NBS10396

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PRESSURE TYPE LIQUID LEVEL GAGES

NATIONAL BUREAU OF STANDARDS,

WASHINGTON, D. C

14 SEP 1971

U.S. Department of Commerce

National Technical Information Service
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U.S. DEPARTMENT OF COMMERCE

Technology Administration

National Technical Information Service

Springfield. VA 22161
NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT

2320190

NBS RE

10 390

PRESSURE TYPE LIQUID LEVEL GAGES

by

R. M. Schoonover

and

J. F. Houser

Sponsored in part by

Atomic Energy Commission

N uciear Material Safeguards Program

This raporl wm |W«p«r*4 M M kccount of work

•TonKirod by tha Utttlad SutM Corommaat. Notthor

tiM United SUUt nor lit* United Siata* Alomk Ewarfy ComntlMion, nor any of thair ampioyaaa, iwa aay of

lhair contraciora, aubcoolraclon, or lltair aoiptoyaai, lakaa any warranty, anpraaa or iihpUad, or awuitiw aay

lacal UabiUty or raapooaiMUty for tha accoracy, conplatanaai or uaafninaw of any Infomatlon, apparatva, product or proem diactoaad. or rapraaanti that tta mm

would not iaffiaM prtvataly owraad righli.

NATIONAL BUREAU OF S tor uM wittrin the Govemmtnl

and reviow. For ttiis reaton, wfwlt or in part, it not autt Burtau ol Standardt, Wathini

tha Raport hat bean specirica'

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

accounlini documants intendad

bjactad to additional avaluation

itint of thla Raport, aitNr in

)ffice ot tho Diractor, National ha Governmant agancy for wtiidi

101 for its own uta.

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
CONTENTS

Page

1. Introduction ^

2. The Experiment ^

3. Deta Reduction * ^

A, Dlacuaalon of Data 9

Uncertainty In the Gran'lmatrlc Testa 12

Uncertainty In the Volumetric Teeta 13

5, Exparlmenta with Wet Walla 1^

6. Recommendat Iona 19

Table I

Appendix 1. The Preaaure Syatem 23
Forward

The Maaa, Length and Volume Section of the National Bureau of

Standards has traditionally been concerned with volumetric

standards. These standards have in turn be >n utilized by the

petroleum industry, either directly or indirectly, to "calibrate"

meters. To a somewhat lesser extent, these standards have been

used by the dairy industry to "calibrate" tark trucks and storage

tanks. Studies over the past few years, in ccnjunction with the

AEC, indicated that such standards may be of use in chemical

processing plants, particularly where invent orief are important.

Generally speaking, in the development of an industry, solutions

to problems are developed which are satisfactory for the moment,

but which do not anticipate future changes in requirements. In

some instances, development and testing is done by many in

unrelated or unrelabCble ways. In this way numerous solutions

to a particular problem are developed, which are adequate perhaps, but which provide no information as to improvements or

limitations of a given technique. At some point in time, it is

highly desirable to conduct at least one carefully controlled

experiment with these factors in mind. The experiment described

in this paper has been done with this express purpose in mind.

This experiment explores the problem of "calibrating" a typical

chemical processing plant. While to sobm extent the problem has

been idealized, the information obtained will provide a sound

basis for judgment. Factors explored include volxunetric and

gravimetric "calibration* methods, and the use of a manometer to

determine liquid level. It is not necessarily intended that the

procedures be adopted by anyone "verbatum”. However, because the

experlatent has been well docuaiented, and because a certain aBX>unt

of exploratory work has been directed toward the study of

limitations, it illustrates the work required to obtain a certain

level of performance. It should be clear that if certain factors

are omitted, the performance will be degraded. On the other

h-^md, more attention to certain details will result in further

improvement. It is specifically recosmended that volusMtric

"calibration" procedures be adopted wherever possible. The

degree of detail required is obviously a matter of local

judgment.
1. INTRODHCTIOH

Although a liquid l^vel gaug« saasuraa the heleht of a liquid

in a tank, the uaer ordinarily interpreta observations terns

cf total voluse of liquid present. In the most uncritical cases

he may assume constant horizontal cross section area from top to

bottom in which case his total \olume Is a linear function of his

ip«s t ick** observation. In mors critical applications he must

detmrmine tank geometry from calibration, and If the tanka have

large top-to>hottom dimensions he may have to consider the

effects of tht compressibility of the liquid on its density. In

thla latter case he should consider carefully whether hie

Intereata lie in knowledge of contained voliae or contained mass.

The ARC has long used observations on manometer syatema to

Infer the height of the liquid surface In a tank. Such systems

depend upon the fact that the pressure difference, ^P, between

two orifices In a tank, one abo ee and one below the liquid

surface, la very nearly proportional to the height, H, of the

surface above the Immersed orifice; thus

H • kAP. [1]

Although there ere simpler systems of equlvalsnt accuracy, the

osa of a properly designed manoneter system has one outstanding

vlrtus, that Is, the high aasuranee against accidental escape of

dangeronely radioactive liquid.

It will be shown that k In the foregoing equation la very

nearly

1
vhsra g is ths sccelerstion of gravity. and and the

dansitlcs of tha liquid and tha gaa in the tank. The parcantage

change in g with H it only 1110 par foot which Is well beyond the

capabilities of this type aianometer systcv to detect. Inasmuch as liquids are not parfcctlv incompraacible » will vary with H.

However, our interests lie in tanks 10 to 2^^ feet high, and under

such circumstances, we are Justified In Ignoring the few hundred

pares par million par atmosphere compressibility of even the most

compraaslbla liquids. In soma AEC systems. a second manometer

(with both orifices Immersed) is used to obtain a measure of

liquid density, and in such cases, this source of uncertainty Is

partly eliminated. The density of the gas abo\m the liquid

surface* is s function of its temperature, gas analysis end

press ure

.

Msnomatric systems are very practical ones, and there is a vide selection of apparatus appropriate to their use. The

studies reported here were addressed to two questions:

1. What ere the ultimate capabilities (accuracy and

precision) of such systemsf

2. What is the minim

w

calibration effort ncceesary to

achieve such performance?

2. THE EXPERIMFHT

Figure 1 shove the details of the axperlmentel set-up. Th>

tank vae obtslnsd from an old MBS axparimant. Aftar thorough

sandblasting it vas coatad with apoxy on tha intarior and a foam

inaulatlng layar vaa appliad to tha axtarior. It vas squipped

vith a hook for vaighing at tha top. Btd>bla levels (not ahovn)

were sttaehsd in both horitontal orthogonal dirsetlons. It was 4 fast in diamater and about 14 1/2 fast from top to bottom. Tha

tvo liquid lavals illustrated ehow the vertical excursions of the

2
HOOK FOR

3
aurfaca daring tha axperlaant. Tha Invar axcvr^lon Halt was

about OB# Inch abova tha affactlva lanal of tha Invar orlflca.

Froa the botton to the Invar axcursion levels tha tank

contained abnot 30 gallona (nominal). From tha lover to the

upper axcuralon level, it contained 800 gallons (nonlnal). The

praanura ayatan for naa8uraac''t of la described In Appendix 1.

Tha basic azparlaant conslatad sf filling tha tank in a aarlaa at kaovn volunatrlc Incrananta and recording tha height

indicated by tha aanonater syaten after the addition of each

incraaant. These increments vere knovn because they vere poured

(duapad) froB our standard volunatrlc vaaaals. The assunad

dallvary volaaaa* of theaa vaaaala van baaed upon saveral prior

calibration axparlaanta In which water was the calibration

liquid. This daaandad that we ana water as a calibration liquid

In those filling axparlaants. Tha uoc of water yielded another

bonus. By virtue of knowledge of the temperature-dena ity

relationship for water, we were able to Infer density from a slnple teaperature neasureaent, so we avoided the effort required

to asks Independent density oeasurenents on the liquid.

The first Inerenent in each filling experiment was 30 gallons

(nominal) from our standard 30 gallon test vessel. This 30

gallons of water "heel’* placed the Internal liquid surface about

an Inch above the lower nanoneter orifice. Following this, eight

Increments of 100 gallons (nonlnal) each wa* added from our 100

gallon standard test vessel. The last (eighth) of the 100 gallon

Increnents raised the liquid surface In the tank to about three

Inches below the upper nanomater orifice.

eg^^gy etendard vessel has two volunetric calibration constants.

The "delivery volune" is the volone of water which Is poured^iX£n

the vessel when It is awptlsd, and the "containnant volume Is

the volsne of water which must be poured Into the "dry vessel to

fill It, These two constants are not equal.

4
Thlfl Increnental filling experiment was conducted nine times.

In conjunction with three of these filling experlmantSf the

fourth, fifth and sixth, the tanV was weighed before filling

(when empty) and after the last 100 gallon Increment (tank full).

The difference between these two weighings gave us an Independent

measure of the total water poured into the tank during the

filling experiments. This provided us with a check on our skill

in the conduct of the experiment as well as upon the accuracy of

our standard teat vessels.

Prior to three of thr filllnr, experiments the seventh, eighth

ad ninth, che Internal tank walls were thoroughly dried, and

pri,r o all othars, thay were thoroughly wotted by water. In a practical situation tha tank walla ara naver either thoroughly

or thoroughly dry. The differences In the experimental

results derived In theaa teats provides us with the volumetric

limits on dlffsrsnces associsted with walls of varying degrees of

wetness.

It la noted that the filling increments from che standard

teat vasaelo ware said to be **nomlnal ly** 30 or 100 gallons rather

than ’’exactly'* 30 or 100 gallons. This Is because we have found

that the error associsted with failure to fill a standard test

vessal to a particular level on its neck gauge la significantly

greater than tha error associated with reading the neck level

actually schlevad on this gauga. Inssaiuch as tha experiment la

not conductad under thermostat conditions, it is nscessary to

measure the temperature of the water In the test vessel before It

is poured Into the tank. After the dump Into the tank each

voluaetric Increaient is thoroughly mixed with previously dumpad

incrsasnts by comprsased air blown into tha tank from below.

After mixing the (new) temperature of the water in the tank was

maaaurad.

Tha asparlBantal data which must ba takan and tha various

calibration and physical eenatanta which uuat ba availabla ara

liscad in tha following aaction on Data Raductlon.

5
3. DATA REDUCTION

Th€ step In the date reduction Is to determine the mess

of w«t*;r In eacii tb" nine dumps, to Mg, This Is obtained

frow the product rf the volume cf water In each dump, to Vg

,

multiplied by the «fen«»lfv of the water In each dump to pg . The volumes are ''htalned from the cal 11 ration coefl^lrlents

reforrlnft to the 'itandord vessel associated with each dump, the

neck reading and the water temperature. Subscripts refer to the

duan nuaber.

»N <Jn ‘ W'“

where J_ the vessel volume at the base of the

neck at 20*C

k„ * the volume of each neck division at 2n*C

N

N • the neck reading

N

Tjj - the water temperature In the jug prior

to the dump

B • the volumetric coefficient of expansion

(per *C) of the jug

The water density is approxlaated by • nodlflcation of the TaylorTllton formula for the density of water which. It la believed,

makes It suitable for use with tap water rather than distilled

water, and provides density in grams/ cn^ rather than grans/ml.

PM

1

(Tj, - 3.9863)^_

508929.2 * Th + 288.9414

68.12963 .999973

I + QXIO

L [3]

6
wher« Q • th« solid iapurlcles (In ppa) in the tap water.

An adequate eatlnate nay be obtained froa the

local water company.

After calculation of and p

"n

*

''n^n t«l

From

table of

duap,

a table of values of

values of total aaa

to , by adding the

to It Is possible to devise a of water In the tank after each

asses of all previous duaps, thus:

Rj - Ml

R- • Ml + M3

R

M

nZM

1

1

[^A]

As stated above, the teaperature of water In each duap, to

is carefully aeasured before It is poured out of the standard

into the tank. The experlaent Is conducted with cap water

(whose Caaperatara variaa widely) and the axperlasnt is conducted

a In non*tbaraost ated- apacea. Values of Ti to aay vary by

aavaral dagroaa. Whan the water Is duaped into the tank under

calibration, although the aass la constant. Its teaparature

ehaagaa froa to a new value In the tank . This new value,

S|l , is aaaaurad by a th«raoaatar In the tank which Is observed

after thorough alxlng of the water in the tank.

The total voluae of water In the tank after each dump, Di to

la caleulatad froa the quotient of total aasa, R

1 to ^divided

7
by the (new) density of water in the tank, to T)^ , associatf^d

with the (new) water tenpe rat ure ,

. D to is calculated

from equation 3 bv substituting S„ for T„, then

n N

The volumes to U9 refer to the water in the tank from its

bottom to the heiRht of the liquid surface, to Hq o»hich 'ill

be calculated from manometer data). Uj^ to 1« vnlld />- 1 . experimental water temperatures S to Sq. It Is equally correct

to say that U to Uq are the volumes of the tank from the bottom

to levels H to Hq when the tank la at temperatures to , since the walls of the cank follow the water temperature v^ry

precisely. To find the volume of the tank, to Uq , at 20*r

from the bottom levels d to Hq

where ^ is the linear temperature coefficient of expansion of

The onlv calculation remalninR is that of the he'*chts of the

liquid surface. Equation 1 shows that we eenuire information on the density of the liquid end the density of the gas IN ADPITION

TO ftP, The liquid density, Dj,, wee calculated above for usa in

« Ujj[l +(20)(20 - S^)] [ 6 ]

the tank.

[ 7 ]
vhere t^^ g«B temperature

p “ barometric presaure

n r^ relative humidity

The calculation of heights to Is mad* by

\

vhere Is the manometer indication corrected '

2 aa neceaaary to yield dynes/cm

g Is the local acceleration of gravity

The calibration la a two»coluvn table showing heights of

liquid surface* * alongaid* associated values of tank volume

at 20*C* . As previously stated the calibration experiment was

conducted nine times. The experimental data* reduced as •feacribed above* la presented In table 1 which shows associated

values of and W^.

Por clarity* the above-described data reduction format Is

diagrammed in Figure 2. The figure also Indicates a sat of appropriate and Internally consistent units for the various required

data parameters.

4. Discussion OF DATA

In this experiment the primary effort was not In the

calibration of the 830 gallon tank* but* rather to determine the

capabilities of ths gsneral type of syetem which we set-up for

teat. Accordingly* the experimental set-up was quite

artificial in terms of a working system. For example* we made

temperature measurements within the tank so that we could

9
THE

COMPLETE

CALIBRATION

CONSISTS

OFA

TABULATION

OF

VALUES

OFH

ALONGSIDE

THE

ASSOCIATED

VALUES

OF

W
ealeulat* th« liquid dunalty dlractly rafhar than dapaad upon a aacoud aanoBatar. Wa aalaccad a vary naarly cylindrical tank ao that thara would ba very faw dlacontlnultlea In our praaaura--

halght curva. Ua did not uaa a at ata-of-the-art ualghlng ayataa

Inaanuch aa our gravlaetrlc data vaa Intended only aa a protection agalnat groea blundara In our volumetric data.

Aa pointed out prevloualy the tank vat weighed lamadlataly

before and after each of the 4th, 5th and 6 th filling aeriaa.

The difference between theae **tank empty** and **tank full**

welghinga ylelda a naasure of the true amount of water dumped

into the main tank during each filling aarlea. Theae three

valuaa will ba different from one another inaanuch aa no effort

la node to pour In a particular anount of water In each dump.

After the ninth dump in each of theae three aarlea the

temperature of the water In the tank, S9 , was uaed to calculate

the denelty, Dg , In the tank, which when combined with knowledge

of the maaaured maaa of water yielded a calculated volume for the

water in the nominally full tank.

Thia calculated volnme waa compared to the maaaured volume 0^,

baaed upon the aum of all nine volumetric Incremental dumpa in

the aeriea. Thla comparative data ia ahown helow with all

volumaa reduced to gallona at temoerature S^.

Bun Temp

o. *€(89)

4 11.769 "C

5 10.673

6 IU.193

eat. atd. dev. “ 0.072 gallona

VoluBM

(Calc.- awaaured)

0.077 gallona

0.006

0.128

11
V« Initially fait that va had aada a blundar In tha

graalaatrlc (that la, welghlnt) chaek on tha 6th ran, and wa

aarloualy conaldarad a rapaat of this oart of tha axparlnant.

Hovarar, tha arror banda aaaoel*tad vlrh tha voluaatrlc and

gravlnatrlc taata overlapped, ao we could ocly conclude that tha

axparltaant vaa valid. Calculation of tha uncart ilntr banda la

dlacuaaad balov.

A. Dncartalntv In tha Gravlaatrlc Taata.

Tha uncartalnty In a welRhlng axparlaant la ganarally said to

bo the eua of tha uncartalnty In tha atandard walghta uaad In tha

axparlnant plua thrae tlnaa tha randon arror of tha walghlng

axparlnant. Tha randon conponnnt la uaually aacrlbad to tha

randon variability In tha balance. Thla variability la

ordinarily obtainad fron tha peat hlatory of work with tha

balanca, and la Judgad fron tha variability In tha balance

Indication of tha dlffaranca batwaan two loada whan conparad

aavaral tlnaa. In the praaant axparlnant aavaral obaarvatlona

wara nada on tha dlffaranca batwaan tha anpty tank and a 2500

pound atandard waight. Also aavaral obaarvatlona wara nada on

tha dlffaranca batwaan tha tank "fall" and a 10,000 pound

atandard weight. Fron thaaa axparlnanta and nueh pravloua work

with thla baianca, wa aatlnata Ita randon variability to ba about

0,1 pound.

Tha uncartalnty of tha atandard walghta uaad waa about .08

pounda for tha 2500 pound waight and 0.1 pounds for tha 10000

pound waight. iaaad on tha convantlon atatad above, tha

uncartalnty In tha "anpty" waight of tha tank la about .38 pounda

and tha "full" waight about .40 pounca. On tha dlf faranca

batwaan waight "anpty" and "full" tha uncartalnty la aatlnatad to

.08 <f .10 a .4 « .58 pounda

which aaounta to about .06 gallons.

12
B Uncertainty In the Volunetrlc Tettn

The uncertainty in the volumetric transfer value la almost

entirely contained in the uncertainty in the aaaumed values of

the **dellvery** volumes of the two standard vasaela (one 100

•alien and one 30 gallon) used in flllint the main 830 gallon

tank. Thli ignorea minor or nnlikaly errors such aa evaporation

loaaea and miscounting of the number of dumps. The uncertainty

in the delivery volume of the standard vessels contains two

significant componentst

a) The first component is three tines the standard

deviation of tha calibration enperlaant, which is

parferned anough tines to provide a ralisbla value of

this standard daviation. Also involvad here is the

uncertainty in tha standard waighta used in the

calibration, hovevar thesa are small to the extant of

insignificance. Thp uncertainty in the delivery volume

of the 100 gallon vassal is 1.38 cubic inches and for

the 30 gallon 0.60 inchas. Inaaauch as tha 100 gallon

vassal was used sight times there la a valua of 11.04

cubic inchas plus 0.60 for the 30 gallon (uaed only

once). This component totals up to 11.64 cubic inches

or 0.05 gallon.

b) Tha sacond conponant is the product of the uncertainty

in the temperature coefficient of volumetric expansion

of tha standard vassals (about 4 parts per million for

each vaaael) multi pliad by the difference in

temperature between the calibration experiments (about

20*0 and the average temperature of the experiments of

interest (about 10*C) so the value of this error

component is 4(20-10) " 40 parts per million. This

fraction of 830 gallons amounts to .03 gallons.

13
Th* aaa of th«i« two coapononts (.05 gallono plus .03

gallona) la 0.08 galleaa. Tha Baxiaua dlffaranca batwaan

voluaatrle aod gravlaatrlc axparlaanta occarrsid in run 6, during

which run tha dlffaranca waa 0.I2B gallona. If now wa look at

tha auB of tha uncartalnt laa aaaoelatud with thaaa two procaduraa

(0.08 gallona for tha voluaatrlc taata PLUS 0.06 gallona for tha

grawlsatric taata tetallag 0.14 gallona) « wa eoneluda that tha

obaarvad dlffarencaa, 0.128 gallona. If aaallar than tha EXPICTED

MAXIMUM VALUE of 0.14 gallona. ao that both axpar4.Banta ara

alld. A graph of tha run 6 data would ahov tha arror banda of

tha two axparlaanta owarlapping.

Hawing concludad that tha axpariaantal work waa walld. tha

woluaatrlc data will now ba eoaaldarad In datail. It ahould ba

polntad out that two antlraly dlffarant woloaatrle axparlaanta

warn parfornad -- tha flrat alx filling axparlaanta (In which tha

tank walla warn wat) and tha laat thraa (la which tha tank walla

wara drp).

Exparlnanta with Wat WAlla.

Flgaraa 3. 4 and 5A ara pleta of tha data praaantad la Tabla

1. Tha horlxontal axaa In aach caaa rapraaant tha woluaa of

water In tha tank aa calculatad froa tha ana of tha woluaatrlc

iacraaanta pourad Into tha tank froa onr ataadard waaaala. Tha

unita ara la litara at 20*C. Plotted wartlcally ara tha halghta

la cantlaatara calculatad froa tha AP obaarwationa • Tha dotted

llnaa j£g. fitted. They ara conatant alepa llnaa rapraaantlng

tha axnactad rata of height changa with woluaa change, and baaed

upon tha aaauaptlon of parfactlw wartleal tank walla (that la,

conatant croaa aactlon area tank).

14
HCPIE 3

tM •

l»4

LSt

C5I

SSOh

OM

*• ®

IIS.S IIS.« MS.T

ist.et

IM CS •

I3«.t4 >

I9«.C9 -

I9«.tt '

I9«.tl •

I3« SO >

5 tn dump

0«t

MtT.7 iter.i itert lott.o
FIGURE A

i .dv'

tmj 87ut tTM.i im.« tms tmt trtsr

1ft
Ficon ik

e«*.7« ' M« 74 -

t<» 7 7

•

t«».7t - Mt 7% - Mt 74

ti» 75

tt» 7Sr

t«t.7l -

*•• 70

*•••• -

L5*4I.« 9141.7

04«

9tm. dump

» * ^ 9Mi.e 9I44.9 9«4t.O 9l4t.l 914*. * 5l4t.9

ESTIMATE OF

"EXPECTED" DIFFERENCE

O

JL ^

J- ^ DUMPS

I

I

I

I

I

I 17
Data froa ruoi I thru VI vara uaad to aatlaate tha atandard

davlatlon of a raadlng of tha aanoaatrlc Inat ruaanCatlon

.

Straight llnca were fitted to aeta of alx data polnta for each of

the nine duapa , yielding a realdual atandard deviation of O.OOS

CB with 36 dagreea of freedom. It la aaaumed that reading arrora

are the aaBe at different voiune levels* although the data from

the flrat and second duBpa showed a analler scatter.

Tha atandard deviation of tha volume Baaauraaenta la known by

independent axperlaent to be about 0.004 liters* or equivalently

about one*>tenth of the estimated standard deviation of the

aanoaater readings. Hence errors from this source may be assuntd

to be negligible.*

Ue now look to the observed difference in liquid level height

between filling experimenta conducted on the tank with Internal

aurfacea Initially wet and Initially dry. We would expect the

obaerved height to be lower under Initially dry conditiona than

under Initially wet conditions. Additionally* we would expect

thla difference to increase with Increasing dumps. Finally*

after a fairly long period of tlae* we would expect that all

water initially clinging to the walls would hava drained down

into the aaln body of water in the tank* and when this process la

coBpleta* va would expect the obaerved difference in height to

reaain constant regardleaa of tha nuabar of duaps. An

examination of Flgura SB verifies that our observed data follows

these expeettd clrcuastancea . It is noted chat during the last

three duaps (7th, 8th and 9th) that the height difference is

about 0.046 caa which represents a volume difference (the cross

aaction area of tha tank is about 1*1 square aacars) of about 506

ca^. Thla is for e tank of about 800 gallons. For a 100 gallon

tank* the difference between "containment** and **dellvery** voluaaa

la about 50 ca^. The ratio of 50:506 is roughly proportional to

thin voluaa ratio (100:800) which iadleatas strongly that there

is ao gross error ic our aeaaaraaant of tha 0.046 height

diffaraace betwaea "wet** sad "dry" testa.

*Thla paragraph by Dr. H.Ku froa the MBS Applied Matheaatlca Dlv.

18
Rg commendations .

1. The uncertainty in the "delivery volume" of a 100 gallon

vessel is stated In the report to be .Oft cubic Inches

made up of an 0.05 comnonent and an 0.03 component. The

second component Is associated with the uncertainty in

the coefficient of expansion of the vessel. This

component could be reduced to near zero by direct measurement of this coefficient which would reduce the

uncertainty In a volumetric calibration to tliat

associated with a gravimetric calibration.

2. The pressure gage performed, admirably well in these

tests. While it is not suggested that a secondary

device such as a bourdon tube be used to calibrate a primary Instrument such as a U-tube manometer, Ic occurs

to us that the bourdon instrument might well serve the

purpose of a portable tee'e Instrumant to check the

overall system responre of the numerous U tube systems

already employed by AEC.

3. Although water is almost universally used as a calibrating fluid, there may be some virtues in using the fluid

which a tank will he called upon to store in a working

situation. Ws believe, without proof, that the delivery

volume of a standard tent vessel would change slightly

with different fluids, so special calibrations would be

required on such vessels if they are to be employed in

large tank calibrations. The parameters of interest are

probably the tendency of the fluid to cling to the

vessel wall, viscosity, surface tension and density.

Inasmuch aa the AEC tanka of Interast hers are used to

store dangerous fluids, this procedure would be quite

Impractical

.

19
The volutne of a tank aa a function of liquid level la a function of tank geonetry, which is relatively constant

regardleaa of the contained liquid, and water will more

than adequately define tank geometry. This knowledge

ay be wasted in a working situation, e.g. when the

tank Is filled with a dangerously radioactive slurry,

if the astuaptlons upon which the measurement system is

baaed are not perfectly achieved. There are two such

assumpt Ions

:

1. that the density gradients In the contained

fluid are Insignificantly s .all after compressed

air mixing

2. that Che effective vertical distance between the

orifices associated with the density measurement

manometer is well known.

These two assumptions are subject to experimental verl*

flcatlon with only minor modifications to hardware and

water calibration procedures. In which a switch to distilled water may be required.

It is our understanding that AEC tanks are equipped

with two manometers -- one for measuring /.ontalned

fluid density (with both orifices immersed) and one for

meaauring liquid level (with one orifice immersed). If

all three immersed orifices are cut to the same

geometry and a valve system (external to the tank) can

connect any two orifices. Immersed or exposed, together

into a manometer configuration. It would be possible to

obtain six independent manometers. Three of these

manometers would have both orifices Immersed and would

therefore be capable of measuring the contained fluid

density, and three would have one orifice exposed and

would therefore be capable of measHring liquid level.

20
The validity of the density aeasureaents Is based upon

our knowledge of the effective vertical separation cf

Che Imnersed orifices. In a water tallbraclon situation

we can utilize our knowledge of the density of water to

determine these effective values. In a working neaaure-

# ent situation we can obtain three values of density and

If the Immersed orifices are suitably placed

(vertically), any differences in calculated values of

fluid density can .'lert the operator to the necessity

for additional compr.-saed air mixing. By additional

valve manipulation It will be possible to obtain three

values of liquid level, the average of which Is probably

more rrelia than a single value.

This general technique may be expanded upon by the addition of orifices and Improved datP handling.

The general working relationship stated In equation 1

u .

«<»1, - »e>

la written in slightly dlffarant farm for the density

meaauring manometer (a). Thus

where Hj la the effective vertical separation of the

orifices and the externally measured pressure

difference. When these two aquations are combined it is

evident that the fluid density, per ae, la of little

Importance, but that the validity of H as a function of

dP depends almost directly on our skill in meaauring

and P^.

AP

H

" Hj " *®G

21
TABLE I

K (CBS)

Volunc

(llcerf

)

H (CBS)

Volunc

(llteril

2. .^310000 113.534 2.5410000 113.616

36.C620000 492.136 36.0700000 492.137

69. 3870000 870. 744 69.3950000 870.670

102.8400000 1249.298 102.8390000 1249.170

136.2570000 1627.960 R;:n I 136.2470000 1627.721

169.6620000 2006.570 169.6370000 2006.198

203.1340000 2385.145 203.1050000 2384.765

236.4460000 2763.714 236.4140000 2763.309

269.7890000 3142.293 269.7520000 3141.909

2.5400000 113.601' 2.5020000 113.605

36.0700000 492.144 36.0280000 492.191

69.3900000 870.714 69.3600000 870.751

102.8480000 1249.289 102.8000000 1249.268

136.2580000 1627.871 Run 11 136.2030000 1627.773

169.6710000 2006.624 169.6040000 2006.306

203.1470000 2385.277 203.0660000 2384.865

236.4470000 2763.702 236.3710000 2763.370

269.7750000 3142.218 269.7050000 3141.834

2.S3VOOOO 113.592 2.4940000 113.552

36.0720000 492.217 36.0240000 492.065

69.3930000 870.771 69.3550000 870.662

102.8460000 1249.325 102.8040000 1249.279

136.2580000 1627.933 Run III 136.2100000 1627.874

169.6500000 2006.418 169.5910000 2006.222

203.1230000 2384.969 203.0420000 2384.635

236.4370000 2763.554 236.3460000 2763.174

269.7700000 3142.055 269.6780000 3141.620

2.5340000 113.553 2.5060000 113.590

36.0650000 492.086 36.0390000 492.190

69.3880000 870.689 69.3630000 870.709

102.8380000 1249.254 102.7980000 1249.190

136.2410000 1627.794 R«n IV 136.2000000 1627.735

169.6420000 2006.368 169.6010000 2006.326

203.1150000 2384.997 203.0590000 2384.830

236.4380000 2763.698 236.3710000 2763.443

269.7700000 3142.226 269.7070000 3141.946

2.5350000 113.594

36.0680000 492.222

69.3960000 870.806

102.8260000 1249.172

136.2270000 1627.667 Run V

169.6240000 2006.167

203.0670000 2384.500

236.4240000 2763.548

269.7640000

Run VI

Run VII

Run VIII

Run IX

22
APPENDIX 1. THE PXESSDEE SYSTEM

Plgu re 1 !• « diegrev of our e::perlnent«l set-up. For

clarity, the two aaaurlng legs of the aanoaeter aysteB are

croaa-hatched . The porpoae and uae of the non»croaa-hatchad

plumbing will be explained below. The Inverted U'-trap In the X

leg aervea to prevent accidental Iona of liquid from the tank.

The vertical height of the Y lag la H-fh where R la the

vertical diatance from the leearaed orifice In the X leg to the

Inatantaneoua position of the liquid surface, and h, from thle

surface to the exposed orifice. If we assuna that the avaraga

dansity of the gas In the T lag, o^, la a^ual to that In the tank

above the liquid surface, then the significant prassora applied

to the X Input of the differential pressure gauge la gHPi^'t-ghp^

and to the y Input, g (H-fh)PQ where g la tha local acceleration

of gravity. If the eeasurad pressure difference Is Ap then

. .

Bo’

end with adaquete values of g, and it is possible to infer

the height of the liquid surface in the tank based upon a eeasuraaent of ^P.

Tha AEC has long used such systaes for Indicating H in tanks

containing dengerouslv radioactive liquids. It has haan

custoeary to use U-tube aanoeeters for Indicatien of ^P, however

we rejected mercury eanoeetara in this service due to their lack

of sensitivity. Water eanoeeter* are aore than .an order sore

sensitive but their large bulk (12 or aore feet high depending

upon tha tank height) and their cost (Rasa estlaatvd $6000) lad

os to select a quarts bourdon tube davice asnufactured by Ruska.

23
This dsvice photo-slsctricslly tenses the bourdon tube deflection

end (using the photo-electric voltegr ss an error signal) servos

the genevs-gesr digital read-out to an appropriate value. The

sensitivity of this device lies between wercury and water

Bianonetars.

For any value of H, the liquid in the tank will penetrate the

open leg of the trap In the X leg. If valve B Is cracked open

and ve allow nitrogen to flow out of Ita tank, the liquid will be

forced out of the open leg and the nitrogen will bubble out of

the lawersed orifice and rise to the surface of the liquid.

Under these clrcuastancea the pressure at X will be higher than

that at t*'e orifice by an awount which Is s function of the

viscosity and voluae of gas flowing and aystaa geoaetry. If the

valve B Is throttled down to a level at which the gas flow rate

Is essentially zero, the pressure rise at X (above the orifice

pressure) Is essentially zero so that the pressure at X Is

Insignificantly different from that at the orifice.

The bourdon tube la an elaatlc device and, like all auch

devlcea, requires exercise before use to stabilize Its **sero**.

This Is accoapllshed by closing valve A and opening C which

raplaees the orifice laaersed in the tank liquid by an orifice

iaaarsed In aareury. laasaueh as the aercury Is 13 tiaes as dense as the tank liquid, the depth of the orifice In aercury

ttsad be only 1/13 the depth of Che tank in order to raise the

pressure at X to an aaount equivalent to that associated with a "full” tank. To drop the pressure at X to an aaount equivalent

to an "eapty" tank valve D la opened long enough for the bourdon

Indicator to drop to zero. After a few such cycles, the

Indicator sere Is stabilised (at soae .^alue other than sero). To

correct this situation valves R and G are closed and E and f

opened. This places ataospheric pressure et the bourdon tube

level at both X and T, and Che Indicator dials are aechanically

24
Aft«r rttttclfig thft to tht position ahova In Flgnra 1 and adjuatlng B for slov nitrogan flow, the ayacaa provided

reliable data.

The adjttstaant of valve B vaa the subject of conelderabla

study, and we observed the systea with B adjusted to provide

bubble formation rates of several per aacond to as slowly as 1/3

bubble par ainuta. At rapid rates (more than 8/ainuta)) the

litjald sarfaeo in the tank is kept in tnrbnlant wave notion at

aaplitudas of 1/8 inches clearly visible to the naked eye.

InasBuch as the bourdon tube aanoneter was sensitive to changes

in aurfaca height of about 1/100 inch, it was lapossible with a turbulent snrfeee to obtain good observations. as the bubble

rate vaa reduced, surface turbulence died down, and at about 8

bubbles per minute the systea performed nicely. We found that

the preseurs pattern with time was about as illustrated In Figure

6. The pressure would commence building up immedietely after the

lose of a bubble, would then attain a maximum value proportional

to H, would then begin to decreaae, and after e kiaall retreat

from maximum would drop sharply as the bubble broke away from the

orifice. We watched the bobble formation in a clear glass

container and believe that the decrease in pressure just before

breakawsy is associated with the horlsontal increase in bubble

sise (and decrease in bubble depth). We did net have a praaouro

recorder so the curves shown in Figure 6 are highly subjective,

but we believe they are representative of true conditions. It is

significant that the maximum pressure observed in cycle was quite

reproducible, and the data used in the calibration was t aaimum

pg^waure achieved . We finally settled on 4 bubbles par minute aa

ou.' "standard” and all calibration data vaa taken at this bubble

rate.

As H changed, the setting of valve B (to obtain a rate of

4/minote) changed, but the proper adjustment was highly

proportional to height and we found that we were able to predict

25
PRESSURE

PRESSURE DECREASE BETWEEN

MAXIMUM AND THE INSTANT OF

BUBBLE BREAKAWAY WAS VARIABLE

WAS EXTREMELY VARUBLE

<^TIME (SUCCESSIVE BUBBLES)

Figur« 6

UNSATISFACTORY

ORIFICE

|"cOPPER PIPE

MANOMETER TUBES

FLAT SURFACE

SATISFACTORY

ORIFICE —FILED AWAY TO

SHARPEN EDGE

. » SB Figure 7
th« Astttlar position of thm st^a which woul4 adjact thv^

rata to 4 /b1b«

Va alao fooad that tha oriflea ahoald aot contain horlsontal

flat aarfaeaa* baeauaa tha daeraaaa In praaaura, rafarrad to

abora, waa auch graatar and aaeh aera varlabla with auch

aurtaeaa. Flgura 7 ahowa tha orlflca eonf Igoratloa actually

uaad •

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