^

k' T I (~i cr T" a in G 1x10"-* 1 28.350

X ur^

453.59

X 10~3

0.90718

X Up

35.274

X ur^

35.274 1 16 32X Up

Founds ''^ 2.2046

X 10~3

2.2046 6.25

X 10~2

1 2000

Tons (short1.1023 1. 1023 3.125 0.5 1 X 10"^ X 10~3 X 10"^ X 10~3

All underlined figures are exact

* Avoirudupois

MASS KATE OF FLOW

I'iultiply

Number of

By

To Obtain

Grams

per

second

Kilograms

per

second

Kilograms

per

minute

Pounds*

per

second

Pounds*

per

minute

Grams per second 1 1000 16.667 453.59 7.5599

Kilograms per second

0.001 1 1.6667

X 10"^

0.45359 7.5599

X 10~3

Kilograms per

minute

60 X 10~3 60 1 27.216 0.45359

Pounds* per

second

2.2046

X 10~3 2.2046 3.6744

X 10~2

1 1 .6667

X 10"^

Pounds* per minute

0.13228 132.28 2.2046 60 1

* Avoirudupois

o ^ ^ 'Z

k. o

OQ CO

0)

COo o «^ S O >oEEo

10

CO

COo

CO I < I m O o m LL

lU ooooooooo

00oo

(Ooooo

LU

QC3

I-<

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Q.u

OOGQ

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CMOo

10

CMo o

CMO

10o

10oo ooo

lO

0)

u

03E

•rl oco

•H

Klc

cxe

4r

>-< CM Ou w

Cv3 4-1 M-i C

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5-1 3

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®d *ao±ovd vaav

B-8
01- X d 'AllSOOSIA 0I1VN3NI>I

O 0) 00 (O U) ^ C9 CM y- O 0)

d

CO rs. d d

(O

d

U)

d d

COd

CM T- d d

o

0)

o

00

o

o

(O

o

10

o

o

C5 cMT^oooor-oju) t-T-,-odddo O 0) 00 d d

s-»i/qi 'gOI. X ri 'A1IS03SIA OmVNAQ

-74

» 17-

I

1

/- —

r

i

— L

-4

/

d

water —I

-)

000

psi<

Saturate i -*

// ft 1

\

V

> >

a. t

o o

o

o

o

(O

o

o

o

o

o

o

CO

o

o

CM

o

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oc3

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UJ

Q.

UJ

f^<oio^coeM^ °

d d d d d d d

>

>>

4J 0 •H 0

w

C0 1

t/) C

•H r-i > e 00 —

•H U CN

COe 0) CU t-) CD c n) u

•H u ^ tfi U3

-O 0) CUu

CO 3 a

CO 3. >-i 0

QJ U D. 4-1 OJ e a

ai

CO J-i

0) 01

<4-i 4= 0 J-i CD

>^ 13

4-1 C H

•H CO tJC cn D- •H 0 J< .-H U 01 00

U) CU •H tfl c

> ai> CD 0 1-1 s:

•H 3 u

e 0

CO d)

4-J >i 0 0 0 H

pa

<uVj3

00

•H

fn

B-9
B-10
Figure B.5. Kinematic viscosities of steam and

water [6]

B-11
o o O O

U) CO w

S-U/qi 'gOr. X ri 'AllSOOSIA OIVVVNAQ

B-12
APPENDIX C. TEMPERATURE AND PRESSURE RELATIONS

C.l TEMPERATURE

The units of temperature commonly used are the degree Fahrenheit, °F, and

degree Celsius, ° C; and the corresponding units of absolute temperatures,

degree Rankine, °R, and the kelvin, K. Absolute temperature in degrees

Rankine, designated by the symbol °R, will be used frequently in our compressible fluid calculations. Temperature in degrees Fahrenheit will be designated

by the symbol t.

The relations existing among these different units of temperature are:

°F = 1 (° C) + 32 (C-1)

5

° C = 1 (°F - 32) (C-2)

9

°R = °F + 459.67 (C-3)

K = ° C + 273.15 (C-4)

°R = i (K). (C-5)

5

C.2 PRESSURE

The unit of pressure to be used in our calculations is pounds force per square

inch. We will also express differential pressure in terms of the pressure

exerted by a column of water at 68 °F and subjected to standard acceleration of

gravity, 32.1740 f t/s^. It will be necessary to designate whether a value of

pressure is:

a) Pressure difference between two points in a flow system

AP in psid (pounds per square inch differential ) , or

Ap in inches of water at 68 ° F;

b) A pressure relative to the existing atmospheric pressure, using negative

values to indicate pressures below atmosphere

p in psig (pounds per square inch gauge); or

c) Absolute pressure

P in psia (pounds per square inch absolute).

C-1
In the direct measurement o£ pressure difference AP , it Ls necessary that both

sides of the pressure sensing element he connected to pressure taps in the flow

system. The pressure difference between these two taps will be derived from

the Instrument indication. Instruments used for the measurement of pressure

difference include Liquid manometers, differential pressure gauges of the

elastic element type, and AP transducers using electrical sensing elements.

Instruments used for the sensing of pressure p relative to atmospheric pressure

have one side of the pressure sensing element vented to the atmosphere. Instruments used here incl.ude manometers, Bourdon tube and diaphragm capsule gauges,

and electrical transducers.

For the direct measurement of absolute pressure P, it is necessary that one side of the pressure sensing element be exposed to zero absolute pressure.

Barometers are one form of such instruments. However, the absolute pressure of

a point in a flow system usually is not measured directly. Rather, gauge pressure p in psig and barometric pressure P]-, in psia are measured. The absolute

pressure is then computed by the relation

P = p + Pj3 = absolute pressure in psia. (C-6)

Barometric pressure, absolute pressure, gauge pressure, and differential

pressure are sensed by many different types of instruments which read out in

many different units of pressure or head. These instruments will be classified

into three types: namely. Mechanical Pressure Gauges, Manometers, and Electrical

Pressure Transducer Systems, defined as follows:

Mechanical Pressure Gauges contain an elastic element such as a Bourdon tube,

diaphragm capsule, or spring bellows having a free end whose position changes

with variation in pressure and a mechanical linkage system to transmit these

variations in position to a revolving pointer located adjacent to a scale calibrated in units of pressure. Such a device senses and indicates directly, and

will measure pressure difference AP, gauge pressure p, or absolute pressure P depending upon its design.

Manometers contain a liquid such as water or mercury in which the difference in

liquid levels increases with increased pressure difference. In elementary

designs the positions of the liquid levels are indicated by a scale, calibrated

in units of length, placed beside the manometer column(s). Thus, this device

senses pressure directly, but its indication, i.e., the difference in liquid

levels, is only proportional to pressure. Like the pressure gauge, a manometer

will measure pressure difference, gauge pressure, or absolute pressure depending

upon its design.

Electrical Pressure Transducer Systems use electrical sensing elements such as metallic or semiconductor strain gauges, variable capacitance or variable

Inductance devices, differential transformers, potentiometers, or piezeolectric

elements to sense deformation of the elastic element. The electrical output of

these elements is usually an analog signal which is processed using electronic

circuitry producing an analog output such as 4-20 mA DC or 0-10 volts DC, or a variable frequency digital signal.

C-2
C.2.1 Corrections and Use of Conversion Factors for Mechanical Pressure Gauges

Calibration of a pressure gauge may show a measurable scale error which varies

with gauge reading. When significant, scale error corrections should be applied

to change the indicated readings to actual pressures. Aside from applying the

scale error correction, it is only necessary to convert from units of pressure

in which the gauge is calibrated to pounds per square inch (psi) or to inches

of water at 68 °F (h„). When gauges are calibrated in units of pressure other

than psi, the Conversion Factors for Pressure, table C-1 , will apply.

C.2.2 Corrections and Use of Conversion Factors Manometers

In converting an indicated level difference or height, h, of a manometer column

to pressure in psi, it is necessary to consider the following:

i a) The units of length in which the height is expressed (inches, centimeters,

etc . ) ,

b) The manometer liquid (water, mercury, etc.),

c) The temperature of the manometer liquid,

d) The density of the fluid in the high pressure leg of the manometer. (This

correction is usually applied only when the manometer is used to measure

pressure differential between two pressures taps in a flow system.)

e) The local acceleration due to gravity, gL.

At times, corrections d) and e) will be too small to affect significantly the

accuracy of the pressure determination. They may be omitted when such is the

case. Correction procedures for each of these five items will now be discussed.

Corrections for Units of Length of the Manometer Scale.

When the scale of the manometer is calibrated in units of length other than

inches, it is convenient to convert the length to inches using the conversion

factors of figures C.l and C.2.

Combined Conversion Factor for the Manometer Liquid and its Temperature

A conversion or multiplication factor F^-^ will be used to convert inches of

water at a known temperature to pounds per square inch. Similarly, a multiplication factor Fjjj]^ will be used to convert inches of mercury at a known temperature to pounds per square inch. Values of these two factors may be obtained

from figures C.l and C.2 for water and mercury manometers, respectively, by

entering these figures with the temperature of the liquid in the manometer

column. This temperature is usually equivalent to room temperature. Figures

C.l and C.2 cover just the manometer temperature range 50 °F and 110 °F, but a larger range 32 °F to 200 °F is covered in tables 12 and 16 of reference 7,

for water and mercury, respectively.

C-3
Co rrection for the Density of the Fluid in the High Pressure Leg of the Manometer

Usually a differential pressure is measured simply by the height of the liquid

column. Actually, when air is in the high pressure leg, the differential pressure is proportional to the difference of the densities of the liquid column

and of the column of equal height of the air on the high pressure side.

Multiplication factors, F^^2 ^ water manometer and ¥-^2 fc>^ ^ mercury manometer,

will be used to correct for the density of the air in the high pressure leg or well of a manometer used to measure differential pressure between two pressure

taps in a flow system. Values of these factors are given in figures C.3 and

C.4 for the water and mercury columns, respectively. These figures apply for

manometer temperatures in the approximate range of 60 °F to 100 ° F. For practial purposes, the factor F^2 have an assumed value of 1.000 except when

the manometer is used to measure differential presure between two pressures

taps in a flow system at an elevated pressure.

When liquid water is in the high pressure leg of a mercury manometer, the

multiplication factor F^3 will be used to correct for the density of the water.

A value of F^3 = 0.9263 may be used for the range of 60 °F to 100 °F manometer

temperature and pressures to 500 psia.

Correction for the Local Value of the Acceleration Due to Gravity

A multiplication factor Fg will be used to correct the manometer reading for

the local acceleration due to gravity. The value of this correction factor may

be determined by the relation

Fg = gL/32.1740 (C-7)

where g-^ is the value of the local acceleration due to gravity existing in the

laboratory and expressed la ft/s~.

C.2.3 Equations for Converting Manometer Readings to Pressure in Pounds Per

Square Inch

A water manometer reading is converted to psi by the relation:

psi = (inches of water) ( F^^^ ^'w2 ^g^ (C-8)

A mercury manometer reading is converted to psi by the relation:

psi = (inches of mercury) ( F^^ F^2 '^^g) (C-9)

When liquid water is in the high pressure leg, a mercury manometer reading is

converted to psi by the relation:

psi = (inches of mercury) ( F,i^x Fm3 (C-10)

C-4
C.2.4 Equations for Converting Manometer Readings to Inches of Water

at 68 °F, h^^

In all cases:

= 27.729 (psi) (Table C.l)

The following may also be used. A, water manometer reading is converted to h,^^ by the relation:

h„ = (inches of water) (p/P6q) ( F^2 ^'g) (C-ll)

where p is the density of water at the manometer temperature, and p^^ is the

density of v^ater at 68 ° F.

A mercury manometer reading is converted to h^ by the relation:

h,^ = (inches of mercury) (pHg/P68) ^^2 ^g) (C-12)

where p^g is the density of mercury at the manometer temperature.

When liquid water is in the high pressure leg, a mercury manoraeter reading is

converted to h„ by the relation:

h„ = (inches of mercury) (Png/PbS^ ^ ^m3 ^^g^ (C-13)

C.2.5 Barometers and Barometric Pressure

It is essential that the barometric or ambient air pressure existing within the

laboratory be determined with good accuracy during tests involving the flow of

compressible fluids. For computations here, the pressure Vy^ of the existing

atmosphere above zero is expressed in pounds force per square inch absolute,

psia. Barometric pressure varies continually throughout the day and from dayto-day depending upon outside atmospheric conditions and the ventilation equipment used to supply air to the laboratory. Normally, P]-, at sea level will be

within the range 14.2 to 14.9 psia. Exceptions will be noted when severe atmospheric disturbances occur or in laboratories having elevations appreciably

different from sea level, e.g., several hundred feet. Two different types of

barometers, aneroid and mercury column, are commonly used. Their designs and

the conversion of their readings to psia are discussed below.

Aneroid Barometers are essentially a refined version of a mechanical pressure

gauge designed to measure absolute pressure. They contain an evacuated diaphragm capsule whose configuration varies with changes in ambient air pressure

together with a mechanical linkage system which moves an indicating pointer

positioned adjacent to a calibrated scale. The scale units are usually inches

of mercury at 32 °F or millimeters of mercury at 0 ° C.

Readings from the aneroid barometer do not require corrections for the local

acceleration due to gravity. Also, temperature correction factors applicable

to mercury columns must not be applied to readings of this instrument. If the

C-5
aneroid barometer is not self-compensating for changes in ambient temperature,

a temperature correction chart or table will be required.

The special temperature correction, if any, as well as any correction for scale error should be applied to the reading of the aneroid barometer to obtain a corrected barometer reading. Conversion factors for pressure from table C.

are then applied to the corrected reading to convert from the instruments units

to psia.

Mercury Column Barometers contain a reservior, vented to the atmosphere, and a vertical column of mercury. A brass scale, calibrated in inches or millimeters,

is placed beside the mercury column; and arrangements are provided for the

adjustment of this scale prior to each reading.

To obtain an accurate measure of the barometric pressure, the reading from a mercury barometer must be corrected for the thermal expansion of both the

mercury and the brass scale, and for the local acceleration due to gravity. It

is also necessary to convert the corrected reading of length into pressure

units, pounds per square inch absolute, psia.

Tables 17 and 18 of reference 7 give Temperature Corrections for Mercury

Barometers with Brass Scales. Correction factors obtained from these tables

compensate for the combined thermal expansion of both the mercury and the brass

scale. The temperature to be used in entering these tables is the temperature

of mercury in the barometer. This is usually indicated by a thermometer

permanently attached to the instrument.

C.2.6 Corrections and Use of Conversion Factors for Electrical Pressure

Transducers

The pressure transducer system may include readout instrumentation indicating

pressure directly, or the output may be an analog signal such as 4-20 mA DC or 0-10 volts DC, or it may be a variable frequency signal. In any case, calibration may show a measurable error which varies with pressure or pressure differential. When significant, error corrections should be applied to change the

indicated reading to actual pressures, or corrections should be applied to the

electrical output.

The transducer should be calibrated periodically, preferably on site, first to

establish and then to monitor any significant errors. The calibration equipment may range in complexity from liquid manometers (vertical, inclined, or micro type using water, mercury, or special manometer fluids) to laboratory

reference type pressure transducer equipment incorporating a digital readout

and automated computational features.

When the pressure transducer is part of a flowmeter system, its output signal

may be expressed in the meter calibration factor CF, for example:

CF = GPM/(mA)l/2 (C-14)

C-6
The mA value may refer to transducer (or transmitter) output current, uncorrected.

Although corrections v^ould not be made directly, it is still very important

that a calibration program be established to determine the transducer error and

that the transducer performance be monitored by periodic calibration checks.

Otherwise, the meter calibration factor will no longer represent the actual

system performance.

C-7
CM

O

o

H

O

<

u.z

o

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QC

UJ>

z

o

o

3.612

3.608

3.604

3.600

3.596

3.592

3.538

3.584

3.580

3.576

psi= (inches of water) x Fy^|

50 60 70 80 90 100 110

MANOMETER TEMPERATURE, °F

Figure C.l. Conversion factor Ft for water columns [7,9]

C-8
0.4908

0.4904

0.4900

E 0.4896

O

»-o

<

u.

(/)

UJ>

z

o

o

0.4892

0.4888

0.4884

0.4880

0.4876

0.4872

psi = (inches of Mercury) x F

50 60 70 80 90 100 110

MANOMETER TEMPERATURE, °F

Figure C.2. Conversion factor F^^ for mercury columns [7,9]

C-9
1.000

0.998

0.982

0 50 100 150 200 250 300

MANOMETER PRESSURE, psia

Figure C.3. Water manometer correction factor F^,2

for air column density [7,91

C-10
CM

E

o

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(0

flC u

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z

o

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1.000

0.999

0.998

0.997

0.996

0.995

0.994

0.993

0.992

200 400 600 800 1000 1200

MANOMETER PRESSURE, psia

Figure C.4. Mercury manometer correction factor F

for air column density [7,9]

m2

C-11
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C-12
APPENDIX D. RELATION BETWEEN MASS AND VOLUriE )<ATE OF FLOW

Whea calibrating a working meter on site, the occasion may arise when the flow

at the transfer conditions of temperature and pressure need to be expressed

in terms of the flow at a different temperature and/or pressure existing at the

working meter; or at a single station, a mass flowrate may need conversion to

a volume flowrate. Thus, the relation between mass and volume rate of flow

needs consideration.

Under steady-flow conditions, the mass flowrate M is constant throughout a system provided no leakage occurs. For example in figure 5, using subscripts

to denote positions with the system, the conservation of mass flowrate M may be

stated by:

Mass flowrate = M = M][ = M2 = M3 = M4 = ....= (D-1)

The volume rate of flow at any point x in the system is the mass flowrate

divided by the fluid density at that point, or

Qx = '•t/Px fi^om which (D-2)

Ql = M/Pi; Q2 = M/P2; Qx = M/Px

When water (incompressible fluid) is flowing, density p will be essentially

constant at building system pressure levels and

Ql = Q2 = Q3 = Qa = = Qx (D-3)

When a gas (air, steam) is flowing, the density pj^ varies point to point as a function of the temperature and pressure. Since

M = M]^ = M2 =....= Mj(., then

(Pl Ql) = (P2 Q2) = = (Px Qx) (D-^)

D . 1 DENSITY OF DRY AIR, STEAM, AND MOIST AIR

With dry air, the density p can be calculated from an equation of state:

p = P/(Z R T)

where P is the absolute pressure and T, the absolute temperature.

The quantity R is known as the "gas constant" with its value different for each

gas and also dependent on the units used in expressing p, P and T. The quantity

Z is known as the "compressibility factor." It corrects for small variations

in the behavior of real gases compared to ideal gases, and its value depends

on the gas, and its temperature and pressure. The value of Z is dimensionless

,

and it is not dependent upon the units of pressure and temperature. A graph

giving the Compressibility Factor Z for dry air as a function of P and T is

given in appendix B, figure B-1.

D-1
For dry air, with P in units pounds force per square incVi absolute, psia, and

T, the absolute temperature in degrees Rankine °R, the relation for density is

p = 2.6990 P/(Z T) lb/ft3, (D-5)

where 2.6990 equals the molecular weight of dry air (28.964 Ib/lb-mole) divided

by the Universal Gas Constant R, (10.7315) ( psia* ft^) /( lb-mole °R),

and lb has units pounds mass.

With steam, the properties including specific volume, ft-^/lb, are given in

tabular form as a function of temperature and pressure in reference 6. Thus:

o p^ = l/(specific volume) lb/ft , (D-6)

where p^ is the density of steam or water vapor.

For moist air, a relation for the density p^ of the mixture is:

2.6990 (P - P„) o Pm = + Pv Ib/ft^ (D-7)

(Z T)

where P - P,^ = partial pressure of the air, and

Py = partial pressure of the water vapor

The relation for Pj^ is valid at low values of Py where the behavior of steam

.approaches ideal gas behavior. The value of P^ depends on the relative humidity,

RH, expressed in percent and Pg, the saturation pressure for steam at

temperature T, as follows:

Pv = (RH/lOO) Pg - (D-8)

Example calculations E.l, E.2, and E.3 in appendix E deal with relations between

mass and volume rate of flow. Example E.4 gives results of calculations for

Pj^ for moist air at sevtral pressures, temperatures and moisture contents.

It is noted for both air and steam flow calculations, when the actual volume

flowrate at a definite temperature and pressure is known, the volume flowrate

may be determined at some other location having a definite temperature and

pressure with computation of the mass flowrate unnecessary, i.e.,

Qx = (Pl Ql)/Px- (D-9)

With air flow, substituting equation (D-5) gives:

(P. T^) , , Qx =

, , Ql , (D-10)

(P^ Zl Ti)

since R for any gas is constant. Thus, this relation is convenient to use when

mass flowrate is neither known nor required, and volume flowrate at a definite

temperature and pressure is known.

D-2
D.2 "STANDARD CONDITIONS," ITS MEANING AND USE

As discussed above and shown in example E.3, the actual volumetric flowrate

ACFM is not a convenient nor direct measure of the quantity of matter because

the numerical value varies with both temperature and pressure. The absolute

pressure and temperature of the gas at the particular location must also be

stated if the actual volume at that location is to be meaningful in terms of

the quantity of matter.

It has also been noted that mass flow is a direct measure of the quantity of

matter and its value is independent of the pressure and temperature at the

location under consideration.

One other quantity is used, especially in commerical transactions, as a direct

indication of the quantity of matter involved in gaseous flow. This is volume

flow converted to selected standard conditions of absolute pressure Pg and

absolute temperature Tg . Values of volume flow converted to these standard

conditions will be referred to as standard cubic feet per minute, SCFM.

The selected standard conditions of pressure and temperature are not necessaril

the same for all industries or for all laboratories. Any organization may

select any value of Pg and Tg for its standard conditions; however, to prevent

confusion, once values for Pg and Tg are selected, they should be used without

exception. When two organizations select different standard conditions of pres sure and temperature, their values of SCFM will not concur because their standard cubic feet will refer to different quantities of matter. Therefore, the

value of SCFM has no definite, accurate meaning unless the values of Pg and

Tg associated with the value of SCFM are definitely known.

From the preceding, it should be understood that the "Standard" in SCFM is not

standard at all but varies among different industries and laboratories. Hence,

this term SCFM has a tendency to confuse as well as help.

D-3

APPENDIX E. ILLUSTRATIVE EXAMPLES

Example E.l Kass and Volume Rates of Flow, Superheated Steam . Steam flows at a mass rate of flow of 2000 Ib/hr in a pipe. It is desired to calculate the

actual volume rate of flow, cubic feet per minute (ACFM) at two stations, 1 and

2. Pressures are measured with bourdon tube gauges, with cases vented to the

atmosphere. Following are the measurements made:

Measurement Instrument Reading

Barometric pressure Aneroid barometer, inches 29.83 in. Hg at 32 °F

of mercury at 32 °F

Pressure pi , Bourdon tube gauge 35.0 psig

Temperature ti Resistance thermometer, 300 °F

output converted to °F

Pressure P2 Bourdon tube gauge 15.0 psig

Temperature t2 Resistance thermometer 260 °F

Compute barometric pressure P^, in psia. No corrections for temperature or local acceleration due to gravity are applied to the aneroid barometer reading.

Refer to table C-1 for the conversion factor for Pt,.

Pb = (0.49116) (inches of mercury at 32 ° F)

Pb = (0.49116) (29.83) = 14.65 psia

Computation for station 1:

Pi = (PI + Pb) = (35.0 + 14 .65) = 49 .65 psia (C-b)

To determine p ]^ , use data from steam tables, reference 6, table 3.

Interpolation of data for 300 °F gives:

P, p sia V, ft3/lb

48 9.147

49.65 8.835

50 8.769

The specific volume at station 1 is:

.3

v-L = 3.835 ft-^/lb = 1/p^

Pj^ = 1/8.835 = 0.11319 Ib/ft^

E-1
The volume flowrate is:

Ql = M/Pi = (2000)/(60)(0. 11319) = 294.5 ACFM, or (D-2)

Ql = (M vi) = (2000)(8.835)/(60) = 294.5 ACFM

Computation for station 2;

P2 = (P2 + Pb) = (15.0 + 14.65) = 29.65 psia

Interpolation at t2 = 260 °F:

P, psia V

ft3/lb

29.00 14.447

29.65 14.127

30.00 13.954

V2 = 14.127 ft^/lb

Q2 = (M V2) = (2000)( 14.127)7(60) = 470.9 ACFM

The actual volume rate of flow at station 1 is 295.4 ft-^/minute and at station

2, it is 470.9 ft-^/minute. It should be noted that while the mass flowrate is

constant, the volume flowrate is not constant, but varies with the density or specific volume.

Example E.2 Mass and Volume Rates of Flow, Wet Steam . This example deals with

wet steam, that is, steam in the saturation state which contains both liquid

and vapor. While it is outside the scope of this document, a basic computation

for mass and volume flowrates follows. Consider steam flowing at a flowrate

of 100 ACFM, at a temperature of 288 °F, and a pressure of 55.8 psig. It is

desired to compute the mass flowrate in Ib/hr.

Referring to reference 6, it is noted that the temperature and pressure

correspond to saturation conditions. Therefore, no determination of density

is possible with the information given. In addition, the steam quality "x"

(ratio of the mass of vapor to the mass of mixture) is needed.

Assume the quality x is 97.0 percent.

For the saturated state, the specific volume is

v = (1 - x)(vf) + (x)(vg) (E2-1)

where x is expressed as a decimal, is the specific volume of saturated liquid,

and Vg is the specific volume of the saturated vapor.

E-2
Using equation E2-1 and data In reference 6, table I, at temperature 288 ^F,

the specific volume is

V = (0.03) (0.0174) + (0.97)(7 .6807) , or

V = 7 .451 ft3/lb

The mean flow rate, M, is:

M = (p Q) = Q/v

= (100)(60)/(7.451) , or

M = 805.3 Ib/lir

Example E.3 Mass and Volume Rates of Flow, D ry Air . Dry air flows through a system as shown in figure 5. Valve VI is closed. The' mass flowrate is known

to be 18.00 pounds per minute. It is desired to determine the flowrate entering Qi, and leaving, Q4 in actual cubic feet per minute, A.CFM. Local acceleration due to gravity is 32.150 ft/s^. Pressures and temperatures have been

measured as follows:

Measurement

Barometric pressure

Pressure

Temperature t^

Pressure h4

Temperature t^

Instrument

Aneroid barometer, in. Hg

at 32°

F

Bourdon tube gauge, case vented to atmosphere, psi^

Mercury thermometer, °F

Mercury manometer, low

pressure leg vented to

atmosphere, in. Hg

Mercury thermometer, °C

Reading

29.836 in. Hg at 32 °

F

105.0 psig

73.7 °F

55 .47 in. Hg at 81 .0 °F

23.5 °C

Compute the barometric pressure P^ in psia. Note that corrections for

instrument temperature and local acceleration due to gravity are not applied

to the aneroid barometer reading.

Pb = 0.49116 (inches of mercury at 32 ° F)

= (0.49116)(29.836) , or

P^ = 14.65 psia

Computation for location 1

(Table C. 1

)

E-3
Pi = (pi + Pb) = (105.0 + 14.65) = 119.65 psia

Ti = (ti + 459.67) = (73.7 + 459.67) = 533.37 °R

Zi = 0.9973 (for air at 120 psia and 533 °R)

p, = 2.6990 P,/(Z = (2.699Q)(119.65) or

1 111 (0.9973)(533.37)

(C-6)

(C-3)

(Figure B.l)

(D-5)

Pi 0.6071 Ib/ft^

M/p-]^ = (Ib/min )/(lb/ft3)

(18.00)7(0.6071) = 29.65 ft^/min (at 119.65 psia and 533.4 °R)

Computation for location 4:

Determine the mercury manometer correction factors Fg- , F^^i and F^2

F^ = gL/32.1740 = 32.150/32.1740 = 0.9993

0.48873 psi/in. Hg (at 81.0 ° F)

(D-2)

g

Fml

Fm2

P4

P4

P4

t4

T4

Z4

P4

P4

Q4

Q4

0.9998 (at = 42 psia)

(inches of mercury at 81 °F) (F F F ) ml m2 a

(C-7)

(Figure C.2)

(Figure C.4)

(C-9)

(55. 47) (0.48873) (.9998) (0.999 3) or

27.09 psig

P4 + Pb = 27.09 + 14.65 = 41.74 psia

(°C)(9/5) + 32 = 23.5(9/5) + 32 = 74.3 °F

t4 + 459.67 = 74.3 + 459.67 = 533.97 °R

0.9991 (air at 42 psia and 534 ° R)

2.6990 P4/(Z4T4) = 2 .6990( 4 1 .74 ) /[ (0 . 9991 ) (533 . 97 )

0.2112 Ib/ft^

M/P4 or

18 .000/0.2112 = 85.23 ft-^'/min (at 41.74 psia and 534.0 °R)

(C-6)

(C-1)

(C-3)

(Figure B.l)

(D-5)

Thus, is 29.65 ftVmin at 119.65 psia and 533.4 °R and Q^^ is 85 .23 ft^/min at

41.75 psia and 534.0 ° R. It should be noted that the quantity of air flow is

constant at 18.00 Ib/min. However, the volume rate of flow is not constant

throughout the system, but rather varies with temperature and pressure. Thus

E-4
whenever the volumetric rate of flow Q is used as a measure of quantity of

matter, is is necessary that the absolute pressure and temperature associated

with this measurement be stated along with the value of Q.

Example E.4 Density of Moist Air . Calculate the density, Pjjj for moist air at

pressure P = 14.7, 50 and 100 psia, temperature t = 80 °F and 170 °F, and

relative humidity/100 = 0.50 and 1.0 (saturated air). Compare with dry air

(RH = 0).

Calculation for P = 14.7 psia, t = 170 °F and RH/100 = 0.5:

Density of the moist air:

2.6990 (P - P„)

P,ii = ^ ^ + Pv e^-^) m (2 T) V

i T = 170.0 + 459.67 = 629 .7 °R (C-3)

At t = 170 °F, the saturation pressure of steam is:

Pg = 5.9926 psia (Reference 6)

The partial pressure of the water vapor is

Pv = (RH/100)(Pg) = (0.5)(5.9926) = 2.9963 psia (D-8)

The partial pressure of the air is

P - Py = 14.7 - 2.9963 = 11.7 psia

Compressibility Z (air) at T = 629.7 °R and pressure 11.7 psia

Z = 1 .000 ( Figure B. 1)

When RH/ 100 < 1.000, the water vapor is superheated, and its properties are found in the tables for superheated steam. At t = 170 °F and pressure P^ = 2.9963 psia, the specific volume v is found through interpolation:

P, psia v, ft^/lb

2.9 128.81 (Reference 6,

table 3)

2.9963 124.66

3.0 124.50

The density p„ is:

= 1/v = 1/124.66 - 0.00802 lb/ft 3

Substituting the data above into equation (D-7)

E-5
p = (A-A990)11JL-Z0). + 0.00802, or m (1.000)(629.7)

in = 0.05817 Ib/ft^

For dry air:

p = (2.6990)(P) = (2.6990)U4.7) . 0.06301 lb/ft3

(Z T) (1 .000)(&29 .7)

(D-5)

p,^/p = 0.05817/0.06301 = 0.923

The following table suramarizes the remaining calculations

Table E.l. Moist Air Data

P RH/100 Pv

psia psia

Pv

, Ib/ft^ Ib/ft^

P lb/ft 3

Pffl/P

t = 80 °F

100 0.0

0.5

1 .0

0.0

.2534

.5068

0.998

.998

.998

0.0

.00079

.00158

0.5011

.5006

.5001

0.5011 1 .000

0.999

0.998

50 0.0

0.5

1.0

0.0

.2534

.5068

.999

.999

.999

0.0

.00079

.00158

.2503

.2498

.2493

.2503 1.000

0.998

0.996

14.7 0.0

0.5

1 .0

0.0

.2534

.5068

.9997

.9997

.9997

0.0

.00079

.00158

.07354

.07306

.07256

.07354 1 .000

0.993

0.987

t = 170 °F

100 0.0

0.5

1.0

0.0

2.9963

5.9926

1.0002

1 .0002

1.0002

0.0

.00802

.01611

0.4286

.4237

.4190

0.4286 1.000

0.989

0.978

50 0.0

0.5

1 .0

0.0

2.9963

5.9926

1 .0001

1.0001

1 .0001

0.0

.00802

.01611

.2143

.2095

.2047

.2143 1.000

0.978

0.955

14.7 0.0

0.5

1 .0

0.0

2.9963

5.9926

1.0000

1 .0000

1.0000

0.0

.00802

0.1611

0.06301

.05818

.05343

0.06301 1.000

0.923

0.848

E-6
The previous table may be helpful In deciding when a correction for the density

of moist air is needed. The data show, for example, with ambient temperature

(t = 80 ° F) and ambient pressure and higher (P = 14.7 to 100 psia) , that the

correction would never exceed about 1 percent, and may often be ignored. On

the other hand, when temperatures are higher, the partial pressure of the water

vapor becomes more significant and the density may be quite different from

that of dry air. For example, at 50 psia with saturated air, this difference

amounts to about 4.5 percent (p^/p = 0.955).

Example E.5 Direct Calibration of an Orifice Meter on Site with a Gravimetric

Calibrator . An orifice meter with flange taps and diameter d = 1.200 in. is

mounted in a 2-inch pipe and monitors the flow of water. It is desired to

calibrate the meter over a flow range of 10,000 to 20,000 Ib/hr using a direct

calibration method with static weigh operation as shown in figure 8. Five

repeat runs will be taken at four flowrates in the above range. The meter AP

will be measured by means of a vertical water manometer. Local acceleration

due to gravity is 32.145 ft/s^. Following are the measurements made:

Measurement

Barometric pressure

Inlet water

pressure

Inlet water

temperature

Manometer

temperature

Meter pressure

differential, h

Weigh time

Mass of water

Instrument

Aneroid barometer, in. Hg

at 32 °F

Bourdon tube gauge, case vented to atmosphere, psig

Mercury thermometer, °F

Mercury thermometer, °F

Water manometer, inverted,

air in the low pressure

leg at 59.0 psig; inches

of water at manometer

temperature

Electronic timer, 5 digits,

start/stop actuated thru

switch connected to

diverter valve

Beam type scale, 1000 lb

capacity

Reading

30.41 in. Hg at 32 °F

59.0 psig

See data below

See data

See data

See data

See data

The following data were collected during five repeat runs at four flowrates.

Flowrate was adjusted as necessary through the flow control valve to maintain

h within + 0.10 inch of water. The manometer temperature was measured with a thermometer attached, sensing ambient air. The indicated flowrate is net

mass/ time, designated M'

.
Table R.2. Sample Data for Calibration of an Orifice Meter

Temperature

Mass Flow

Man. Water h Time Tare Gross Net M'

° p ° p in.H20 s lb

. .

lb—lb —Ib/s

, .

80.0 82.0 64.00 —

77.799 162.3 615.4 453.1 5.824

+ .10 80.843 139.3 609.0 469.7 5.810

72 .008 140.9 562.0 421.1 5 .848

80.3 82.3 74.238 191 .1 624.5 433 .4 5 .838

70 .805 175.6 590 .8 415.2 5 .864

5.837 Avg

80.3 82.7 46.00 77.225 179.3 561 .1- 381.8 4.944

+ .10 67.376 155.6 490.8 335 .2 4.975

70 .264 166 .8 513.2 346.4 4 .930

71 .919 156.5 512.5 356.0 4 .950

79.8 83.0 72 .546 138.2 498.1 359 .9 4 .961

4.952 Avg

30.00 84.837 173.0 514.3 341 .3 4.023

79.7 83.3 + .10 97.446 185.1 574.2 389.1 3.993

95.675 188.5 571 .2 382.7 4 .000

75.927 155.2 460 .2 305 .0 4 .017

80.0 83.5 83 .579 206 .8 541 .7 334 .9 4 .007

4.008 Avg

16.00 103.55 188.6 491 .7 303.1 2.927

80.0 83.6 + .10 1 19 .06 183 .6 534 .6 351 .0 2 .948

107.88 162.4 478.7 316.3 2.932

129 .62 in/ o 194 .2 573 .6 379 .4 2.927

80.2 83.6 104.29 199.0 505.2 306.2 2.936

80.0 83.0 Avg 2.934 Avg

Calibration results are to be expressed in terms of the discharge coefficient

C, as a function of the pipe Reynolds Number Rj^ , where C will be determined for

each flowrate from equation (2-1):

M= 358.93 (CY d^ FJ [ ( p h„)/(l - 3^)]^/^ Ib/hr

Fluid expansion factor Y = 1.000 since a liquid is flowing.

Orifice thermal expansion F^ = 1.000 since the average water

temperature is 83 ° F.

(2-1)

(Figure B.2)

For 2-inch pipe, D = 2.067 inches (schedule 40). Thus 3 = d/D = 1.200/2.067 = 0.5806.

E-8
At t = 83.0 °F and p = 59.0 psig, the water is only slightly compressed and

density p may be assumed equal to that at saturation temperature with

negligible error (0.02 percent). Therefore, p = 62.191 Ib/ft^. (Table B.l)

Since the water was weighed in air, the indicated mass flowrate M' needs a correction for the air buoyancy. A nominal value for air density will suffice

for this correction. Let p_^-„ = 0.075 lb/ft .

Buoyancy Correction = 1 + (p . /p ) = 1 + (0.075/62.191) = 1.0012, and

3.XTC W

M = 1 .0012(3600)(M')

where M' has units Ib/s.

(E5-1)

Before calculating C, the meter pressure differential h (h is in in. of H2O at

the manometer temperature) needs correction to account for the local acceleration due to gravity (Fg), the air in the low pressure leg ( F^^^ ) , and the water

manometer temperature of 80 °F ( F^]^ ) . These corrections are explained in

appendix C. Using table C. 1 and equation (C-8):

h^ = ( 27 .729) (h) [(F^i)(F„2)(Fg)i ,

At t = 80 °F

Fwl = 0.036005 psi/inch of water.

At p = 59.0 psig

P = 59.0 + (0.49116)(30.41) = 73.94 psia, and

Fw2 = 0.9940

with g^ = 32.145 ft/s^

Fg = gL/32.l740 = 0.9991.

Thus, at a water temperature of 68 °F:

h„ = 27.729 (0.036005)(0.994)(0.9991)(h) , or

h^ = 0.9915 (h)

(Table C. 1) , ( C-8)

(Figure C. 1

)

(Table C. 1 ) , (C-6)

(Figure C.3)

(C-7)

(C-8)

(E5-2)

Substituting equations (E5-1) and (E5-2) into equation (2-1), and solving for

C:

_ /'(1.0012)(M')(3600)\ / (1 - |3^) V^^^

(358 .93)(d2) / \(p)(0-9915)(h)7

Substituting above data for p, 3, and d, this becomes:

C - 0.83608(M')/(h)l/2 (E5-3)

E-9
where M' has units lb/ s and h has units inches of water. Next, the quantity

pipe Reynolds Number Rq needs calculation.

= (D V p)

where D = pipe inside diameter

V = average velocity

p = density of the water

y = dynamic viscosity

Since H = (p A V) , where cross sectional area A = tt D / 4 , R^ can be written,

after substituting for V:

R = D(M/p A)p ^ (D M) or

° ^ (U TT d2)/4

Rd = 4(M)/(,J D)

Rq is dimensionless , thus (E5-4) becomes

(E5-4)

R_ = 4 M or

D (3600 \i) ir (D/12)

Rq = 0.004244 (M)/(ii D) (E5-5)

where M has units of Ib/hr, m has units of lb/(ffs), and D has units of inches,

At a water temperature of S3 °F, y = 0.56 x 10"^ lb/(ft-s). (Figure B-3)

From the data collected and equations (E5-3) and (E5-5), the following final

results are tabulated:

h

in. H?0

at 80""°F

M'

W_s_

M

Ib/hr

C M/(h)^/2

lb/hr(in.)l/2

64.00 5.837 21038 77130 0.6100 2630

46.00 4.952 17849 65450 .6104 2632

30.00 4.008 14446 52960 .6118 2637

16.00 2.934 10575 38770 .6132 2644

Thus, this orifice meter has been "calibrated". Its performance has been

demonstrated and is known through the discharge coefficient C as determined

from direct physical measurements. With such an on-site calibration using a static weigh procedure, quite accurate results for C are possible, comparable

to those produced routinely by primary calibration laboratories, about 0.2

percent uncertainty.

,E-10
Wlien tliis orifice meter is in service, the above data may be used in several

ways. With the discharge coefficient being kaowi\ as a function of Reynolds

number, the orifice could be used In different fluids within the above range of

R^j. Siace in this case, tne discharge coefficient G varied only through a small

range of about 0.5 percent (frora 0.6100 to 0.6132), an average value of C = 0.6114 could be utilized and the flowrate M determined directly froa equation

(2-1). If higher accuracy is desired, an iterative procedure is needed since

is never known initially: Using C = 0.61, one would calculate d from equation (2-1), then calculate Rq froia equcition (h;5-4), then determiae C exactly

from the data artove (by plotting C vs. Ry and interpolating at the measured

value of Rl)) ; and finally calculate •! from equation (2-1). When the meter

is calibrated with water at or near 83 °F, one could plot the quantity

'd/{i\)-^'^ as a function of h and calculate il directly. In this latter case, some variation in water temperature in the pipe and in the manoiaeter can be

tolerated with a small sacrifice in accuracy. For example, when temperature t varies within a range of +10 °F and pressure p varies within +10 psi, the

"worst case" effect on M would be about +0.2 percent, explained as follows:

from figure C.l, F^j^ varies about -0.17 percent/ 10 °F at 80 °F as does the density p of water from table ii . 1 . From figure C.3, F^2 varies -0.08 percent/ 10

psi. The worse case occurs whea t and p both increase (or both decrease)

together. In equation (2-1), accounting for effects of t on p, and t and p on

h^, the absolute value of the error becomes (1/2)(0.17 + 0.17 + 0.08) = 0.2

percent for a change of +10 °F and +10 psi (or -10 °F and -10 psi). The "1/2"

factor comes frora the exponential 1/2 in equation (2-1) and differential calculus. The change in C (through temperature effects on p and p in Rq) is negligible. Thus, under limited conditions, accurate measurements of M can be made

directly froiQ h.

Example E.6. Calibration of an Orifice Meter on Site Using The Transfer Ileter

Method . A. stainless steel orifice meter with corner pressure taps and d = 3.750 inches is mounted in a 6-inch pipe flowing chilled water. A differential

pressure transducer system calibrated to read out in incnes of water at 68 °F

measures the orifice meter AP. It is desired to calibrate the orifice meter

using a transfer reference meter system located dov/nstream, as shown in figure

5. The transfer meter is a stainless steel nozzle venturi with a throat diameter of d = 4.030 inches and a coefficient of discharge C = 0.9512 as determined by calibration on water at 65 °F at a primary calibration facility. This

calibration was on water at b5 °F covering a range 1.5 x 10^ < R^^ < 1 x 10^. A

mercury manometer is used to measure the nozzle venturi AP. Local acceleration

due to gravity is 32.172 ft/s-.

The following represent average values of data taken from 5 repeat observations

at a single flowrate:

E-U
Measurement

Chilled water

temperature

Water pressure

Working meter (orifice)

pressure differential h^^

Transfer meter (nozzle

venturl) , pressure

differential, h

Manom.eter temperature

Instrument

Dial type thermometer, °F

Bourdon tube gauge, psig

Pressure transducer system

inches of v«7ater at 68° F

Mercury manometer, inches

of mercury, water in high

pressure leg

Mercury thermometer, °F

Reading

42.0 °F

85.3 psig

320.32 in. H7O

at 68 "F

7.26 in. Hg

at 78.0 °F

78.0 °F

Calculations for the nozzle venturi meter:

C = 0.9 512

d = 4.030 inches

D = 6.065 inches (6-inch pipe, schedule 40)

3 = d/D = 0.6645

P = 62.443 lb/ft3 (at 42.0 °F and 100 psia)

Y = 1.000 (liquid)

Fa = 0.9995 at 42 °F (300 Series Stainless Steel)

(Table B.l)

(Figure B.2)

Obtain h„, inches of water at 68° F, for the nozzle meter as follows:

h^ = 27 .729 (psi)

h„ = 27.729 (inches of Hg at 78 ° F) (F F F ) ml m3 g

Full 0.48892 psi/in. Hg at 78 °F

F^3 = 0.9263

Fg - gL/32.1740 = 32.172/32.1740 = 0.99994 (neglect)

h„ = (27.729)(7.26)(0.48892)(0.9263) , or

(Table C.l)

(C-10)

(Figure C.2)

(Appendix C)

(C-7)

h„ = 91.17 inches of water at 68 °F

E-12
Next, calculate the flowrate M;

M = 358.93 (C Y d2 F^) [p h^/(l - 3^)] ^''^ (2-1)

/(62.443)(91. 17) \

1/2

= 358. 93(0. 9512)(1 .000)(4. 030)2(0. 9995) ) , or

\ 1 - (0.6645)^ /

M = 466,100 Ib/hr

The pipe Reynolds Number is also needed.

Rd = 0.004244 (M)/(m D) (E5-5)

y = 1.00 X 10~3 lb/(ffs) at 42 °F (Figure B.3)

Rp = 0.004244(466,100)7(1.00 x 10"^)(6.065) , or

Rj) = 326,000 .

The calculation for the transfer meter is complete. The reference flowrate M

is 466,100 Ib/hr. The pipe Reynolds Number is 326,000 which lies within the

range of calibration for the nozzle venturi meter.

Calculation for the orifice meter:

Y = 1.000

d = 3.7 50 inches

3 = d/D = 3.750/6.065 = 0.6183

Fa = 0.9995 at 42 ° F (300 Series SS) (Figure B.2)

p = 62.443 lb/ft3

M = 466,100 Ib/hr

h„ = 320.32 in. of water at 68 °

F

Solving for the discharge coefficient C in equation (2-1)

1/2

C = r M 1 fd - 3^)1

[(358.93r)(Y)(d2)(F^)J [(p h^)

J

46 6,100 1 r 1 - (0.6183)^

"

I

( 358. 93 )( 1.000) (3. 750) 2(0. 9995

)J [(62 .443) (320 .32)J

1/2

, or

C = 0.6036

, E-13
Therefore, the coefficient of discharge C for the orifice (working) meter is

0.6036 at Rd = 326,000.

In particular, it may be noted:

1. The calibration is usually conducted at several flowrates which

correspond to building s e r \7 i c e conditions. Thus, a set of values of C vs. Rj) , would be obtained. With an installation conforming to good

metering practice, the data for C should be in good agreement with the

discharge coefficient data given for corner taps in appendix A.

2. Once a particular meter has been calibrated, i.e., discharge coefficient

C established as a function of R]?), it may be used in different fluids

within its calibrated range of Rp . Since C changes very slowly with

Rp when R^^ > lo'^ , a single value can be used for C with small error,

usually not exceeding 0.2 to 0.3 percent, when flowing a given fluid over a flow range not exceeding, say, 2:1. When the flow range is

larger, or when maximum accuracy is needed, C should be plotted as function of Rq and an iteration approach used to determine C. (See

discussion at the end of example E.5.)

3. The coefficient of discharge C for the transfer meter system applies

only to a designated range of Rq , as determined from calibration at an independent facility. Thus, use of the transfer meter outside its

calibrated range as expressed in terms of R^ should be avoided.

Example E.7 On-Site Calibration of a Positive Displacement Meter Using The

Transfer Meter Method . A positive displacement meter monitors the flow of

water at 150 °F and 100 psig. It is to be calibrated on site at nominal 20

GPM using an orifice meter as the transfer reference installed downstream of

the PD meter as shown in figure 5. The orifice meter has been calibrated with

water with results given in previous example E.5 and plotted here in figure E.l.

Salient features of the PD meter and associated electronics equipment are:

Size: 2-inch

Type: notary piston

Output: 1 pulse per 0.15 gallon, nominal

Rating: 200 psig and 300 °F

Installation: The PD meter is mounted in a horizontal 2-inch pipe,

insulated, with 75 diameters of straight pipe upstream,

5D downstream, no flow straightener

The orifice meter has the following features:

Size: Diameter d = 1.200 inches mounted in a 2-inch pipe

(D = 2.067 inches), 3 = 0.5806

E-14
E-15
Calibration: On water at 83 °F, using a gravimetric calibrator, with AP

measured by a vertical water manometer. (See example E.5).

Installation: The orifice metering section is installed in a horizontal

position downstream of the PD meter as shown in figure 5,

with a flow straightener and with the metering section insulated. Temperature and pressure taps are installed at the

exit. The differential pressure taps, including the reser- voirs are insulated. The sensing lines to the manometer are

bare, and installed adjacent to each other. The AP is

measured by the vertical water manometer.

The time for a preselected number of PD pulses is measured. From the flowrate

as measured by the orifice meter, the calibration constant K for the PD meter,

gallons per pulse, can be determined for the flowrate of interest.

The following are the measurements made where "Reading" data are the average

of 5 repeat runs. The local acceleration due to gravity is 32.10 ft/s^.

Measurement

Exit water pressure

Exit water temperature

Manometer temperature

Orifice meter AP

PD meter, test time

Instrument

Bourdon tube gauge, case vented to atmosphere, psig

Dial type thermometer with

bulb and capillary, °F

Mercury thermometer, °F

Water manometer, inverted,

air in the low pressure leg

at 102 psig, inches of water

Electronic preset counter/

timer, timer start/stop

activated to time period for

150 meter pulses, preset

Reading

102.0 psig

152.0 °F

72.0 °F

17 .20 in. at 72 ° F

63.150 seconds

The flowrate for the orifice is calculated from:

Q = 5.982 (C Y d2 F^)[hyp(l - 3^)1^/2 (2-2)

Quantities first needing evaluation are C, F^, h^^, and p.

The (flowing) fluid properties p and v are as follows: At 152 °F and 102 psig,

the water is a compressed liquid. While the density is nearly that of saturated

liquid, interpolation oE table B.l data gives p = 61.172 Ib/ft^. At 152 °F, the

kinematic viscosity of water v is 0.47 x 10"^ ft'^/s, from figure B.3. Thus, at

15 2

° F:

E-16
p = 61.172 lb/ft3

V = 0.47 X 10-5 ft2/s

The coefficient of discharge C is needed at pipe Reynolds Number Rq for water

at 152 ° F. Estimate Rq from the PD meter using the nominal output of 0.15

gallon/ pulse as follows:

( 150)(0.15)

[

pulses'] fg allon"] f

s J [p^lse J I

f t- (63.150)(7.4805)

Q = 0.047 ft^/s

Rd = (D V p)/lJ = (D V)/v = 4 (Q)/(tt D v)

since v = p/p , and V = O/A = 4 (Q)/(tt d2). Thus

(4)(0.047)

gallon

J

(E7-1)

TT (2/12)(0.47 X 10

Rq = 75,000 estimated

From figure E.l, C = 0.6100 at R^ = 76,000

Since the fluid is incompressible, Y = 1.000.

With the orifice plate at the fluid temperature, 152 °F, a small correction for

the expansion of the plate caa be made through F^. The orifice plate material

is 300 Series SS (stainless steel). From figure B.2:

Fa = 1.0015

The orifice AP manometer reading in inches of water needs correction to 68 ° F. The manometer temperature is 72 ° F.

"w

K =

p =

P68 =

Fw2 =

(inches of wate r ) ( p/ P53 ) (F^^ ^g)

( 17 .20) (62. 2902 762. 3205) (0.9903 )( 0.9977 ) , or

16.986 inches of water, where

62.2902 lb/ft3 (at 72 °F)

62.3205 Ib/ft^ (at 68 ° F)

0.9903 (at 102 + 14.7 = 117 psia)

2

(C-11)

and with g^ = 32.10 ft/

¥a = gL/32.1740 = 0.9977

(Table B.l)

(Table B.l)

(Figure C.3)

(C-7)

E-17
Inserting the above data into equation (2-2), the actual volumetric flowrate

through the orifice is:

Q = 5. 982(0. 6100)( 1 .000)( 1. 200)2(16. 986)l/2/[61. 172( 1 - (0.5806)^) ] 1/2

= 2.9 41 ft^/min, or

Q = 2.941(7 .4805) = 22.00 GPM

Next, recalculate and check C through Rq :

= = ^(2.941)760 . 80,000 (E7-1)

(it D v) tt (2/12)(0.47 x 10 ^)

From figure K.l, the corresponding value of C for the orifice is 0.609 and,

through equation (2-2), the flowrate Q can be adjusted:

Q= 22.00(0.609/0.6100) = 21 . 96 GPM

This completes the flow calculation for the orifice. Now, compute the

calibration factor for the PD meter. Express K in units gallon/pulse.

K = 63 . 15(21 . 96) ^

("seconds | ["gallons I fminutes 1 150(60) |_ pulse J (_minute J (_secondsJ

K = 0.1540 gallon/pulse

"Thus, the calibration factor for this meter is K = 0.1540 gallon/pulse when

water is flowing at or near 22 GPM, 152 °F and 100 pslg. At other flowrates,

temperatures, and for large changes in pressure, K could vary. With these

conditions of 150 °F and 100 psig, and with this orifice meter and manometer,

thus PD meter could be calibrated at flowrates down to about 10 GPM, as limited

by the orifice calibration for C in the range 40,000 < Rj^ < 80,000. However,

in this case h^ 4.00 inches of water; accurate measurement becomes increasingly

difficult at such a low AP . To calibrate the PD meter at flowrates greater than

20 GPM, the orifice would need additional calibration.

Example E.8 On-S ite Calibration of a Vortex Shedding Meter Using the Transfer

Meter Method . A vortex shedding meter monitors the flow of steam at 360 °F and

45 psig. It is to be calibrated on site using a nozzle venturi meter as the

transfer reference meter. The venturi meter is installed downstream of the

vortex meter as shown in figure 5. The nozzle venturi meter has been previously

calibrated using water as noted below. Salient features of the vortex meter and

associated electronics are:

Size: 6-inch

Output: 8 pulses/ft3, nominal

E-18
Rating: 250 psig and 600 °F

Installation: The vortex meter is installed in a vertical 6-Lnch

insulated pipe within a metering section as shown in

figure 7 including a perforated plate flow s traightener

.

(See figure 13.)

The nozzle venturi meter has the follov<7ing features:

Size: Throat diameter d - 2.426 inches. Meter mounted in a 6-inch pipe, D = 6.065 inches, 3 = 0.400.

Calibration: On water at 60 °F, C = 0.9675 for range 3 x 10"^ to

1 X 10^

Installation: Mounted in a metering section with a flow stralghtener

.

Installed in a vertical pipe, downstream of the vortex

meter as shown in figure 5, with the metering section

insulated. A temperature tap is installed at the metering

section inlet and the pressure taps are located at the ven- turi inlet and throat (P2)' The sensing lines with

drain and vent lines connect to a AP transducer system

calibrated in inches of water at 68 ° F.

MaterialBronze, 6 percent tin.

Pulses are counted from the vortex meter with an electronic counter for a preset

gate time to accumulate at least, say, 5000 pulses. When the meter frequency

is low resulting in excessive run time, a preset counter measuring a time period

for a preset number of pulses may be used instead.

From the flowrate measured by the nozzle venturi meter, the calibration constant

K for the vortex meter, ft^/pulses, is calculated for the flowrate of interest.

Following are the measurements made where "reading" data are the averages of 5 repeat runs.

E-19
tleasurement Instrument Reading

Barometric pressure

Inlet nozzle venturi

pressure, p^

Inlet nozzle venturi

temperature, ti

Nozzle venturi AP, hw

Vortex meter pulse

count

Aneroid barometer in.

Hg at 32 °F

Bourdon tube gauge,

psig

Thermocouple, °F

Differential pressure

transducer system, in.

water at 68 °F

Electronic preset

counter/ tiuier , pulses

tor a 45-second time

interval, average of

five runs

30.41 in. Hg at 32 °F

44.6 psig

360 °F

123.83 in. water at

68 °F

5478

The flowrate for the nozzle venturi meter is calculated from;

Q = 5.982 (C Y F ) lti^/p(l - |3^)]^/2 f^'^/^i^ (.2-2)

Quantities needing evaluation are: Y, F^ and p. First, evaluate density p as follows. The inlet pressure and temperature at the nozzle venturi inlet are:

?l = (pi + P^) = 44.6 + (30 . 41)(0. 49116) = 59 .54 psia (Table C.l), (C-6)

ti = 360 °F

Using steam tables, reference 6, table 3, and from interpolation, the specific

volume v_L at 360 °F and 59.54 psia is 7 .989 ft^/lb.

Pj_ = l/vj_ = 1/7 .989 = 0.1252 Ib/ft^

To evaluate the expansion factor Y, first find P2/Fx'

AP = (Pj^ - P2) = (3.6063 X 10"^) (in. water at 68 °F) or (Table C.l)

AP = (3.6063 X 10~2)( 123 .83) = 4.466 psia

^2 " ^^"1 ~ " 59 .54 - 4 .47 = 55 .07 psia, and

P2/PL = 55 .07/59 .54 = 0.925 = r

The expansion factor Y is found from table A. 16 or figure A. 2. With r = 0.925,

the specific heat ratio y = 1«3 for steam, and 3 = 0.400, then with interpolation

Y = 0.9544 (Table A. 16)

E-20
With the nozzle venturi at a fluid temperature of 360 °F and constructed of

bronze, 6 percent tin:

Fa = 1 .0056 (Figure B.2)

The flowrate Q can now be calculated. Reynolds number will be calculated

later and compared to the Rq range for C. In equation (2-2):

Q

^ 5 . 982(0. 9675) (0.9544) (2. 426)^( 1. 0056) (123. 83)^^^

[0.1252(1 - 0.400^)]l/2

Q

-= 1042 ft^/min.

Now check that Rq falls within range of calibration for discharge coefficient

C. For steam at 360 °F and 59.54 psia:

M - 1.02 X '10~5 ib/s ft (Figure B.4)

P = 0.1252 lb/ft3, and

V = y/p = 8.147 X 10~5 ft2/s

Rp = 4 (Q)/(Tr D v) = (_4 )( 1042 ^01 = 5.4 x 10^ (E7-1)

(7t)(6/12)(8.147 x 10"^)

which conforms to the calibration range for C (3 X 10^ < R^ <_ 1 X 10^).

Finally, calculate the calibration constant K for the vortex meter.

K - pulses/ ft^ = (pulses/min)

( f t3/min)

From the vortex meter measurements:

f = 5478 pulses/45 seconds = 121.73 Hz, or

f = 121.73(60) = 7304 pulses/min

From the nozzle venturi measurements:

Q - 1042 ft3/min

Thus:

K = 7304/1042 = 7.010 pulses/ft^

This value of K applies to one set of conditions: namely, steam temperature

360 °F and steam pressure 45 psig at the vortex meter exit, and to a meter frequency of 122 Hz. Normally, the meter would be calibrated over a range of

flowrates, and with constant steam temperature and pressure, the calibration

E-21
constant K would be plotted as a function of frequency, f. When the steam

temperature and/or pressure vary, K would be plotted as a function of f/v to

account for variation of viscosity v with teraperature and pressure. See figure

18, for example. Since the vortex meter has no moving parts, its performance

can be predicted through the f/v plot from results with a single fluid (steam at

constant T and P) . However, by actual calibration for a few test points with

"different" fluids (sets of T and P covering the operating range), the meter

performance over a range of conditions can be validated.

Note that the volumetric flowrate measured by the vortex shedding meter is the

volume flowrate at the meter exit temperature and pressure. If the volumetric flowrate is needed at a different location in the system or at different values of

temperature and/or pressure, or if the mass flowrate is needed, these quantities

can be calculated by procedures discussed in appendix D and illustrated in

examples E.l and E.2.

Note also that while the nozzle venturi was calibrated using water, it was used

as a reference meter on a compressible fluid (steam in the case mentioned) through

use of the fluid expansion factor Y and the meter expansion factor . This is

done, in particular, when primary facilities flowing steam are not available but

at the expense of an increase in the calibration uncertainty through tolerance

values assigned to Y. (See table A. 18.)

Example E.9 On-Site Calibration of a Turbine Meter . Water at 160 °F and 50 psig

is being monitored by a turbine meter. It is to be calibrated on site using a positive displacement meter as the transfer reference meter. The PD meter has

been calibrated previously using water at 160 °F, and it is Installed upstream

of the turbine meter as shown in figure 6. Salient features of the turbine meter

are

Size: 3- inch

Output: 45 pulses/gallon, nominal

Rating: 600 GPM rated flow, 300 psig and 400 °F

Pressure Loss: 5 psi at rated flow, 600 GPM

Installation: The turbine meter is installed in a horizontal 3-inch

insulated pipe within a metering section as shown in

figure 7. The flow straightener is a tubular type as shown in figure 12.

The transfer reference (PD) meter has the following features;

Size: 3-inch

Output: pulse type, 10 pulses/gallon nominal

Rating: 700 GPM rated flow, 150 psig and 300 °F

Pressure Loss: 2 psi at rated flow

E-22
Installation: The PD meter is Installed in the insulated horizontal pipe

immediately upstream of the turbine metering section in the same (horizoatal) position existing during calibration. No

flow straightener is used since previous tests showed no significant influence of swirling flow on meter performance.

Calibration: Water in the range 145-180 °F at a primary facility yielded

an average value of the calibration factor K = 10.145 pulses/

gallon, and K data scatter +0.2 percent for the flow range

30 to 700 GPM.

Pulses are counted from each meter with an electronic counter during concurrent

time intervals, counting at least 500 pulses from the PD meter and at least

1000 pulses from the turbine meter. The flow range to be covered by the

calibration is 50 to 500 GPM.

The test should be conducted at a pressure level sufficient to avoid cavitation

in each meter. At 160 °F, the vapor pressure of water is about 5 psia. From

guidelines mentioned in section 5.3, a (minimum) inlet pressure to the turbine

meter of 55 psia should be adequate to prevent cavitation. For the PD meter,

an absolute pressure level equivalent to the vapor pressure plus 3 or 4 times

the meter pressure loss at the rated flow is probably sufficient, as discussed

in section 5.1. For this PD meter, this amounts to 5 + 4(2) = 13 psia. Since

the PD meter is upstream of the turbine meter, cavitation in the turbine

meter would likely occur first. It is noted, however, cavitation usually

occurs initially at higher rates of flow, resulting in (sometimes) an abrupt

increase in pulse rate/ throughput

.

Table E.3 summarizes the measurements made and results of the calibration,

where the pulse data are averages of 5 repeat runs. The results show no abrupt

changes of the calibration factor K for the turbine meter, and it is assumed no cavitation occurred.

Calculations for the PD meter are:

f = pulses/ time

Q = 60(f/K) (4-1)

For Run No. 1:

f = 2561/30.000 = 85.37 Hz

Q = (60)(85.37)/(10.145) = 504.9 GPM

Calculations for the turbine meter are:

f = pulses/ time

K = 60(f/Q) pulses/gallon

E-23
Table E.3. Turbine Meter Calibration Data

Water: 162 °F + 2 °F, 50 ± psig

Positive Displacement Meter

( Reference)

K = L0.145 pulses/gallon Turbine Meter

Run Pulses

Time

Seconds

Frequency

Hz Flowrate

GPM Pulses

Time

Seconds

Frequency

Hz K Pulses/gallon

1 2561 30.000 85.37 504.9 11 180 30.000 372.67 44.29

2 1943 30.000 b4,77 38 3 .0 8484 30.000 282 .8 44.30

\ 1 1281 30.000 42.70 252 .5 5602 30.000 186.7 44.38

4 717 30.000 23.9 141 .0 3154 30.000 105.1 44.61

5 820 60.000 13.7 80.8 3580 60.000 59.67 44.3

6 512 60.000 8.53 50.5 2204 60.000 36.73 43.6

E-24

\
For Run No. 1

f = 11180/30.000 = 372.67 Hz

K = (60)(372. 67/504. 9) = 44.29 pulses/gallon

A plot of the calibration results are shown in figure E.2 where K is plotted as

a function of frequency f. These results show that the calibration factor K

varies 0.5 percent for a flow range of about 70 to 500 GPM (50 <_ f 37_5 Hz).

Also, it should be noted, these data apply only when the water is near 160 ° F.

Example E.IO On-Slte Calibration of a Target Meter . A target meter monitors

water flowing at 45 °F and 100 psig. It is to be calibrated on site v/ith a transfer meter system consisting of two turbine meters mounted in series. The

turbine meters have been calibrated previously on water at 42 °F. Two turbine

meters are used instead of one as a check on the transfer-meter operation. Should

differences in turbine meter performance be (or appear) larger than an allowed

maximum, meter trouble would be suspected and this performance would be investigated

This approach is favored since this type meter tends to be incompatible with

foreign material entrained in water and since water is considered to have poor

lubricating properties. However, these meters have definite advantages for

transfer meter applications, including small size, digital output, and a calibration factor that is essentially constant over large flow ranges when used

with a low-viscosity liquid such as water. The turbine meters are installed

downstream of the target meter in a metering section as shown in figure 5. At

the entrance to the metering section a 50-micron filter is installed. The

target meter is installed in a metering section including a flow straightener

.

Salient features of the target meter are:

Size: 2-inch

Output: 4-20 raA DC, slope and span adjusted for 0-270 GPM nominal,

transmitter output varies with

The turbine meters have the following features:

Size: 2-inch

Output: pulse type, 3300 pulses/ft-^ nominal

Rating: 300 GPM rated flow, 300 psig and 250 °F

Calibration: On water in the range 40 ° F to 42 ° F at a primary facility.

Meter No. I has a calibration factor K = 3303 pulses/ft-^

with a variation of +_ 0.2 percent in the upper 3:1 flow

range. Meter No. 2, K = 3286 pulses/ft-^, with a variation

of + 0.2 percent in the upper 3:1 flow range.

The target meter will be calibrated over a range of 100 to 270 GPM, expressing

the calibration factor CF in units GPM/(raA)^/2 33 discussed in section 4.4.

E~25
E-26
The reference flowrate will be based on the average readings of the two turbine

meters. The target meter transmitter output current will be measured by a digital voltmeter (OVM) (4 1/2 digits) and the two turbine meter ouputs by

variable-tlme-base electronic counters. The time Interval should be set large

enough to assure a steady count; I.e., no Influence of random flow fluctuations,

or set to accumulate at least 5000 pulses, whichever Is larger.

To check on the turbine meter operation, the frequencies f]^ and ^2 will be

compared. To account for the difference and the variation (j^ 0.2 percent) In

calibration factors for the two turbine meters, and to allow for meter repeatability, a criterion of 1.000 ;< fi/f2 ^ 1.010 will be used to signify satisfactory transfer meter operation. (Note 3303 + 0.2 percent = 3309; 3286 - 0.2

percent = 3280; 3309/3280 = 1.009). In particular, values of fi/f2 which show

drift or large scatter outside this range should be Investigated.

Table E.4 summarizes the measurements and results of the calibration of the

target meter, where data for each test are the average of 5 repeat runs. Note

that the transmitter current, 1, was checked at zero flow at t'ne beginning and

end of each run, test points 1 and 6. Also note that frequency ratio f]^/f2 for

the turbine meters stayed In the range 1.000 to 1.010, Indicating satisfactory

meter operation according to the criterion stated previously.

Calculations for the turbine meters are:

f = pulses/ time

Q = 60(f/K) (4-1)

Qavg = (Ql + Q2)/2

For test point No. 2;

f]_ = 7224/10 = 722.4 Hz

Ql = (60)(722.4)(7.4805)/3303 = 98.16 GPM

f2 = 7202/10 = 720.2 Hz

Q2 = (60)(720.2)(7.4805)/3286 = 98.37 GPM

Qavg = (Ql + Q2)/2 = 98.27 GPM

Calculations for the target meter are:

Iq = di + l5)/2 = (3.998 + 4.002)/2 = 4.000 mA

The calibration factor is:

CF = GPM/(mA)l/2, and (4-10)

CF = 98 .27/(6.074 - 4 .000)1-^2 = 68 .24 GPM/(mA)l/2

E-27
The calibration results are plotted Ln figure E.3 showing the calibration

factor CF, GPM/ ( I - 1^)^ plotted as a function of transmitter current 1.

These data apply only for water at or near 45 °F. To obtain the

flowrate at any current I, equation (4-11) is applied. For example, when

I = 16.00 mA:

CF = 69.41 GPM/(mA)^/2^

Q = (CF)(1 -Iq)^^^ = (69.41)(16 - 4)^/2 (4-11)

Q = 240.4 GPM

E-28
Table E.4. Target Meter Calibration Data

Water at 45 °F

Turbine Meters (Reference)

No. 1 No. 2 = 3303 pulses/ft^ K2 = 3286 pulses/ft

Test

Point

Pulses Time fi Qi

s Hz GPM

1

Pulses Time £2 Q2

s Hz GPM

123

4

56

0

7224 10' 722.4 98.16

10281 10 1028.1 139.70

7372 5 1474.4 200.3

10176 5 2035.2 276.55

0

7202 10 720.2 98.37

10196 10 1019.6 139.27

7364 5 1472.8 201.2

10095 5 2019.0 275.77

0

R(2ference Meters Target Meters

Qavg

f^/f2 GPM

I CF Q

1 — 0

2 1.003 98.27

3 1.008 139.49

4 1.001 200.8

5 1.008 276.16

6 0

3.998 — 0

6.074 68.24 98.27

8.139 69.56 141.52

12.447 69.08 200.8

19.736 69.62 276.17

4.002 — 0

E-29
E-30
NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publ ication Date BIBLIOGRAPHIC DATA

REPORT NO. SHEET (See instructions) NBS BSS 159 January 1984

4. TITLE AND SUBTITLE

On-Site Calibration of Flow Metering Systems Installed in Buildings

5. AUTHOR(S)

David W. Baker and C. Warren Hurley

6. PERFORMING ORGANIZATION (If joint or other than NBS. see /n struct/on s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 2Q234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State. ZIP)

Naval Civil Engineering Laboratory

Port Hueneme, CA 93043

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 83-600626

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT , The measurement of flow of the various fluids (air, water, steam) used in building

service systems is usually the most difficult parameter to obtain and maintain.

Consequently, in energy management and control systems (EMCS), the flowrate or the

total quantity of flow is often the least accurate measurement. However, in most

systems the energy consumed depends directly on this parameter.

Since the majority of fluid flow measuring techniques require the sensing

element to be located in the stream of the fluid being monitored, flow measuring

devices often are the most difficult instruments to calibrate initially and to

maintain in calibration within the required accuracy. This report summarizes the

various types of fl ov/meteri ng devices used in EMCS, various methods for their

initial calibration and, when practical, techniques for maintaining their calibration while they are in service. Emphasis is placed on the use of transfer

reference meter systems, where the working meter is calibrated on site by connecting

it in series with a calibrated transfer meter of any variety. Other methods of

calibration are also described.

Reference tables and the necessary equations for flow calculations are presented

throughout the text and in the appendicies. Illustrative examples are given in

detail for the calculation of flow using each type of metering device described.

These examples are extremely helpful in field calibration when the metering being

calibrated is of a different type than the meter being used as a reference.

Because of this, the reader is encouraged to review these examples.

12. KEY WORDS Calibration methods; flovmetering devices; flow nozzle meters

P] tot-static tube assemblies; orifice meters; positive displacement meters: piLOt tube assemblies; target meters; turbine meters; ultrasonic flovmieters

shedding meters.

multiple

reverseventuri

13. AVAILABILITY

Unlimited

I I For Official Distribution. Do Not Release to NTIS

[X] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Q]] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

154

15. Price

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