CE427 - CHEMICAL ENGINEERING LABORATORY III FALL 2004 CONTRACTION COEFFICIENTS AND TANK DRAINING

Transcription

1 CE47 - CHEMICAL ENGINEERING LABORATORY III FALL 004 CONTRACTION COEFFICIENTS AND TANK DRAINING Skill Outcoms: In complting this particular xprimnt, th studnt should dvlop or improv mastry of th following skills: Ability to safly oprat th Tank Draining apparatus locatd in 11 Jarvis Ability to dtrmin th Fanning friction factor for smooth pip. Ability to apply a mchanical nrgy balanc to th draining of liquid from a tank. Dfinition of a contraction cofficint and ability to stimat cofficints from mpirical formulas Undrstand th diffrnc btwn a sharp-dgd and a roundd contraction. Ability to dtrmin uncrtainty limits for physical masurmnts and to us rror propagation to dtrmin uncrtainty limits for calculatd valus Ability to us uncrtainty limits to draw conclusions from data Objctivs: 1.) Estimat th contraction cofficint at th xit of th tank, for both th larg and small tank locatd in 11 Jarvis..) Compar prdictd drain tims to masurd drain tims. 3.) Dtrmin th ffct, if any, of th lngth of drain pip on th draining tim of a tank. Systm: Two tanks locatd in 11 Jarvis hav diamtrs of inchs and 4.0 inchs. Th two tanks hav xit lins that ar rplacabl with 0.49 inch diamtr tubs having diffrnt lngths. Th lngths availabl ar approximatly 6, 1, 4, 36, 48, 60, and 7 inchs long. Thr ar two typs of contraction assmblis that can b placd on ithr of th tanks. On is sharp-dgd and th othr is roundd. Th tanks can b filld with watr using a pump and plugs for th drain lins ar availabl. A prssur transducr, locatd at th tank xit, transmits data to a PC running a LabViw program which rcords th watr lvl as a function of tim as th tank drains.

2 Thory: If th tank systm is opratd as shown in th figur blow, th flow in, F, is sufficint to maintain th lvl in th tank at H inchs whil th tank is bing draind through a pip of lngth L. F H L In this stady stat situation, Brnoulli s quation with friction taks th form: V V 4 flv V L + H = Kc + K + + (1) g g gd g Whr L = lngth of drain pip H = liquid lvl abov th bottom of th tank K c = Contraction loss cofficint K = Expansion loss cofficint (at xit) V = vlocity in drain tub

3 g = acclration of fr fall f = Fanning friction factor d = drain pip diamtr Th loss cofficints and th Fanning friction factor ar discussd in Chaptr 5 of McCab, Smith, and Harriott (M,S,&H) and it is xpctd that th xprimntr will consult th txt for furthr information. For th systm in this assignmnt, th fluid laving th pip is somwhat confind sinc it is a fr jt (it dos not spray out as soon as it lavs th tub xit). Thrfor, K is small and can b nglctd. Equation (1) can b mor compactly writtn as: 4 fl V L + H = [1 + Kc + ] () d g If th tank is draining without an inlt flow, thn an unstady stat matrial balanc on th tank and xit pip givs: S V b dh = Sa (3) dt (not that th minus sign is ndd bcaus th drivativ is ngativ) S a and S b ar th crosssctional aras of th tank and th drain pip, rspctivly and it is somtims convnint to dfin th paramtr,?, as follows: S d β = b = whr D= Tank diamtr. (4) S D a Substitution for V from Eqn.() into Eqn. (3), rarrangmnt, and intgration yild: t H 1 α dt = β H + 0 Hi dh L (5) Whr t = drain tim H i = initial liquid lvl H = final liquid dpth 4 fl 1 α = (1 + K c + )( ) d g Aftr intgration, w obtain: α t = { H i + L H + β L} (6) 3

4 (In th intgration of qn (5) it was assumd that th friction factor, f, is a constant throughout th draining procss. Explain why this is valid) Commnts and Itms to Considr Dtrmination of Contraction Cofficints: It can b sn from Eqn (1) that if thr is no drain pip, L is zro, th friction factor trm in th pip is zro, and K c is th on rmaining unknown. Thus, in a stady stat run, with watr flowing into and out of th tank at th sam rat, a stady stat lvl, H, can b masurd. Th flow rat can b masurd by collcting watr in a buckt ovr a timd intrval. Hnc th contraction cofficint can b calculatd. Howvr, du to considrabl spraying of watr in th actual xprimntal systm whn no drain pip is usd, it is not fasibl to calculat th contraction cofficint in this mannr. On mthod (but not th only mthod) to ovrcom this complication is to prform a sris of tsts with th two shortst xit pips. By assuming a linar rlationship btwn flow rat and pip lngth nar zro pip lngth, th data can b xtrapolatd to dtrmin th flow rat that would xist whn L=0. 1. Dtrmin th contraction cofficint for both tanks. Rmmbr, th typ of contraction is diffrnt for ach tank.. Us a buckt and stop watch to mak th flow rat masurmnts. 3. Tak at last thr radings at ach flow rat using both th 6 inch and 1 inch drain pips. Try to maintain th stady stat watr lvl th sam for all runs. 4. Compar th K c s you obtaind to litratur valus for sharp-dg and roundd contractions. Provid possibl xplanations for your rsults. Includ uncrtainty limits for th K c s you dtrmind. (Hint: whil an mpirical formula for sharp-dgd contraction is givn in MS&H, a contraction loss cofficint for a roundd xit must b found in anothr sourc) Drain Tim Masurmnts: For masurmnts of drain tim, initially fill th tanks to th ovrflow lin whil plugging th drain tub. Thn rmov th plug whil simultanously starting th data acquisition systm to rcord th drain tim. 1) Us both tanks and at last 4 drain tubs. Obtain at last thr radings for ach tub. ) Bcaus it is difficult to dtrmin xactly whn th tank is mpty, rcord th tim to drain to a consistnt dpth (1 or inchs) abov th bottom of th tank. 4

5 3) Obtain prdictd drain tims using Eqn (6). Not that you will nd to stimat th friction factor. To do this, you will nd to calculat th avrag vlocity of th watr laving th tub basd on th volum of watr in th tank at th bginning and how long it took for it to rach th bottom. 4) How do th masurd valus compar to thos prdictd? Includ uncrtainty limits for both your masurd and prdictd drain tims. 5) Dos changing th pip lngth significantly altr th flow rat masurd in th rang of your xprimnts? Rfrncs 1. McCab, Smith, and Harriott, Unit Oprations of Chmical Enginring, 6 th Edition, McGraw- Hill, Prry, R.H. and D.W. Grn (ds.), Chmical Enginr s Handbook, 7 th d., McGraw-Hill,