2



NBSIR 75-900

Liquid Level Instrumentation in

Volume Calibration

R. M. Schoonover

H. H. Ku

J. R. Whetstone

J. F. Houser

Institute for Basic Standards

National Bureau of Standards

Washington, D. c. 20234

October 1 975

Final

Prepared for Mechanics Division

Institute for Basic Standards

Washington, D. C. 20234

NBSIR 75-900

LIQUID LEVEL INSTRUMENTATION IN

VOLUME CALIBRATION

R. M. Schoonover

H. H. Ku

J. R. Whetstone

J. F. Houser

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

October 1975

Final

Sponsored in part by:

Brookhaven National Laboratory

Technical Support Organization

Upton, LI., New York 11973

Prepared for Mechanics Division

Institute for Basic Standards

Washington, D. C. 20234

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Liquid Level Instrumentation in Volume Calibrations

by

R. Schoonover, H. Ku, J. Whetstone and J. Houser

with Appendix by C.R. Til ford

Introduction

Several years ago, the Mass and Volume Section of the National

Bureau of Standards undertook a study, supported in part by the

Atomic Energy Commission, to determine the accuracy of a nuclear

fuel reprocessing tank volumetric calibration. The calibration

technique studied was volume versus liquid level as determined by

head pressure measurements. The results are given in NBS Report

10396 [1].*

The purpose of this study is two-fold: (1) to use the earlier

work as a basis for comparison of several instruments as liquid

level detectors including the appropriate analysis and (2) to

generate data for testing the ANSI Draft Standard N15.19. The

proposed ANSI standard sets forth an analysis technique for

application to tank calibration data.

Data reduction is covered in the previous report and is supplemented by sight glass observations, liquid density measurements,

and more general equations in the appendices of this report.

Included are the data necessary for an independent evaluation and

analysis

.

Review

This study relies on earlier work described in NBS Report 10396

for calibration techniques and data reduction. A short review of

that work is presented here.

That report detailed the calibration and data reduction of

straight-wall tanks via liquid level head pressure. To measure

head pressure, a quartz bourdon gage with an electro-mechanical

readout was used. This type of instrument is sufficiently

sensitive and reproducible, but requires calibration to obtain

suitable accuracy.

With the proper pressure gage coupled to a tank, there must be some means of introducing known volume increments and noting the

resulting head pressure. There are two popular methods of

introducing known volume increments. Both are generally

performed using water during initial tank calibrations. One

The numbers in brackets refer to similarly numbered references

at the end of this paper.
method is to pour water from a standard test measure of known

volume and the other is to weigh out a volume of water and then

pour it into the tank. The second method can be modified by

first pouring an unknown volume increment into the tank and then

weighing the tank to determine the added volume.

Although the two methods for determining incremental volumes were

found comparable [2], the method of volume transfer is more con- venient. The calibration results in the correspondence of liquid

level (height) to tank volume. The uncertainty of the correspondence is about 3 parts in 104

.

In proceeding with the current study, it was necessary to replace

the original pressure probe (bubbler tube) and make other modifications to the tank. These modifications preclude comparing the

tank's geometric profile to the previous one.

Current Study

As stated above, an overall tank calibration accurate to 3 parts

in 10^ is obtainable if proper care is exercised. Our goal here

is to compare three pressure gages and a sight glass as liquid

level detectors, via tank calibration, suitable for field operation at the 1 part in 10 3 level. Included in these measurements

is a test for maximum level detection resolution. Additionally,

the water density is determined by direct pressure measurement

and also calculated based on temperature measurements.

NBS built the sight glass detector and supplied the XR-38

pressure gage. This gage was used in the previous study.

The Brookhaven Technical Support Organization (TSO) arranged for

two other gages, a Ruska DDR 6000 and a Bell and Howell electromanometer, model number 4-336-0050, with servo amplifier 11-169. 1

Although we did not require an experiment at the 3 parts in I0k

level of accuracy, the XR-38 pressure gage and tank calibration

techniques were used as before. Thus, we had a standard of known

performance from which to judge the other detectors and the

techniques used in conjunction with them.

We used volumetric transfer from a standard test measure accurate

to about 3 parts in 10 5 as the means of providing known volume

increments for the tank calibration. A gravimetric check was provided in conjunction with the first calibration test merely to

verify that the system behaved as expected.

i Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the

experimental procedure. In no case does such identification

imply recommendation 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.

- 2

-
It is noteworthy to stress that the calibration of a processing

tank as presented here is a system calibration valid under certain restrictions. These restrictions are discussed in appendix

3.

Hardware

The steel tank was 4 feet in diameter and 14 feet high, but was modified to accommodate three sets of probes. Each set consisted

of two bubbler tubes, the orifice separation of which was 20 cm. Support for the probes is furnished by three horizontal braces

that span the tank's inner diameter. Over the working range of

the tank, these braces cause discontinuities in the rightcircular cylindrical geometry. Placement of the bubbler orifices

near the tank's bottom end provides the maximum detection range

and minimizes the heel volume of the tank. The tank and heel

volumes are, as before, 3000 liters and 200 liters respectively.

A sight glass of 25 mm bore is in direct contact with a measuring

tape and is mounted vertically to the tank's exterior wall. At

the bottom end, a connection is made between the glass tube and

the tank's contents. The upper tube end is in free contact with

the atmosphere. The tape itself is three meters in length and

has one millimeter graduations. The uniformity and correctness

of the graduations has been verified by independent calibration

[31.

Dry nitrogen is used for the bubbler gas source and is regulated

at one cubic foot per hour regardless of head pressure for both

the DDR 6000 and Bell and Howell gages. These two gages both

work in much the same manner. The pressure is sensed by a quartz

bourdon tube in the DDR 6000 and a metal bellows in the Bell and

Howell instrument. In each instrument the elastic sensing element is servoed to a null position. The restoring force is supplied and controlled electronically in each instrument and

requires a five and one-half digit (5h) digital voltmeter (DVM)

for output of the pressure signal. One DVM was used for reading

both instruments.

The DDR 6000 was factory adjusted and calibrated to read out

directly in cm of water at 0 °C with the DVM set on the 10 VDC

voltage range. The manufacturer specifies linearity to be 0.002%

full scale or better with a pressure range of 10 psiG. The Bell

and Howell instrument calibration is 1 volt DC = 1 psi with a range of 5 psi. Early experimentation indicated the voltage

outputs for these instruments required integration to produce a steady DVM display. This was provided by an external RC filter

network with a one-second time constant.

To simulate field use of these instruments, they were not pressure cycled over the expected working range to minimize

hysteresis. Although unproven here, null operation probably

eliminates the advantage of an exercise cycle.

- 3

-
Other than the modifications specifically mentioned, the tank

configuration remains the same as that of reference 1. Shown in

figure 1 is the experimental setup used for this study.

Design and Analysis of Eight Calibration Runs

Four criteria largely determined the number of repeated calibrations and their composition: first, TSO desired each calibration

to contain at least 17 points per run for testing the proposed

ANSI Standard N15.19; second, one calibration run should test the

resolution of the various level detectors; third, from a statistical viewpoint, each calibration should not contain

nominally identical data points; fourth, the tank should be

weighed empty and full in order to demonstrate closure of the

gravimetric and volumetric calibration methods.

We made eight calibration measurements, most of which have some volume variation from each other. Table 1 gives the volume increment for each run in the order of occurrence. Our first mea- surement tested the integrity of the bubbler tubes. This was accomplished by measuring the same liquid level with the XR 38

connected individually to each probe. However, pressure was not

measured for every increment of the run which results in fewer

calibration points. A gravimetric check of total accumulated

volume was done on Run II and was in agreement with the volumetric technique within the uncertainties of the two. Run IV con- tains many increments ordered in a manner to test detector

resol ution.

Except for the additional bubbler tube needed for measuring water

density and the sight glass observation, data reduction is the same as that of NBS Report 10396. (See the appendices of this

report for details concerning data reduction for the sight glass

and water density measurement). The calibration results are tabulated for each detector in reduced form (see table 2). Each

point is standardized to 20 °C and is adjusted for variations in

bubbler depths. That is, the first point, or instrument indication, is subtracted from all others observed with the instrument

to provide a common intercept (volume at zero height). Temperature corrections on the sight glass data have been made for runs 6,7, and 8, but not for runs 1 through 5 because we did not

observe sight glass temperature. A calibration line was fitted

by the method of least squares to data from each of the four

instruments within a run using the following model:

h = a + bV + E + e

where V: The volume of water added, corrected for

temperature and density, in liters;

h: The observed height of the liquid level as indicated by the particular instrument in cm;

- 4

-
HOOK FOR

NOTE: Points F, G, and H are connected

to Dressure source and I is ooen

to the atmosDhere.

FIGURE 1: SIMPLIFIED VIEW OF HARDWARE HOOKUP

- 5

- A
Calibration Runs

#1 #2 #3 #4 #5 #6 #7 #8

1 [50] 50 100 100 50 55 65 30

2 50 100 100 100 50 50 50 50

3 [50] 100 100 100 50 50 50 50

4 50 100 100 1 50 50 50 50

5 C5o: 100 100 1 50 50 50 50

6 50 100 100 5 50 50 50 50

7 [50] 100 100 5 50 50 50 50

8 50 100 100 1 50 50 50 50

9 [50] 100 50 1 50 50 50 50

10 50 1/4 50 50 50 50

11 [50] 1/2 50 50 50 50

12 50 3/4 50 50 50 50

13 [50] 1 50 50 50 50

14 [50] 100 50 50 .50 50

15 [50] 100 50 50 50 50

16 [50] 100 50 50 50 50

17 50 100 50 50 50 50

18 100

19 100

Table 1. Shown above are the nominal volume increments for each

calibration in order of occurrence. For clarity, the

nominal volumes are given in gallons and elsewhere in

the text as liters. Brackets indicate the omission

of the pressure observation.

- 6 -
RUN 1

TR TASK WATER WATER ACCUX. 3ELTA

NO. TE uo . OE'.SITT "ASS VOLL^E VOLUKE

2 10.2»6 999.208

4 14.110 999.227

6 13.675 999.2=7

8 13.125 999.360

10 12.766 999. oc5

12 12.527 999. 030

17 12.CS9 999.086

378.35 756.39

113».76

1513.19

1891.03 2269.78

3215.55

37969 757Q7

13573

00000

3 7 63* 75703

51038 1,13569

89285 1.51015

27100 1.89270

21 77 5 2.83906

SIGHT GLASS HEIGHT

.00000* .00000

.00000

.00000 .00000

.00000

. oc : c c

DELTA =ROBE 1 ACC'JM. «^!;-T ==rs? c- J 5I3~ T DELTA PROBE 1 ACCU*. 1ELTA PROBE 1 ACC'J". "^ELTA HEIGHT PRESS"RE HEIGHT HEIGHT PRESSURE HEIGHT wriG"T

.ooooo

.00000

.00000

,30000

2035.3

5706.5

8971.9

12207.

00000 15517 9 .00000 18797

.00000 26962.0

,2089-r .58337

.91710

.00000

.33000 .66817

.25185 1.00289

,58610 1.33710

92131 1.67230

,75559 2.50662

2088.5 .25001 .00000 5760.5 .58890 .33009 9028.6 .92293 .66853 12300.9 1.25735 1.0029O

1*572.1 1.59165 1 .33720 18853.2 1 .92695 1 .67250 2*999.5 2.75902 2.50*01

?052.0 .25067 .00000 *72o.0 .58516 .33*09 »o=0.3 .91901 . 66*35

12260.5 1.25363 1.00996

15533.2 1.58767 ).

7 7Qn 1**15.6 1.92311 1.67200 26979.8 2.75701 2.50670

RUN 2

13.066 12.532

12.162 12.119

12.069

11.981 11.827

11.797

11.726

999.315

- - - , _ 1 -

, 99° .062

: = - . - = c 999.096

9°9. 516 999.519

999.527

189.12

567.56

: -5 . 55 1320.00 1703.12

2081 .30 2059.01 2637.87

3216.18

.18928

.56797

.90650 1.32535 1.73028

2.08270 2.06103

2.83970

3.21°2*

•OOOOO

.37870 .75723

1 .13607 1.51500

1.8930"' 2.27176 2.650O6

: , : 2

c :

•2O600

.55200

.91700

1 .25200

: . 5s T

:c 1.92270 2.25*00 2.59200

2.927f)0

.00000

.33600

.67100

1 .00600

1 .30100 1.67670 5.01200

2.3O600

2.68100

PROBE 1 788.

0073.8

7337.5

10613.5

13890.9 17167.6

20O33.2 23698.3

26971 .2

41638

,70993

,08070 ,01969

,75056

,0882e OJ195

,75602

.00000 .33573

.66928 1.00009

1 .33900 1.67392 2.00763

2.3*131 2.67578

PROBE 2 780.6

O061.3

7320.0

10596.3 1 13872.1 1 17150. 0 1 P0O22.3 2 23681.0 2 26952.9 2

.07979

.41510 .70855

. 0*2 Q B .01777

.75281 .08716 .»20t9

.75055

•nnooo

.33531 .66879

1 .00319

1 .33798

1 .67301 2.00737

2.340O0 2.67076

PROSE 3 889.9

4171 .0 7036.

10718.2 1 13995.2 1 17261.7 1 20540.5 ; 2

7-BIl.7 J 27083.1 ;

,09097

,02631 ,75999

,09544 ,43035

,76015

, 0992O

,03355

,76786

.ooooo

.S3*7.* .66902

1 .00447 1.33938

1 .67321 2.00*27

2.34258

2.67689

11.9ofc

.-: = 11.113

::.=55

i:.=53 11.012 11.075

1 1 . r 3 3 11 . :-e

=99.5:2 =99.561 999.592 999.607

999.609

=9=. 5:2 999.596

999.601

99c B 599

376.30 756.26

1 1 3 - . 5

1512.88

1891.30 2269.52

2647.76

3:26. :i 3215.21

. 3^555

.75673 1.13*19

1.51377

1.8=241

2.2 , :=e 2.60930

3.G27 32 3.21712

.00000 .37ei7

.75660 1.13522

1 .51386 1.89231 2.2707s

2.60927

2.83857

.01520

.7490(1 1.08350

1 .01920 1.75360

2.08920

2.42900 2.755C0

2.92600

.CC r - .33380 .66830

1 .OOOOO

1 .33800

1 . 6

7 0"3 2.00**3 2.3O280

? . 51 0 °0

2030

5705

8970 12250

15520

16801 22063.2 25326.8

26966.9

.20383 .58308

.91670 1.25193

1 .58602 1.92131 2.25067

2.58817 2.75578

.00000 .33025

.667=1 1.00309

1.33758

1 .67208 2.00583

2.33930

2.5069O

'021 . 7 5689.7

8953.2

12233.0 15090.1

18701.2 22000,8

25306.9

26909.

.20750 .58106

.91495 1.25010 1.58335

1 .91927 2.25279

2.58613

2.75390

.00000 .33396

.66745 1.00260

1 .33585 1.67177 2.00529

2.33863

2.506OO

2530.9

5800.2 9066.1

12308.5 1 1*616.6 1 1B9P9.0 1 2?168.9 2 25033.4 2

2 7 B76.6 2

,25866

,59276 ,92649

,26190 1 ,59587 1 ,93237 1 ,26547 ? ,59906 2 ,76698 2

,00000 ,33409

,66782

,00324

,337?1 ,67371

,00681 ,34040

,50*32

RUN 4

11,

11,

10,

l:10, 11

11,

8 11 9 11

1«11 11 12 11 13 11 14 11 15 11 16 11 17 11 18 11 19 u

: : = 170 895

956

= 5- 044

096

122

160 235

2o9

271

292

332

55- 696 511

36-

999.572

999.586

999. 61o

3 9 = . 6 : e 999.606

999.599

999.590

999.591

99=. 5*3 999.580

099. 578 999.576

999. 570 999.570

=99 . 55* 999.508

999. 53C 999.550 999.566

378.25

""56.36 1130.71

1138. o9 1102.27

1161 . 17 1180.08

1183.86

1187.60

i z : e , : - 12: 7 . -9 1209.38

1212.21 I59o.0o 1972.00

2 3 5 : . = 3 2729.11

3109.53

.37508

.7568?

1 .13537 1.13916

1 . lo29o 1.16186 1.13078

1 .18057 1.1*836

1.20728 1.20323 1.21012

1 .21296 1.21675

1 .59500 1.97376

2.35236

2.7308O

3.11151

..... .37836

.756* 3 .76r:63 .76047

'5339

.80231 .30609

.80983

.82S3C .8297*

.8316o .8300*

.83827 1.21656 1.59528

1 .9738a 2.35236

2.73303

.01370

.74920 1.08350

1.08670 1.09030

1.10680 1.12400

1.12730

1.13070 1.1O7t 0

1 . 1O850

1 . 1O990

1. 15230

1 .15500

i . - = -*? 1.32OO0 2.16030 2.O9500

2.63200

.00000

.33550

.66°*0

.67300 67 66C .69310

.711*3 .71360

.71700

.73360

.73030 .73520

.73860

.70170

1 ,076*0

1 .01070

1 .707)0 2.08130

5. 01 330

2033.1

5706.

*9 7 2.2 9006.2

9040.1

9202.0

9367.0

9001 .3 9430.5

9593.8

9602.0 9618.2

9603.

9676.0

1290*,,

16218.3

19098.

22758.3

26048.3

.20865

.58312

.916* 7 .92035

.92381 .90037

.95727

.96070

.96010 .98002

.98126

.98292 .98546

.98887

1 .32309

I .65752

1 .99267 2.32581 2.66199

.00000 .33007

.66822

.6 7 1 7 0 .67517

.69172

.70863 .71209 .71549

.73177

.73261 .73028

.73681 .74023

1 , o7ooo 1.00887

1.74402 2.07716

2.4133*

2018.7 =6*9.2

89*2.8

B989.0 9021.9

91P0.7 9308.0

9380.

9414.1 °57S.O

9782.0

9602.

9626.0 9657,3

12926.3

16193.3 19078.5

22739.6

26031.1

.2071

.581?9

.910*8

.918*9

.921=5 .938*9

.95533

.95860 .96205

.978*5

.90969

.98131 .98371

.986=3

1 .32101 1.65096 1.99066

2.32389

2.66023

.OOOOO

.33421

.66 7 70 .67141 .67477

.69141 .70*15

.71146

.71487

.73167

.75251 .73413

.73653

.73970 1.073B3

1.40778

1 .74348 2.07671 2.01305

2487.3 *760.9

=02*.

9063.8

O092.5

9261 .6 =023.2

9460.1 9093.6

=655.0

9666.3

=682.3

=708.0 =739.7

1300O.9

16268.0

19561 .5 298??.

26110.6

.25019

.58872

.92260 .92620

.=2=16

.94645

.96340

.96675

.97017

.9R67?

,9*7 83 .=8=52

.99210

.99534

1 .32=0* 1.66260

1 . 90=14 2.33949

2.66877

.00000

.33454

.66*02 .67905 .67498

.60226

.70930 .71256

.71599

.73953 .73364

.73534

.73791 .74116 1.07436

1 ,40»41

1 ,7440ft 2.07*31 9.41458

RUN 5

1 12,

2 11. 3 11, 4 11, 5 11. 6 10

7 10, e 10, 9 10, 10 10, 11 10

12 10 13 10, 14 10, 15 10 16 10, 17 10

219 =99 Ml 995 696 999

374 999

1:2 ----- = ; = =9 = 793 999

691 999

621 999

691 999 806 999

746 999

665 999

612 999

588 999

567 999

502 999

,471 189. .51* 378.

,530 567, ,565 756,

.594 945, .613 1135,

,625 1320,

,635 1513,

.641 1702,

,635 1891-

.623 2080

.629 2270

.637 2059,

.602 2648,

,6-5 2?3 7 .607 3C26,

.6o9 3215,

193544

64

90

12 1 24

33

57

329713

20

294760

96

13932

J 1 3 * r 56 7 ?1 757 U

90606

1357R

32500

51-15

--, = ; 592 =

- 08217 27103

O6059

60977

83905

02829

21760

OOOOO

19927 37809 56779

75710

,90646 13567

32-5' 51420

7 B35 7 39285

,08211 27127 O60O5

60973

83896

02332

. 2O620

.41910

.5 = 2-!: .70950

.916*0 1.08O00

1.251O0 1.41=00

1.58660

1.75400 1.92250 2.08990

2.25720

2. 02030 2.59170

2.75350

2.9260Q

.00000

.16700 .33610 .50330

.67030 83780

1.00520

1 .17280 1.30030

1.50730

1 .67630

1 .84370 2.01100

2. 17810

2 . 34550 2.51230

2.68020

792.2 2032.9

O07O.5 5707.6

7338.5

8975.0

10611.6 1 12208.5 1 13886.7 1 1*522.7

17163.9 18800.7 20O30.8

'2061.2 23694.7

25326.5

26966.9

: = : =' ,20865

,01601 ,58329

,70905 ,91716

, 08000

,25166

,01906

,58625 ,75397

,92123

,08779

,25039

,42130

,58800

,75566

.00000

.16 7 69 .33505 .50233

.66*98

.83620 1.003O3

1.17070 1.33809

1.50528

1.67301 1.84027 2.00632

2.17342 2.34033

2.50708

2.67469

805.6

2007,7 4086.8

5717.6 7308.9

9977.

10619.0

12257.0 13890.3

15520.3

17166.1 18805.2 20436.5 22067.8

23701.6

2*332.9

26970.3

.08230

.25016 .41767

.58432

.75101

.91740 1.08519 1 1.25253 1 1.41943 1 1.586 T 8 1 1.75420 1 1.92169 1 2.088?* 2 2.25506 2 2.422"0 2 9.5*869 ? ?.756?8 9

,00000

,16782 ,33534

,50198

,66*67 ,93506

,00286

,17020 ,33709

,50405 ,67187

,83036

,00604

,17273 ,33967

,50636

,67405

853.4 9093.8

0130.1 5753.5

7391 .2 °029.7

10668.1 1 19307.8 1 !?001.7 1 15570.9 1 17220.5 1 18862.7 1 20000.0 2 22128.9 9 2?762.6 2 25395.5 ? 27037.1 2

,08722 ,25087

,42250 ,58799

,75533

,92276

, 09017

,25773 ,42463

,5915* ,76017

,02756

,09476

,26130

,42824 ,59509

,76284

.00000 .16765

.33528 .50076

.66*11 .83554 1.00295

1 .17050

1 .33746

1 .50436 1.67995

1 .84034 2.0075?

2.17408

2.34102 2.50787

2.67*61

KEY: Probe 1 XR 38 Probe 2 DDR 6000

Probe 3 BAH El ectromanoneter

The abbreviation TR stands for vol 1*1 transfer

UNITS: Temperature degrees Celsius Density

>c' Height

' Pressure Mass

1: - (meters) 3 meters

pascal s * No sight glass observations Mde during Run 1 ** Testperature corrections applied to sight glass for Runs 6, 7, and 8 (see text)

Table 2: Data shown are collected from ea£h of the eight calibration runs on which the reported analysis 1s based. Table continued on next page.

- 7

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a inM3C*-cocp oncuioa^-op
Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8

Slopes (cm/liter)

Sight Glass .088469

(35)

.088492

(18)

.088484

(17)

.088464

(13)

.088493

(12)

.088294**

(16)

.088282**

(12)

.088261

(12

XR-38 .088300

(28)

.088311

(18)

.088312

(25)

.088310

(ID

.088303

(13)

.088292

(15)

.088309

(15)

.088311

(15

Ruska DDR 6000 .088235

(46)

.088258

(59)

.088303

(27)

.088304

(U)

.088280

(13)

.088278

(12)

.088292

(13) .088301(11

bin 1 1 ec tromanometer . UOO £.3 1 (28)

f|QQ "ICR

. U OO J 0 0 (15), JOO oou

(33)

nop. "54 n . UOO JHU

(18)

. Uoooo

(17)

. UOOOilD (12). UOO OLD

(13)

OQOO 1

.Uooolo

(11

TntprcpDt.? (cm)

51oht Glass - 008

"(57) 085'(35)

- 081

"(32) 040"(16)

059

"(22)

- 047

'(25)

035

'(21)

187

(21)

XR-38 .014

He.

}

146)

.106

134}

.037

(48)

.004

(13)

.085

(23) .047

(28) .008(26)

.177

(25)

Ruska DDR 6000 .086

(22) .175(112) V lit /

-.012 -.030

(14) .055(23) .061(22) .019(22) .167(20)

R 1 H F 1 or rnrna norno^ fti* D O n LlCUL.rUlMaIliJM[cLCr (45) (28)

- 024

(63) (23) (32)

04?

(23) (22)

in?

(19)

"Ci 1 JUG 1 i 3 , U

Sight Glass .069 .045 .041 .035 .042 .048 • .031 .038 XR-38 .055 .043 .061 .028 .044 .054 .048 .047 Ruska DDR 6000 .091 .144 .063 .030 .045 .042 .041 .036

B & H Electromanometer .054 .036 .079 .048 .061 .043 .040 .035

Standard Deviation of a Predicted Point (Maximum)

Sight Glass .057 .029 .027 .023 .020 .027 .019 .019 XR-38 .045 .028 .040 .019 .021 .026 .024 .028 Ruska DDR 6000 .075 .093 .041 .020 .021 .020 .020 .022

B & H Electromanometer .045 .024 .052 .032 .029 .021 .020 .021

Number of Calibration

Points 7 9 9 19 17 17 16 17

* Includes both tank configuration and measurement error

** Sight glass levels corrected for temperature

Table 3: Summary of slopes, intercepts and residual standard deviations for all eight runs. (Figures in parentheses are standard errors of values immediately above.)

- 9

-
a: Intercept of the calibration line;

b: Slope of the calibration line;

E: Deviations from calibration line due to tank

configuration;

e: Deviation due to measurement error.

The results are summarized in table 3 for the eight runs. Run 1,

however, cannot be considered as a regular test since the XR - 38 was used for all probes. The residual standard deviation thus

obtained include contributions from both E, the tank configuration errors, and e, the measurement error associated with the

instrument. The decomposition and estimation of the error term

will be discussed later. It will suffice to note here that the

tank configuration error should remain constant at a given level

of liquid whereas measurement errors may be assumed to be random.

The values of the slope of the calibration lines obtained from

the sight glass during the first five tests are higher than the

other three instruments by about .0002, indicating the presence

of a systematic effect. This was traced to the difference in

temperatures, and hence density, of the water inside the tank and

in the sight glass (see next section and appendix 1 for detailed

analysis). Corrections of this temperature difference were possible for runs 6,7, and 8 where the temperature of the water

in the sight glass was measured. The slopes of these three runs agree well with the other three instruments after making appropriate temperature corrections.

We observe from table 3 the following:

1. For runs 2 through 8, the Bell and Howell Electromanometer gave consistently higher slopes than the

XR-38, the DDR 6000, and the sight glass after temperature correction.

2. The intercepts for run 8 are higher than those of

the other runs.

3. The residual standard deviations are of about the same magnitude. The large value for the Ruska DDR

6000 for run 2 may be traced to a possible transposition of a reading in the last two digits. This

"standard deviation" however includes a component

due to the deviation of the tank from the model

geometry.

- 10 -
In fitting the response of an individual instrument's calibration

lines for a run, the plot of each set of residuals suggested that

there is a definite "profile" of the tank which is common to all

four instruments. It would be desirable to plot such a profile

using more than one run to sketch the tank configuration in

detail. Runs 5, 6, 7 and 8 were chosen for this purpose.

To align the four runs to the same starting point, the initial

volume increments, varying from 113 liters for run 8 to 245

liters for run 7, were multiplied by the respective calibration

line slopes obtained for each instrument. This resulted in

liquid levels which could be added to the accumulated heights for

each instrument in a run such that all four runs were referred to

a common starting point. A total of sixty-two points was used

from the four runs Table 4 gives the volume in liters in column

1, residuals from the calibration line for each instrument in

columns 2, 3, 4, and 5, and the averages of residuals in column

6. Figure 2 is a plot of all the residuals from the four

instruments against tank volume in liters, and figure 3 is a plot

of the averages of the residuals against tank volume.

From these two figures, it is evident that the spread of the

points at a given volume is a measure of the measurement errors

of the instruments; whereas the deviations of the averages of

these points from the fitted line is a measure of constancy of

the tank diameter from bottom to top, i.e., a profile of the

tank. The two peaks correspond to the lower two of the three

braces supporting the probes, the third one is at the top of the

tank and is outside the range shown in the figure. The

systematic error in using the calibration lines for the

estimation of volume from instrument readings is less than

1 liter.

Since each deviation (E) of the tank configuration is systematic

in nature, the measurement error standard deviation, a e , can be

estimated from the residual standard deviations. Denoting by 5 the differences between the residuals of an instrument from the

average of all four instruments, e.g., (column 1 - column 6 of

table 4) , then:

ei + e

2 + e3 + e

k

- 11 -
SIGHT AVERAGED

VOLUME GLASS XR 38 DDR 6000 B & H RESIDUALS

302i77?Gu _"I'MT/oibJ' 1l07i1tl7 — . 1 JJT 1] 1 £ J/ I U 1 7££00 1

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192.00200 -.021213108 -."21080597 -.017365375 -.017375152 •UtUUIol n ) nn I i. i 11 567.77599 .0573051 19 ."3381 7501 •062001662 . 10179072 .064479502

586.18199 .062326396 .P. 16870362 . 038035875 . 0591 1 6573 .044162301

621.13299 .088637871 . P2Q261 689 •071532076 .058505278 •060484978

681.312 DJ ,351201873 .C4I226892 .016690009 .012957505 •046 2 69069

757.07599 .025590873 .?08 1 233357 .02053 1 537 -.071919011 • 00^4 18 3239

//5«66 1 '7 .00961 f\ n o a i 38337 t a i ^ *s -.2621 3201 n n *> l. c l. o o l. a • UUl / 37T3UO

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n 50 180 116 - • 063606507 -.030336598 •UjTbio

to 1003.0730 -.03 3 300876 -.017091 796 - • 036169738 -.0117 1 3065 _ .010393868

1059.9120 -.039792071 -.1' 15013671 - . 056083223 - . ill 7262228 - .017015299

1 1 35 . 7 1 9 0 -.031301820 -.0 3971 3101 -.098860196 - . 05 1 792290 « Ub 6 1 6 / 0 0 8

1 151.0920 -.011 9V9379 - . J08S6 )R 1 77 -.039280123 -.02507 1 020 •QZ1ZZ/91Q

1192.1230 - .020396 1 17 • Cl'j 80726177 -. 028 1 30235 -.022172885 •0Ib/J166Z

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1381.1130 -.01871 3202 •P3201 1 829 -.0209831 21 -.001 1328123 • 0097 7 1 835

1138.3620 .321785969 -•0027671911 -.00031178079 .01 1 067129 • 008 1 V Z 7 B 0

15 11. 1530 -.020390710 -.TO 379731 95 •0051936823 .002 10 17893 • 00**1H81M70

1 532.5020 -.021811135 •v 10856365 • 0 1 5515 1 50 -.038358073 .0084502463

1570*61 30 -.039071881 •0 13958890 • 001 1 1 3605 1 .007557 1 298 0033606650

1627.6520 .0319981066 .021 301100 -.0011958628 .0031613123 • 00oZ"Zol a11

1 703.1920 -.025557110 .0 17063968 -.019121897 -.028051109

I'/l.BlJ/iU — • )U£0£JC3D'^ .• Una n 1 il £ 7/

1

1 Jcl 191 •UJOJTtT 1

/

•0104 53 827

1 / 5 9 • V 1 30 -•0Z8Z73775 — • n U2"r73b/11 — .0196*2170 — ii))7UUQQi .UiZZolooo t U 1 w t O J O * Q 18 16.9220 -.023020522 • 0 2 7 1 1 2 1 7 8 •003091 3177 -.0229 72712 • UU*>rvTT£/ |

1 892.8650 -.333733995 •011921 351 -.017310162 -•071218166

19 11.13 2 0 -.011 119575 «•.-» 19151089 -.039050233 -•011077683

1919. 1630 . 056915958 - • 135150156 -.058911895 -•03771 1766 .018789510

2006 . 1 C 20 .01 6922 1 51 .-180929757 • 018625392 .028811691 .013829718

2082.13 70 •067029017 •T7I699879 .033657789 . 051515701 • 056 73309 7

2 1 00. 3720 .010832505 •j 52167017 .055273638 .0011888095 •038 1 90492

2 138.5230 .032139173 . -'123 38708 .012027259 .037 1 19055 • 03 84 6862 4 2195,10 70 .016253207 . 1711 I <5 691 . 363563590 .0600581 15 .nAnoQMAc; i 2271.3970 . 05885 1387 .189535 I 77 • 0757 11 152 .07 1367 319 •U/JOO/Ulo n71(ii7'Ui

2289.7 0 20 .091851132 • 1 U6 1 1 1 20 .07 1 655107 . 09 I 507825 no i nloi i

2327 .8530 .07 3581951 •10277638 •075613276 • 0 71 6 5 6181 nano 1 t *> 7 i 2160 • 5560 .01961 2025 • r 36289827 •036687389 .0771 15600

2178.9620 .075067237 •f85993398 .0312 1 2738 . 055001 1 19 .062569380

2517. 1130 • 352268566 .01671801

. 032793193 . 015697727 .011376950

2573.9720 .027566318 ."031510639 .016088838 . 025 1 39950 .01 7986512

2619.7120 .01 7983956 -. 0093103099 .0052761385 .020175887 .0085989928

2668. 222C -.001721330P .125811679 . 0 1 676861 9 .028502609 .01 6598611

2/06,1230 -.025162718 .''01 6C1 3598 — .0091719721 -•012376262 • nUli 1

i £*)7h ' O i1 ua1 o 2763.252T -.021 335 "28 - • n2 1 897515 -.02720761 1 - • U 1 1878 1 08 n9nc.7ui7i

2839.0210 .0081263171 -."331 8012-.0013121116 -.011381 1 17 ni noiiuuno

2857 .55 20 -.010699156 -.1* 10187262 - . 02685 1 272 -.011179730 » 02 JO b J 1 Ob 2895.8230 -.063206853 -.•"'71111806 -.031736790 -.061051519 n C 7 C *iU7U7 • Ob / 5 J 4 Z 4 Z 2952.512 0 -.031 12019C -•r 67820380 -.011387050 -.019780038 _ .047526990

3028.2530 -.057569811 -.i: 62872565 -.039810986 - • 015085283 - •051334669

3016.8120 -.3731381 1

- • 1 0327901 -. 06691 1 567 - • 053330561 •074172318

3085.0130 -.005331 1 17 1 -.05399 1 228 -.0081090301 -.0038300182 • 111 / o V 1 10 6

3 111.8220 -.010025177 -.022867328 -.0016885t58 .0032009305 •0085950226

J £ I f . O 1 •< U "•Ut"3 1 I TOO _ r\'»"*70nO7n •012950051

3236.1520 -.017352360 -.037817021 -.0087965659 •0057510112 .014559976

Table 4: Above are the volume Increments and residuals from the fitted

calibration line for the combined runs 5-8. Data has been

adjusted to have the same zero. The volume 1s given 1n liters and the residuals 1n centimeters.

•12-
4:illlllll + lllllllll + llllxllll + llllSIIII + lllllltll +

• • •

- IN

•

IN IN • •

•

• • • • • •

IN +

• IN "8

• • IN <*>

* <\1 .

• -

IN • IN • —IO

•

IV

IV +

• • IN

• IN + <N • •

0) S- J=

+-> S_o

01 <*-

ro ui

i. 0) o

> *J 2 <u

ro +->

ID O ra> o

. m >- 0> OC o0

• or q 'XQOJ

o >

.— ai a. i

I I I I I I I I * + • •l I I I I l l I i I I l I XI I I l l l I I I I I i i I I I I I I l

SM313WIIN30 NI 1H9I3H

-13-
a: s &. to >— o •—i o • 3: o. +

I I I I g + I I I I x I I I I + I IX i-i o

o o ,• _i a. » i i i i i i i I l i i i i i a

a

<*•• o c >

+ I i i i i i i i i + I I l l I l • l I I I X I I I I I I I I I t I I I S I I I I I I I +

SH313WUN30 NI 1H9I3H -14-
where the subscripts refer to the instruments. The tank

configuration error, E, cancels out since it is the same for both

individual instrument readings and the average of four readings.

Hence, the variance of 5:

Var(f) = 9/16 Var(eJ + (1/16 Var(e.) + 1/16 Var(e ?

) + 1/16 Var ej

Table 5 lists the residual standard deviation, the standard deviation corresponding to measurement errors.

Table 5

Residual Std. Dev.

C7_

Sight Glass

(cm)

.0405

.0208

XR-38

(cm)

.0448

.0203

DDR 6000

[cm")

.0386

.0181

Bell & Howell

CcTj

.0431

.0218

The pooled value of a

e is 0.0204 centimeters. Judging from the

small spread of the four values of estimated je, the assumDtion

of equal precision of the four instruments seems to be justified.

Therefore, for a 17-point calibration of this tank, the uncer- tainty of a point on the calibration line can be expected to be

less than the sum of the bounds to systematic error due to tank

configuration and the maximum width of the 95 percent confidence

band about the calibration line, or equal to 0.091 + 0.027 = 0.118 = 0.12, equivalently 1.4 liters.

In using the calibration line corresponding to an instrument

reading, an additional error of 3 standard deviations of measurement error, or equivalently 0.7 liter, should be added giving a total uncertainty of 2 liters for a tank volume of about 3000

1 iters

- 15 -
Summary and Conclusions

The results of this study demonstrate clearly that the uncertainty of the calibration of the volume-height relationship of a tank

depends both on the calibration techniques and on the actual tank

geometry. The basis for description of a tank should be a simple

geometrical one which adequately accounts for the tank's gross

characteristics, e.g., straight-walled vessels of appropriate

cross section. With the precision available in calibration

techniques and liquid level measuring instruments, the actual

contours of a tank may be represented as the departure of actual

tank geometry from that of the model. The conditions necessary

for detection of such departures are the following:

1. The uncertainty in the volumetric increments used in

the calibration should be considerably smaller than

departure of the actual tank geometry from that of

the model

2. The level detection apparatus should have sufficient

precision to detect departure from the model

geometry.

3. Temperature measurement should be of sufficient

accuracy and precision to contribute zero variability

to the calibration process.

Under these circumstances, two, at the most three, properly designed calibration passes should suffice to generate sufficient

information to characterize actual tank deviations from that of

the geometric model. This study has met these criteria in that

the uncertainty associated with volumetric increment addition and

temperature measurement are an order of magnitude below that of

the level detection instruments.

Based on the knowledge of the actual geometry, relative to a particular set of operating limits, it may be expedient to accept a linear calibration curve, that is, to assume that the tank is

sufficiently well characterized by the geometric model. The con- sequence of such a decision is to take the maximum deviation of

the actual tank geometry from the model geometry as the systematic error associated with the operation of the tank. However,

should the limits of variability for tank operation be reduced,

the information necessary to construct a more descriptive tank

calibration curve is available with little additional effort.

Such a calibration is limited only by the random component of

variability, assuming that the systematic component has been

minimized. The use of the corrections for departure of actual

from model geometry in this case reduces the measurement uncer- tainty of the tank to 1.4 liters.

- 16 -
It would be remiss not to point out a mechanism for circumvention

of the intent of safeguards and accountability practices. The

knowledge of the magnitude and sign of actual tank deviations

from the model allows the possibility for the measured volumes to

be systematically incorrect. Although the uncertainty associated

with a particular tank load may be within accountability limits,

the accumulated uncertainty associated with the total amount of

fluid processed in this manner could quickly become unacceptably

large, exceeding accountability limits. Rectification of this

problem is two-fold: either construct tanks whose geometry

closely fits a simple geometric model or use the actual tank profile as measured by the calibration process. This calibration

concept is most critical when the tank in question is the

accountability tank or tanks for nuclear fuel reprocessing

pi ants

This exercise has clearly demonstrated the physical reality of

the need for temperature correction when a manometer is operated

over a region of thermal gradients. In this case, water was the

manometer fluid, a fluid having a relatively small thermal

expansion coefficient. In the case of manometer oils, the

thermal expansion coefficients are at least twice as large and

may be three to four times that of water for hydrocarbon fluids

of density 0.7 to 0.8 g/cm3

, Not only does this effect influence

calibration operations but also normal operation of the tank.

One would expect additional complication caused by changing

seasons at a plant site which could induce sizeable changes in

the temperature gradient between sections of the manometer.

Sight glass operation which disregards the existence of temperature gradients may contribute significant error to calibration

and normal operation. Problems of this nature are not encountered with el ectromanometers

Although water has been used as the calibration fluid in this

work, any fluid of known density and thermal expansion properties

could be used. Given the commercial availability of apparatus to

measure these parameters rapidly and with sufficient accuracy,

the use of fluids more suitable to a particular process would

seem to pose no great difficulty.

- 17 -
Acknowledgments

The authors wish to express their gratitude to Leon

Carroll for his help with computer programming and data

table preparation and to Mrs. Gertrude Tesler for her

help in the preparation of this manuscript. The

interest and assistance of S.C. Suda, Brookhaven

Technical Support Organization, and P.E. Pontius, Chief

of the Mass and Volume Section are greatly appreciated.

References

[1] Schoonover, R.M. and Houser, J.H. , Pressure Type

Liquid Level Gages, Nat. Bu. Stand. (U.S.) NBS

Report 10396.

[2] Schoonover, R.M. , The Equivalence of Gravimetric

and Volumetric Test Measure Calibration, Nat. Bur.

Stand. (U.S.), NBSIR 74-451 (1974).

[3] Carroll, C.L., Field Comparisons of Steel Surveyors' Tapes, Nat. Bur. Stand. (U.S.) NBSIR 74-451

(1974).

[4] Lembeck, J., The Calibration of Small Volumetric

Laboratory Glassware, Nat. Bur. Stand. (U.S.),

NBSIR 74-461 (1975).

[5] Wagenbreth and Blanke, PTB Mitteilungen (1971).

USCOMM-NBS-OC - 18 -
Appendix 1

Sight Glass Analysis

In practice, the sight glass is used in conjunction with the

length unit by which the enclosed liquid level of a vessel can be

determined. The liquid surface is visible through the tube wall

and the level is compared with the attached length scale. The

visible liquid surface approximates that of the enclosed surface.

When the liquid level is changed, the difference in level is the

difference between two scale readings.

Usually there is a reference level assignment that may coincide

with an empty tank and an arbitrary head volume. Liquid level is

usually expressed as the height above the reference level.

We assume the length scale is correct and without significant an- gular displacement from a vertical attitude. Also, capillary depression and meniscus uniformity are nearly constant over the

sight glass range.

The sight glass can be considered as a manometer with a different

fluid density in each leg due to nonisothermal conditions in the

legs (see fig. 4). At equilibrium, the pressure of each leg must

be the same. Therefore, we can write the following equation:

P

3 is the pressure in the vessel at level H

3

These pressures can be expressed in terms of liquid density,

height, and local acceleration of gravity as follows:

where P 2 is the pressure in the sight glass leg and

p 2 gH

2 = Pl gH

where p 2 =

Pi

=

H =

2

H, =

liquid density in sight glass

liquid density in vessel

meniscus height in sight glass

1 iquid height in vessel

g local acceleration of gravity

- 19 -

A
FIGURE 4; SIGHT GLASS TUBE AND SCALE ARRANGEMENT

- 20 -
Solving for liquid level of interest, H , of the vessel in terms

of the observed sight glass height, H

2

, we have

p 2 H

2 H

1 = —Pi

Obviously the user of the sight glass method for determining

liquid level in a vessel must know the density ratio p z ^\ or force the term to unity (P^P^) by an appropriate technique as discussed below.

If there is a heel volume to the vessel, then there is a corresponding height, H^, that is, a constant level below which the

contents are not observable and the manometer effect is still

present. Then must be estimated by some means and added as a constant to observations of H

l and H

2 for the adjustment of

temperature effects and hence density differences.

Sight Glass Observation

Sight glass observations [4] of liquid level are made by estimating the intersection of a horizontal plane and the length scale.

The plane is tangent to the bottom of the meniscus formed at the

air-liquid interface inside the tube.

Sight Glass Experiment

At first glance the sight glass appears to indicate liquid level

in a tank without second order effects if properly constructed.

In comparing all of the fitted slope values for the various

instruments, calibrations 1-5 show that the sight glass slopes

are systematically larger than the others. This systematic

difference is about 2 parts in 10 3

, a very significant error for

this case.

In our experiment, as in plant operations, the processing tank

may contain liquids at temperatures considerably different from

the surrounding ambient conditions. When the sight glass and

contained liquid are not at tank temperature, an error exists

between the sight glass indicated level and the true liquid level

inside the tank.

In runs 6 - 8, water temperature was measured by an immersed

thermometer inside the sight tube. This experiment indicated the

water in the sight glass was about 12 °C warmer than that in the

tank. The sight glass data were then corrected for this error by

the method based on water temperature measurements. After

- 21 -
adjustment, all calibration slopes for runs 6-8 agree closely.

This verifies that our sight glass data adjustment is

appropriate. However, if the tank contained a liquid of unknown

thermal expansion, another solution which we investigated was successful and is described below. After the last incremental

volume transfer and all pertinent observations were obtained for

runs 6-8, the sight glass was pressurized. The pressure used

exceeded the tank head pressure, thereby forcing the liquid back

inside the tank. When the pressure was removed, the liquid re- turned to the sight glass. Eight to ten such pressure cycles

brought the sight glass and its scale much closer to the tank

temperature as indicated by thermometry. At this time, the sight

glass was observed again. A large change in the sight glass

level was seen as shown below.

Sight Glass Observation

Before Pressure Cycle After Pressure Cycle Tank Temp .

Run 6 294.22 cm @ 21.60 °C 293.75 cm @ 12.70 °C 10.52 °C

Run 7 280.80 cm @ 20.85 °C 280.42 cm @ 12.38 °C 10.75 °C

Run 8 285.81 cm G» 21.61 °C 285.44 cm @ 12.47 °C 11.10 °C

The merit of pressure cycling the sight glass may be judged by

comparing the height difference between the Initial and final

liquid levels in the tank as measured by the XR-38 and the

sight glass. The pressure cycled sight glass value is used for

the final liquid-level measurement. The Initial sight glass

liquid is much closer to that of the tank liquid at that point.

The height differences for each instrument are shown 1n the table

below.

Calculated Height Difference

Sight Glass XR-38 S.G. Minus XR-38

Run 6 267.30 cm 267.37 - .07 cm Run 7 250.70 cm 250.68 - .02 cm Run 8 267.57 cm 267.58 .01 cm

The small differences between the measured heights for the two

instruments shows clearly the effect of differing temperatures in

the tank and sight glass and that the effect may be essentially

eliminated by the use of pressure cycling the sight glass fluid.

Also, this exercise shows clearly that differing temperatures

between the sight glass and the tank fluids introduces a sizable

systematic effect, especially for tall tanks.

When properly used, the sight glass performs to about the same precision as the other instruments tested and is free of serious

bias

- 22 -
Appendix 2. Density Probe Calibration and Use

In essence liquid density measured by head pressure is two determinations of liquid level from bubbler tubes (see fig. 5) at

grossly different depths as explained later on. These pressure

measurements occur at nearly the same time and liquid density is

assumed constant during the period required.

The two observed head pressures, P

l and P , are written as follows:

Pj = p L gL

x and P

2 = P ,_gL

2

Pj - P

2

= p L g(L! - L

2

)

where p l

is liquid density

Lj-Lg is the difference in probe depth

g is the local acceleration of gravity

If the probe depth separation, Lj-L,* 1s known, then p. is calculated from the pressure measurements as follows:

P - P

The value for p^ is in kg/m 3 when

P

1 and P

2 are in pascals

g is meters/sec 2 (as measured at the site of calibration)

Lj - L

2 is in meters.

The probe separation, L,-L2

» can be determined by dimensional

measurement and as reported here by head pressures in a liquid of

known density. We feel the bubbler technique reflects true

orifice behavior and deserves our attention since dimensional

techniques are well known. When the bubbler tubes are assembled

in place, as ours were, the glass tube of figure 3 can be re- placed by a plastic bag. The bag must be supported externally to

maintain a stable liquid level.

The calibration experiment follows the basic liquid level via

head pressure scheme. Distilled water is the liquid of choice.

It is readily available and the density is well characterized

- 23 -
PRESSURIZED

GAS

THERMOMETER

DISTILLED WATER

FIGURE 5: SIMPLIFIED VIEW OF THE CALIBRATION

SCHEME FOR DETERMINING THE ORIFICE

SEPARATION FOR USE IN THE LIQUID

DENSITY MEASUREMENT.

- 24 -
from temperature measurement to 1 part in 10" 5 or better although

to maintain this level of accuracy, all components in contact

with the distilled water must be extremely clean and nonsoluble

in water.

Since the density of water is known sufficiently well, it follows

from equation (1) that:

eq. (2)

This value for L.-l_

2 can be substituted in equation (1) and

unknown liquid densities can now be determined.

The temperature of distilled water must be measured to 0.01 °C

for adequate accuracy of calculated densities. The recent work

of Wagenbreth and Blanke [5] contains the necessary water density

expansion formula with density expressed in cubic meters.

Liquid Density Measurement

During the calibration runs 2-8, the water density was determined after each volume increment was added to the tank by direct

measurement. These determinations were obtained by observing the

differential pressure between two probes using the XR-38. As

described earlier, the pressure probes were installed in sets

comprised of a level probe and one referred to as a density probe

for each pressure gage. The additional pressure measurement

required to determine density was only observed with the set con- nected to the XR-38 pressure gage.

Both probes were connected to each of the supporting braces

closely adjacent to one another. The probe tips were tied together in a manner such that the orifice separation could not be

changed.

Orifice separation was approximately 20 cm to simulate field use where the density measurement is made in the heel area of the

tank. The upper probe was designated the density probe and the

lower probe, the level detector. Occasionally the first volume

increment failed to cover both probes causing a measurement

ommi ssion

Although the data on measured densities are available for runs

2 - 8, we give only the data for run 2 in table 6. These data

are typical of the other runs. Included in the table is a com- parative analysis for runs 2-8. It is seen that the standard

- 25 -
RESIDUAL STANDARD DEVIATIONS (A)

Run No.

DENSITY (B) HEIGHT CO

Calculated Measured Calculated Measured

2 .0386 .517 .000527 .000974

3 .0270 .475 .000554 .000779

4 O 0183 .545 .000270 .001111

5 .0296 .450 .000468 .000880

6 .0145 .351 000525

7 .0066 .499 .000449 001107

8 .0728 .424 .000592 000903

(A) As successive increments of water were added, the temperature

drifted downward and the density drifted upward. Residual

standard deviations are computed from deviations from the

trend line. A typical set of data, run 2, is shown below.

(B) Density in kilogram per cubic meter

(C) Height in meters

* * * * * * * * ******* ****** ******* *****

NUMBER VOLUME CAL. DEN. CAL. HT. MEA. DEN. MEA. HT. m

3 kg/m 3 m kg/m 3 m

1 ,189278 999.315132 .080646 .000000 .000000

2 .567973 999.433502 .416376 998.724243 .416672

3 .946503 999.477394 .749925 998.435822 .750709

4 1.325350 999.482384 1.084740 999.237724 1.085006

5 1.704280 999.488159 1.419691 999.021103 1.420355

6 2.082744 999.498245 1.754563 999.203156 1.755082

7 2.461034 999.515648 2.088275 997.714760 2.092049

8 2.839735 999.519005 2.421954 998.309845 2.424891

9 3.218276 999.526894 2.756424 998.532867 2.759171

Intercept 999.373276 -0.085870 999.063629 -.086207

Slope .019932 .883291 -.075671 .884305

Std. Dev. of Ave. .028082 .000353 .475361 .000827

Std. Dev. of Slope .004990 .000180 .079783 .000397

Residual Std. Dev. .038655 .000527 .517052 .000974

Table 6: Data from run 2 reduced and fitted using both

calculated and measured density for comparison.

- 26 -
deviations of measured density and height are much larger than

those for calculated density and height. This will result in a much larger calibration uncertainty, near the 1 part in 10 s level. The error, eq, in our measured density has two

components, e

Y and e

2

, which are the random error of the XR-38

pressure gage and the systematic error of the assumed probe

separation respectively.

Assuming the systematic component to be small although in our

case it is not, the random component would occur twice for a given density determination. From table 5 we see that the XR-38

has a random component of 0.02 cm (a

e

), therefore e, is estimated

to be 0.040 cm for a probe separation of only 20 cm, about 2 parts in 10 3

.

Obviously, since we calibrated the probe separation via the XR-38

pressure gage, there is also a sizable systematic error, e„. Of

course, repeated calibration or another technique may reduce e 2 to an acceptable magnitude.

For the random component effect on the density determination to

be made comparable to that of the level detection, we need a probe separation of about 2 meters or more. This could be easily

accomplished if a tank at least 2 meters long and 10 cm or more

in diameter were placed inside a tank and used exclusively for

the density measurement. In this way, the small tank could

always be filled from the contents of the main tank after

thorough mixing even when the liquid level, is low.

Alternatively, the application of some other technique may be

more suitable for measuring density.

- 27 -
APPENDIX 3

Gas Head Corrections for Level and Density Determinations

by

C.R. Til ford

Pressure and Vacuum Section

Heat Division

The non-zero density of the gas in the bubbler tubes used to

determine liquid height and density gives rise to gas head cor- corrections to the simple equations generally used with these

measurements. Under conceivable operating conditions, these cor- rections could well exceed the uncertainties reported for the

measurements in this report and, in any case, restrict the operation of the system after it has been calibrated. Expressions for

liquid height and density including gas head corrections will be

derived and the effect of the corrections discussed.

These equations will be derived assuming that the gas density is

linear with pressure (second order effects are at the parts per

million level); the same gas is used in all parts of the system

and its temperature is uniform throughout the system; and account

is taken of effects due to bubble formation at the end of the

probe tips. Effects due to nonl inearity or changes in

calibration of the pressure gages are not considered.

- 28 -
Def ini tions :

The necessary quantities are defined below and illustrated in

figure 6.

Pi s P

2 , p 4 are the absolute pressures at the gages,

p{, P 3 , P^ are the absolute pressures at the probe

tips,

P 2 is the absolute pressure at the liquid

surface,

h is the vertical separation between probe

tip #1 and the liquid surface,

aL is the effective vertical separation

between probe tips number 3 and 4 and is

positive,

Hi is the elevation of pressure gage #1

minus the elevation of probe tip #1,

H 2 is the elevation of pressure gage #2

minus the elevation of probe tip #3,

p is the density of the liquid, and

pj , p 2

, p 3

, p 4 are the gas densities at pressures P ls

P 2 , P 3

, and P^.

Assuming that the density of gas is proportional to pressure, we

have

p. = AP

i (1 = 1 . . . 4). (1)

For air or N 2 at room temperature we have

A — 1.2 X 10" 8 g/cm 3 Pa

« 1.2 X 10" 3 g/cm 3 Atm.

- 29 -
Level Determination

We have

gp

where g is the local acceleration of gravity and p is the average

density of the liquid. Taking gas heads between the appropriate

points in or above the liquid and the gage #1 into account, we

have

p

i = Pi + PjQHi

p

2 = P2 + P 2 9( H i " h)

From the above and using eq. (1) we have

g p

h = P

x + pjgHj - P 2

- P 2 g(Hi - h)

= (Pj - P

2 )(l + AgHj) + P2gh

So

(2)

Note that Pi~P 2 is the differential pressure at the gage; that if

the tank is open to the atmosphere, P 2 is the atmospheric

pressure at the gage and the correction p-p 2 will be about 0.12%,

and that Ag « 1.2 X 10- Vm.

If gas density is ignored, we obtain the commonly used approximation to eq. (2)

gp

(2a)

The effect of the gas density corrections will depend on how the

system is used. In many cases, including the measurements discussed in this report, what is really desired is not the height

of the liquid but the volume of liquid, or more exactly, changes

in the volume. The volume will be a function of h, or of

(Pi-P2)/(p-P2) » which may be expressed as a polynomial. The

coefficients of the polynomial can be determined by calibrating

the tank with known volumes of liquid. If the same gas is used

in both the calibration and operation and the relative elevation

of gage #1 and probe tip #1 is not changed, the correction

(1 + AgHi) will be the same for both calibration and operating

conditions and will drop out. The volume can be expressed as

- 30 -
V = B + C

+ D

(Pi - P 2 ) (p* - P$)1

(P - P 2 ) - P$)

where the quantities with an asterisk are those determined during

the calibration. For a typical right circular cylindrical tank,

such as is considered in this report, the linear term will be by

far the largest.

If we consider this term we see that since the gas density is

much smaller than the liquid density, we can approximate

The quadratic term is at the parts per million level and can be

dropped. The linear term, (p2-p*)/ps will be zero if the gas

composition, temperature and pressure at the top of the tank are

the same during calibration and operation. Under these

conditions, the approximate eq. (2a) can be used for both

calibration and operation. If the tank is pressurized by, for

example, 1 atmosphere after the tank has been calibrated, then

the use of eq. (2a) would result in about a 0.12% error in the

measured height or volume.

Similarly, if the relative elevation of the pressure gage and

probe tip were to be changed by 8 m after the calibration an error, due to changes in the term (1 + AgHj), of about 0.1% would occur in the measured height or volume if the correction in eq.

(2) was not applied.

It is hoped that this discussion will underscore the importance

of not changing the system after it has been calibrated, or of

making proper corrections if conditions are changed.

—p* - pt p* — - - (1 - p*/p)(1 + p

2 / P )

- 31 -
Density Determination

The density of the liquid in eqs. (2) or (2a) can be determined

by measuring the differential pressure across a pair of bubblers

separated by an effective vertical distance aL.

Thus

p -= 11 p

1 gAL

Taking gas heads into account, we have

P 3 = P 3 + P 3 gH 2

Pi = + P^glHa - AL)

Assuming that the same gas is used in both probes and using the

above and eq. (1), we have

pgAL = P 3 + P

3 gH2

- P4 - p 1+ g(H 2 -AL)

= (P 3 - P4KI + AgH2 ) + Plf gAL

So

P =-^gir

i (1 + AgH 2 ) + \ (3)

Again, note that (P3-P4) is the measured differential pressure

and an approximate form of eq. (3) is

(P 3 - PJ

The correction term, p 4 , occurs because the pressure generated by

the column of liquid of height AL is partially offset by the

pressure generated by the corresponding column of gas of density

P4. The correction (1 + AgH2 ), where Ag ~ 1.2 X 10 _t+ /m for air

or N 2 , arises because the different pressures and correspondingly

different gas densities in lines 3 and 4 give rise to different

gas head corrections.

- 32 -
If eqs. (3) or (3a) are to be used with any pretext of accuracy,

lL must be an effective length. This can be determined by making

an in situ calibration of the entire density measuring system

using a liquid of known density, p*, such as water. From eq. (3) we then have

AL = {?

l

' P P (1 + AqH*)

where p* is the density of the qas at the calibration Dressure

Then

(Pa - Pu)(l + AqH 2 )(P* - c t)

P " (P* - Pj) (1 + AgH*) Pl+

If the relative elevation of qage #2 and the Drobe tips are not

changed after calibration (^H^), we can write

(P 3 - PjJ

p = (p* - p*) (c *

"

C V

+ \

(fa - PJ * . 0 * (Pa - p u)

" (P* - P*)

p P ^

" p ^ (P* - P*j

„

(P3

: p* + ( p

. c*)

(Pf - pj) u

^

since, if the densities of the calibration and measured liquids

are approximately the same, (P3-P1J ~ (Pf-PJ) Thus, if P t+ =pJ we could use eq. (3a) for both the calibration and operation.

Unfortunately, p

4 will change as the liquid level changes, or if

the tank is pressurized. Obviously, the liquid level will change

during operation and the error in using eq. (3a) could be

significant for a large tank. As an example, if the liquid level

differs by 8m from the calibration level and eq. (3a) is used,

the measured density will be in error by about 0.1%. The same sort of error will be introduced if the pressure above the liquid

is changed by 1 atmosphere, or if the relative elevation of the

gage and probe tips was changed by 8m after calibration.

Thus, density measurements by the bubbler techniaue with

uncertainties comparable to those obtained in the height

measurements discussed in this report will not be Dossible unless

the exact form of eq. (3) is used and care is taken in changing

the operation of the system after it has been calibrated.

- 33 -
FIGURE 6: SCHEMATIC FOR PRESSURE DISCUSSION PRESENTED

IN APPENDIX 3

- 34 -
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1 PIIRI [CATION DR RFPORT NO

NBSIR 75-900

2« Gov *t Access ion No.

3. Recipient's Accession No.

A TIT! F ANT") SI'RTTTI F

Liquid Level Instrumentation in Volume Calibration

5. Publication Date October 1975

nV* r** p rr at m i n n 1 Iroan i 7afinn f r\f\ 1 CHUlUlUlfc Ul gall 1 Z. al 1U I) UUL

7. AUTHOR(S)

H.H. Ku, J.F. Houser, R.M. Schoonover, and J.R. Whetstone

8. Performing Organ. Report No. NBSIR 75-900

07. rtKr DPR PflD UKMlINu VillVr fXQfZ. UKuAI\ AMI7iZ- AATI1 ivJIN AM \TAkiC INAMt AINU 4MH AUUKcjo AHHD TCC

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract /Grant No.

12. ' "» Sr>r>n '-'l/UllOUl <? r\r ililt n & Oro X—'l K, ull 3n iL 7£- arUl 1i Ull nn .wamp * a ann Q. 1 i vi t*— nmrlprp UuiutCLC '^VJUICSi ArirJr^cc l*-*<*CCl, t t t \S I I Y , w((|tC, ^tat& £-d 7l&\ 1 A J Sponsored in part by:

Brookhaven National Laboratory

Technical Support Organization

Upton, L.I . , New York

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The technique of pressure head measurement for determining

liquid levels in tanks has been used for the intercomparison

of commercially available electromanometers with themselves

and a sight glass. In addition to obtaining intercomparison

information, the high precision of these devices coupled

with that of volumetric transfer techniques demonstrates the

applicability of the calibration method in determining departures of the actual tank geometry from that of a model

straight-walled geometry. It is shown that the calibration

of the volume-to-height relationship of a 3300 liter tank

may be accomplished with an uncertainty in this relationship

of ~ 4 parts in 10,000.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Key Words: Density measurement; electromanometer;

large volume calibration.

18. AVAILABILITY Unlimited

P 1 For Official Distribution. Do Not Release to NTIS

1 1 Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13

Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

37

22. Price

$4.00

USCOMM.DC 29042-P74


^6-191*