Osnıanga^i Ünivürsiîesi Müh. Mim. Fak. Dergısi. C X, S. î. S997Eng. &Arch. Fac.. Osmangazi Uııiversily. Vol. X. No. l, 1997

DESIGNAND CALIBRA TION OF A ROTAMETER SET FORMEASUREMENT OF GAS FLOWS

Menderes LEVENT'

ABSTRACT : This study tiiscusses design and calibration of a rolameter sel farmeasıırement ofgasflows. in Ihis study, various gases (such as hydrogen, carbon clioxide,methane, nitrogm and argon) are usedfor calibralion oflhe rotameter set. Each rotameteru'as calibraled wilh om or lwo gases and resıılting gas flmvrates Ihrough ıhe rolamelers(R/, R2 and R3) compared with ecıch oîher according to îheir moleçulur weigh[.Tha gases suppliedfrom high pressure gas bollles and passed to each rotamelers. Outlet ofîhc rotameîers are connected to needîe valves (see Figure î). With îhe needîe vaîves, outletgas flo\vs of each rotcımeter were adjusted before passing to a bubble flowmeter . Eachlime. gas fio\vs fhrough the bubbie jîowmeter were monitored and residence time wasrecorded hy ifsing a stop watch.

KE YWÖRDS : Rotameter, bubbîe flowmeter, desıgn of rotameters

GAZ AKIŞLARININ ÖLÇÜMÜ İÇİN BİR ROTAMETRESETİNÎN DÎZA YNI VE KALİBRASYONU

ÖZET : Bu çalışmada, gaz akışlarımn ölçümü için bir roîametre setinm dizaynı vekaUbrasyonumı yapılmıştır. Bu çalışmada, farklı gazlar (örneğin, hidrojen, karbon dioksit,metan, azot ve argon), rotametre setinin kaîihrasyonu için kullanıldı. Her bir rotametre biryada iki gazla kalibre edildi ve rolametreterden (Rl. R2 ve R3) geçen gaz akışları molekülugırhklanna göre birbirleriyle karşüaştınidı.Gazlar yüksek basınçlı gaz silindirîerinden sağlandı ve herbir roîametreden geçirildi.Rotametre çıkışları iğne vanalarına birleştirildi (şekil l 'e hakiniz). Ignefaçma/kapama/vanalarıyk. her bir rotametrenin çıkış gaz debileri, bir kabarcıkîı akışmetreye geçmedenönce ayarlandı. Her defasında, kabarcıkh akışmetreden geçen gaz akışları gözlendi vegazların kubarcıklı akışmetreden geçiş süreleri bir kronometre yardımıyla kaydedildi.

ANAHTAR KELİMELER : Rotametre, kabarcıklı ahymelre, rolametrelerin dizaynı

Menderes L^M WT, Atatürk Üniversitefi Mühendislik FaküUesİ Kimya Mühendisîiği BöH'tmü,25240 Erzurum

4-

/. INTRODVCTION

The main purpose ofthis study is îo design and calıbrate of an experimental flow system far

measurement of feed gases of an analysis systern, a reactor system and a ciiffusion celi.

A rotameter consisrs essentially of a solİd float or pfumb-bob shaped rotor which is free to

move vertically in a transparent tapered tube. The fluid to be metered enters at the bottom,

narrow end of the tube and moves upvvard, passing to some point through the armulus

formed between the float and inside wall ofthe tube. As the flow increases the Pıoal rises.

thereby providing a greater cross-sectional area ofîhe annulus.

in order to keep the float centered in the fluid and sensİtîve to flow changes, small diagonai

slots are usualîy provided under its head, which cause the float to rotate slow!y. At any

particular rate of now the float assumes a definite position in the tube, its location being

indicated by means ofa graduaîed scate etched on the tube[t],

Since the tube is tapered, the annular cross-sectional area for flow is variable. Increasing

flow rates do not, therefore, increase the pressure drop across the float but cause the fîoat to

takc higher positions in the tube. The fluid flows vertically upward through the tapered

rotameîer tube, and the float comes to equilibrium at a point vvhere the annular flow area is

such that the velocity increase has produced the necessary pressure difference.

The pressure difference, P| - P;, is found by making a force balance on the stationary float.

The downward force caused by graviîy is balanced by the upward buoyant force plus the

force exerted by the pressure clifference across the float caused by the velocity increase in

the annular constriction,

Thus we write,

Pr V,g<

and

p, -p, =

= pV,.^- + A, (P, -P,)c

v, (p, -p)gArS,

(l)

(2)

48

Bernoulli's equation for the orifice meler is adapted to the rotameter by defining a

coeffıcient CD by

u, = c»2 g. (PI-P.) (3)

Ubris the velocity inthe annLilarconstriction. The substitutionofEq. (2) into Eq. (3)gives;

wu» = c,,2 gV, (p, -p)

A, . p

Ifthe area ofthe annulus between the float and tube is A^ and the cross-sectional area ofthe

tube is A[, then equation (4) gives the mass flow G for a rotameter, hence[ l,2,6,7, 8];

G = C^A;2 g V, (p, -pj

A J l -A,

(5)

The Reynoîds number is defıned as;

(D-D, )U,, p,.,R. = (6)

tf the rotameter is already calibrated for one gas, say at 760 mmHg and we wish to change

the gas at a different pressure, then[3, 4, 5];

G». = Co A,2gV, (p, - p,,,. )p,.,

A,.; l -

(7)

If the calibration is expressed as volume flovv, Q = G / p, the division of Equation (5) by

equation (7) gives:

G 'J^v p,.,.

""ly 'f p,. r « Pr (8)

For caîibration, we wish to use a bubbie flowmeter at temperature Ta and gas pressure

pb = Paıııü, iiıı - ^H, U-

wtlere PH, O ls î^e pressure of water vapoar in the taboraîory. As the

mass flow G = Q p, where p is measured at Pbubbi^ Tambieni' then;

y ^ ü.. x '":

o. o.. J^xp^ 1<)|"-"V ...

Ihı. ' üi^ deı~ı>îi}v>, [vv nnınui-tiumıl ıı. ı ıliL' tnolerıılüi . ^.. <. 'iülıt, s. y. tS pres>. ıırc an(. ! !!-!\I'!^L'I>

ni'üpt )i'ıiüiuu uı IİK' ı. 'ı. ı. ': lı;[Tiper<:î!-Lire. Theretoi'e. EqLiat!on (9) can be '-Anik'n çiş lo!îov\s <)i:

o - y.. ,i r- . .M"L x ^- ̂ -^-"""V f\,, u, " MI,,,,,,, " T. ' P,,,,,,,,

dul

Caiihratton of Rotamctcrs

TİK- flo^ (.'il'yas ihroush tîıe t-oîameter is.

n,. - n, ... |ÜBİM» x -~, ;--"- i alld °u>Mt! = Oiim» x l

i h. - h,

h,,(li!

\Ve can pİoî Q,(.-. İ)<' (.^ R'juımcteî' agah-ist QP,. \K) of the bubbîc ilovvıııetei'. 'J'lıe flovv U-iî'ot'^h

îhr caiibmtcd rotan'ieîer for i\ uas scalc j'Cctüing and îc'npci'ti'Lii'e corî"ection ibr tlıc sanit.' gch

?nay be (.'alcLilaîeci Sroi'n îiıe lbiSt)wing eqi ialıüii [9],

y.,,,.., - y,,,,,,,,...,,. -- -l'^-hl-i-^ f1 ".. -''-L

(l.

//. TEsrsE'r

An e'vperimenirtl i>yslem vvas desİyned as i'iyLire l. Various v. 'd'ı flows tı'üîu iıiüh pressure

hoities (A) feci to a rotameteı- set (Bl Tbe !1o\vs ol' !ndi\'ıdual gnses tİu'ougİı each roîameter

aı'e reüulated by meaııs 0!' needle \:dl\'es (C). Then. Jlovv df each gas at difierenı

experiincnts is pa.sSî. 'cl tu a bubble tlovvmetcr (D) 'AİIİCİI havin^ a so;ıp i-eseî-vior (T;) ;mci

moıınted on a suppon (F).

50

ö oh

CH4

fas BoitlR!

w

î

H2

Ot

co;

"î j UES73 ?7^n

Efî w17TO31 IW//H fnrrı-1

Rotomrief s«t

(8)

^»ud*»(tın

-A-

-l*».

-e^

Needlefolres

pannel

(O

Fisure l. Schemaîic diagram ofrotameter set.

The measurement of the wet gas flows were taken from the bubble flowmeter against each

scale reading of the rotameters. The gas flow was gradually increased through each

rotameter and corresponding wet gas fiows were taken from the bubble meter. The wet gas

flows, QBFMW where then converted to dry gas flows, which is QBFMD. Then tor eachrotameter. the rotameter readings were drawn against QBFMD values (see Figures 2 to 9).

///. DISCUSSION OF RESULTS

This study is a typical practical study tor applied chemistry , chemical engineering and other

engineering areas. The desıgned experİmental system can be used for measurements of feed

gas flows of any reacting system without doing any fürther calibratİon studİes fbr some

particular reactions. By using this type of experimental systems. various gas flows can be

regulated and measured et'fıciently before doing any dit'fusion, reaction and gas analysis

studies,

5!

1SO.OO -ı

^ 120.00 -jd

acc:

S so. oo -^£ 3

öor

40.00 -l

0. 000. 60

Calibratîon condîtions:746 mmHg and 20 °C

,'JJ,-!T T J!3TZ1"I. rJ' ' L'-li' L'J ' ' l. '-tlTTT")'1 ı'L'Ji ı 1. 1 ı ı 11 ı ı ı ı

100.00 200.00 300.00 400.00 SOO'.OÖ GOO'.OOFLOW RATE, Oamo (cc/mfn)'

Figure 2. Calibration curve ofthe rotameter R3 for measurement ofhydrogen flow.

According to Figure 2. the rotameter readings and dry gas (QBFMD> Howrates having a linear

relaîion. The rotameter R3. having a scale range of 10 tol50. and correspondip. g floıv range

ofhydrogen at the bubble flowmeter is 42-545 cc/min. The measurement ofvery small gasüov.'s was altered because the rotameter is suitable only far a certain range of gas flows.

The calibration conditions of the rotameter for hydrogen were 746 mmHg abs. 20 °C(see Figure 2).

As shown on Figure 3, the rotameter readings and dry gas(QeFMD) flowates having anapproximate linear relation as graph RCM- The calibration curve of the rotameter for

methane shows a slıght variation from linearity. From this curve, the gas fîo\vTates of

methane wil] be read against the rotameter scale readings. The measurement range of gasflows is 29 cc/min upto 364 cc/min and corresponding rotameter scale reading will be 10 to

150. The calibration conditions ofrotameter R2 for methane were 746 mmHg. abs. and 20 °C.

52

1 60. 00 -ı

^ 120. 00 ^

§0^.

S 80. 00 -3E

o0£:

-4.0. 00 -\

0. 00

RCH^

Calîbratfon Conditîons.:74-6 mmHg and 20 "C

o. oo ' ' '' ' 'ı'o'o'. do ' ' ' ' z'ob'. od ' '. ' ' s'pb'. öd 400. 00FLOW RATE, OBFMD (cc/min)

Figure 3. Calibration curve ofthe rotameter R2 for measurement ofmethane flow.

Figure 4 shows calibration curve of nitrogen for the rotameter R l. As seen on graph RN;,the actuat flowra[e ofnitrogen through the rotameter Rl is not greather than 200 cc/min for

maximum rotameter scale reading of 200. On Figure 4. there is a linear relation between

rotameter reading and actual flowrate of nitrogen. The molecular ıveight of nitrogen is

heavier than the molecular weight of hydrogen and methane, so the flov^Tates of nitrogen

through the rotameters will be less than both flowrates of hydrogen and methane.

Figure 5 shows rotameter readings against the carbon dioxide flowrates through therotameter R3. The rotameter reading and the floıvrate ofCO; having an approximate linear

relation this means that resulted calibralion curve slightly differs from linearity as seen on

graph Rco2. From this curve, the flouTates of CO; through Ihe same rotameter can be

deîermined tor the various experimental conditions offeature experimental studies.

200.00 -ı

^ 150.00 ^Q

scc

S 100.00f-ÜJ

iö

50. 00

R N3

Caiİbrotion Conditîons:746 mmHg and 20 °C

0. 000.00

f 'ı l ı v-ı- r ı ı ı50. 00

"fi'T|i l ııı ıı ı'iji ı ı ı ı'rı l ı'l100.00 150.00 200'. 00

FLOVV RATE, OBFMO (cc/min)

Figure 4. Calibratioa curve ofthe rotameter Rl for measurement ofnitrogen flow.

On Figure 6 the calibration curve of argon gas was presented far the rotameter R l as a

function of flovvrate. For a rotameter scale range of O to 160, a flowrate of O upto 200

cc/min ofargon was passed through the rotameter R l.

The flonıates ofnitrogen and argon through the rotameter Rl are presented on Figure 7. As

seenon graphs RlıN;, and RI(A, | , the flov/rates ofnitrogen Ihrough rotameter-Rl is higher

Ihan the flowrates ofargon because the ınolecular ıveight ofnitrogen is less than argon. The

calibration condilions ot'the rolameter Rl tor nitrogen and argon gases in this experiment

are 746 mmHg and 20 °C.

FIowrates ofcarbon dioxide. methane and hydrogen through the rotameters R2 and R3 are

represented on Figure 8. The floıvrales of hydrogen is higher than the flowrates of methane

and carbon dioxide for same roîameter scaîe readinys. The calibration conditions for this

etperiment were 746 mmHg and 20 "C.

54

1 SO.OO

^3. ı. zo. oo -I

Q=:

s

BO. OO -j

-4.0. 00 -i

Rı

Callbfatlon CondIttonB:.7Se77-mmHa and 23. SO -C

°'°°o. Ao ' '' ' ' 'so. 'o'o' ' '_._' 'ı'oo'. öd . ./ . 'ısö'. o^ri_ÖW RATE. OBFMD (cc/min

200. 00

Figure 5. Calibration curve ofthe rotametcr R3 lor measurement ofcarbon dioxideflow.

1 60. 00 -)

^ 1 20. 00 -!

CtT

S ao. oo 9tj

oar

-4-0. 00 -İ

Calîbration Condîtîons:74© mmHg and 20.5 "C

o. <!>6 ' ' ' '' ' so. üb' ' ' ' r^ıb'o'. 66 ' . 'ı'5'o'. o6^FI_ÖW RATE, QSFMO (cc/min:

200. 00

Figure 6. Calibration curve ofthe rotameter Rl for measurement ofargon flow.

55

200.00

O 150.00o

wLJen

g100.00 -l

o

lCt:

o_lLL.

50. 00 -!

0.000. 00

Calibratİon Condİtions:746 mmHg and 20 °C

T-]-l-1111 -T80.004Ö.OÖ BO. OO . ' ' ' . {z'O^O'O'

ROTAMETER READINGS

Figure 7. Calibration curves ofthe rotameters Rl, R3 fer measurement ofnitrogenand argon fiows.

Flomates ofhydrogen, methane, niîrogen, carbon dio.tide and argon are represented againstthe rolameter readings of Rl, R2 and R3 on Figure 9. Aş seen on graph, the f1owrates ofhydrogen through the rotameters are higher than floıvrates of other four gases, bccausehydrogen is lighter than other gases. Flowrates of carbon dioxide and argon through therotameters are less (han floıvrates of hydrogen, methane and nitrogen. The calibralionconditions for this experiment n'ere 756 mmHg and 20 °C.

The calibration curves ofeach gas will be quite useful fer any experimental studies ofgasanalysis of a reacting system and a diffiısion system with same gases and rotanıeter set infeature. in case of different experimental conditions with same rotameter set. there is noneedlo use the bubble flowmeter for measurementsofeachgasflow at the exit of each

56

160. 00 -ı

CS 120. 00 -i

i^

30^

tlj 80. 00 "|

-<o

40. 00 -1 Calibration Conditions:746 mmHg ond 20 °C

0.00 . )"m'"rT ı ı T-r-ı'"ı-rTT-T ı'r'ı rT-r'T'T-t-ı T-n-TTn'TT I"TII'T!'IIIIİ ıın |i ı fi ı ı 11 ı [0. 00 100,00 200.00 300.00 400.00 500.00 600.00

FLOW RATE OF GASES (CC/MIN)

Fİ^Lirc 8, Calihî-atiün curves oftlıe rolan-ıei. ers RIJ<2 <ın<l R3 tor nıeasLirentenıs of

carbon dioxide, nıetlıane ancl lıydrofieıı fiows.

ur->

ic5

.4-00. 00 -3

300. 00 -3

200.00 -3

loo. oo -3

o-öo

«_a-a-u_p R .1 CCH.̂ -)R 2 ÇH2'R3 ÇCOÎ2)R1 (N2)R.3 (Ar)'

d i b rot! o n condltlona;

756 mm H g arıd 20 °C

.<1--.-^

4-Ü.ÖO £10. 00 1 20. 00ROTAMETETR READINGS

Figııre 9. Calibration cıırves ofthc i'olameîers Rl) R2 and R3 for measureıııuıts ofSıydi-ogen, mcthane, nitt'ogeıı, carbon dioxkİe asıci aı-gon flows.

rnlameıer smce JİLIS llaıv rate., ı\'ıll be fuund in İIK] ol' tho.sc ^aiibjiilıoıı cıınc's and

mmıneiers yc'ıde s'eaıiiıiüs.

IV. CO\CLUSKWS

So f,u. ııı ıhis stuıly. a roıamctcr sel M. I.S tlesigııed ;uıd calibraıed tor mea.surenıenıs ol' ya',

tloıv. s. Oases sııpplıed Irom high pressure bolllcs and passed tlırotıgh each rulanıeur atvanous tiınes. Uuıiıiş expenıne]itaı sıudy. each gas nowrates throuKh thc rotameters are

leacl via a bubble tlınvnıeler agaiıısl nrtaııuter scale rcading. '['lıcn. irom recordecl u'el sas

Howrales. ılıe aclııal dry yas flonratcs arc caiculaed. )-'inal!y. oblained actual uas flınvrates

are graphicuily represcnted as Figuı-cs 2 lo 9,

NOMENCLA TÜREVr voluniL' ofl'îtiat Cm )

pt densıty of fiııaî (ky/'m''}A| nuı\imunı cı-oss-sectiomıi arü'd of flt);ıt (m )A; area »flhe anııulus bclıvcen the floaı and lube (m ')(r m;ıss t1o\\ tor a rol. ımeter (S^s/nı. s)Cn draü coeffîcıenl

D dinmeter oftııhe . it level ol'noat im)D,- m^imum Jiîimeter ot'Hoat (îr;)proı Jaısity oi'gas ut ı-otameîer (kg/m }A| cross-sectional arca ofthe tiibe (nı )pi çi den.Sity of relerence gas ('kg/nT')\\\y pressLire ol'vvater vapour in iaboraturyî., tiıi, K;ıii asnbiünl lenıperaLut-e (C)Pr,.. ı ı-derence pre.ssuı-e (har)p,, i^h ^ıs jire^sLii-e Jt thc bubbie nıe'ci- fbariM,, ı molecular \veigin ul'gases at ihc ı-L'fcrence condttions (k^/k.Lî. nıol)M;^ molecLitar vveıyht ofgases ar îhe hııhble flnvvmeter conditinns (SsK/ky-mo!)! biibb y<.ıs t. empeı'LitLire at the hiibl-ıle novvmeter cnndilinns (°C)i

r,-]' l^ Lt;nıpeı-aturri al Üıe relerence conditions (l1 C)

l'1,,,, pres.suce ol îhe aas in tlıc rotametcr (bar)Qm-M\\ voiumL-tnc tlcnv ofgas in tiıe bubble flovvmcter (nr/s)Qiîi, \ın corrected bubhie f1o\vmeter rcaciing Jbr correspcııuliı-ıy vvatcr va]ioıu' (m /s)h(ı burumelric pressure (bar)ilmi, gau^e pressure oi'the rol. ametcr (bnr)iii.120 waler vapour pressure at lctboı-atüi-y tempcratuı-e (bar)QsMk- sc^ie reaciin^ ol'.üases in rotatncterQ,ıciit;ıi actuaE voiıın-ıctric }1o\\ ot'yases Ihrougiı tlıe rotamcu'i-s (m /.s)

58

REFERENCES

[l] E.M. Schoenbom, Jr. and A. P. Colbum, The Flow Mechanism and Performance ofThe Rotameter, American Institute ofChemical Engineers, Ohio Meeting, pp. 359-389,1939.

[2] M.C. Coleman, Variable Arca Flow Meters, Trans. lnsl. Chem. Engrs.,\. 3a,, pp. 339-350,1956.

[3] JJ. Martin, Calibration of Rotameters, Chemica! Engineering Progress, pp. 338-342,1949.

[4] H.H. Dijstelbergen, Rotameter Dynamics, Chemical Engmeering Selence, pp. 853-865,1964.

[5] G. S. Harrison and W.D. Armstrong, The frequency response of rotameters, ChemicalEngineering Selence, pp. 253-259, 1960.

[6] J.M. Coulson and J.F. Richardson, Chemical Engineering, Vol. I, 4 Ed., PergamonPress, Oxford, 1990.

[7] C.O. Bennett and J.E. Myers, Momentum, Heat and Mass Transfer, 3 .Ed., Mc0raw-Hill Book Comp., London, 1982.

[8] N. De Nevers, Fluid Mechanics far Chemical Engineers, 2 . Ed., McGravv-Hill Inc.,Paris, 1991.

[9] M. Levent, A Microreactor far The Determination of Intrinsic Kinetics on Catalysts,PhD Thesis, University ofWales, Swansea, United Kingdom, 283 pages, 1994.