EAT 223Thermofluids and Engine

Tutorial Seven

Question 1

Water at 15oC (density = 999.1"kg1m3 and pt = 1.138 x t0 3kg/nrs) is flcwing steadily in a 5.0cnr

diameter 30m long pipe made of stainless steel at an average discharge of 9L/s. Determine

a) The pressure drop,

b) The head loss, and

c) The pumping power requirement to overcome this pressure loss.

.4ssuutlstiotts I The flr:rlr is steailS' and iucr"nnpr,r:siir1e. 2 Tlre ettiarcr eil-ects ar* negli-aib1e" alrl tlnrc llie flor.", is full1'cler,elop*<i, 3 fhe pipe in.,ol-;es no cot:t]t]nrftr such as bendr. r'a1res. atiti ccrmrector:. { Tlic pil;irig rectior iLilclr-rs non"{":rk clelicei *rch as puu:i:s aud ftu'biles.

Proper{ies The elslsitl' aud d1'rrauric r-isco;ri1 of -,i'atel are g:iler lo be p = !-rF9.1 kqjru: aud r: = I 1-1fi:.1*-3 itg.'ut.t.rerpectir:e13,. The louglurels af :tainlei', stee{ is fJ.D*f aun.

"{rrn{i,sri First n:e caiculale rilre ar,erag: r,rlocil..'ald tle Reyrcii{s u*r:ti;er to d€ielnilre ihe tlw, resiirre:

r =!-.'l- il: t-+ .;'U.(r-i ruil -l

;i'il , irOi..] l:g in r rtJ. q.i-l ,tl 5 rir.,l '.,r-i r1J , ..r[=-,.. l"l3$xltr-3kgrrn.l

il'hich il grratrr thau 4l')$tl. Therefole. th* ilor: is turbrileni. fher*laiir,e ferlrlulrss aftlie prire is

\\iarrr'D=5cin

tr = .1{.: it:

9 L:s

-,._)' 1{.i-tLt_, rr,-SJji/---a:tL,ii i1\ i!1

Tlie fu"ictiol fact'u c;ui be deter:i:.irred f'orn ihe l{o*d1' chart. t-ir-n tn iir"oid th* leatliue error. 1r'e deie:nd"ue it ilour t1i*

{'slebi+ok equ*tior} rr;irr-s irr eqrutirir roilrr ioi'aa iterad',-e scitrme),

I ^., li fj :-i! | I i+ iu-'t :.5i. j -- f ll.r0l

i.f -l -1.: 8.e ,i.I i .i"l

-t -l : l.{ul r 10'1t.1 i

It gir,*i.X= S.Sl5 j]+. Tireu th; prersLtf- ili"op. hearl kxr;. nird tlir leqnil'ed piit.r,er iryut btcome

.tr,=lpr = 1- ,r- =0.il1,{q{

'lfittr iirg'r'-l'-ttttr-ti + 5sJttrrir: --]lt\ l-!3, r=i,,rri. li"pa,100ilt a

-L "'D : ---'"*.fi5n1 3 11*f0kgnr.rsj, lkN,rrrl\P. I f'l iftrrr tli(lrrritl

i:, = -- | 1' =(r.1rl<t)J---'i" ' '''..' -- -10.2 m" itr J) ig 0.1t5 oi :(q.gl nrjsr I

Fr*oe = k3P= fil.{,r{i9r}iJ,'.r.}i1fllr.i fif.:i;ffi i=O.SA4 kW

Thelefcrle. u:.:iirl 1:+r.:r uritut iil the nulrriutt a."C.9*J Llf i; ireeti.rcl ie i.-:rifr.sl:'re tire f ictiorr*l issie* iu the pipe.

Lu\rllsioil fire iiiclion llrctor coulci nh* br'det*rmired *nri.l,v iorn tire e::piir'it i{a*land ielatirru. It touid give.f =0.11:;4" u'ld{r i-i *it}icier:ttrrv clrrie trr 0.f115q.1. A1ro. tire il'i.ciir:rr: ihct+r eolrertrrorir-iiis i{-: s = tt ir thir cil;e is {t.L}l561.r'"}iic1tirrclicirte'ri1af$tainle5ssr*tlpi1resirrthiscasecariLlee.ssLuttcr1totleslttr.rot1rlriit}rnrlettot.irfahtrttl]+'.,*.

;.rilrr.erirr1:r':ttte|etrtrilredisthenrec1rIr}ica1pr.;l.elthair:eedslcrbeiriri:artedtt.'ltIretuicl.ihis dn': iol]tliltll iuefflcielcl: tlr: eilttlicai r:ou'er i11Llut 1\iil be er,*lr urore rlne to ll]ot*r ineillcienc--.'.

Question

EAT 223Therrnofluids and Engine

Question 2

Consider a fully developed laminar flow in a circular pipe. lf the viscosity of the fluid is reduced

by half by heating while the flow rate is maintained, how does the head loss changes?

Ansl3'sit In tr{l,v rntlrl*peil lirrninnr lkin, itt a cirrllar pipr. ihe pl'ersur* la:r ani:l the henii I*:i ;rre eii'eu t:;r'-

- -il iJ tr' IP' -ll rlt- I-l1J - ' a'r,l"'t L" {}' - rB ptrD-

\\iren tire florr rafe ancl lhn'. ti:r ar'*uge le!:cirr' ar* helcl cor,itaili. tire heacl L'i:i becornr: prcptulirxal to r irceisi['.There fcrre. f he head lass il reduce6l fu1 fu;1lf 1"'|1".1i tire liscori{11. of the fluitl is Lednced bv hnlll

lli"rcsssion Tifs result is iroi vnlid ibr tulhulent flcr'- r"'ul_r: for laiiflar tlo',v. It is al:c rot r.nlid ibL trarfn.:r flow rrsiruiijlroils.,itere tlr enffa$cr l*lsih rft'rctr ar'* lot ueslisiljle ,

Question 3

Consider a laminar flow of air in a circular pipe with perfectly smooth surfaces. Do you tirink the

friction factor for this flow is zero? Explain.

Jrr*{r'srt Frrirg lamimi fl*:r al air i* ,l eiictiar pipe uitir peil,-itl.y ili}filtli suiacfr. thr frtction faiior is fit}i z.rc

b*ilur *f the n*-;lip bour**r-r, e**rlitiau. rihicl: uxrit ircirl ei'et i,ir p:lfictl;; tiricsth s11rl'arei.

nfirrrsirur lir,e cnniprrr* the iiicii*ir ihct+r ibl rr:ugh aucl inklrih -{iulac:i. r*ug1'cr;i hai no rii*et on Si*lioit ftrt*rrir fulli dri*lop;d t,uunar pipe t)0,.r'rnleri tli* rouglu,"rs heiglrt ii',:t1;\'lin'F€. Frit nulrtdtni pipe ilon. h.*trie'",ei.

ioushileri rcr'1,511oun1t impacti tire fi"irticu lhcf*r,

Question 4

Hcw does surface roughness affect the pi'essure dr-cp in a pipc if the fl':w is turbuierrt? \,Vhat

w ruld lour fespcnse be if the flow w as larninar?

Jlla{t,'rl'i1trnu"lrri]errtfc'..l..rlrbesrvitirrtrllg}rsr::thces}rai"eirruc1rlrigiteifitticrlfii:'orrttri.irrihefir[res:rufacer. alrJ thlrs mLfuce ronghness leads t* ;r muclt largel plet,rure rll'o1t itr furbtilt,ut pipe li*rr. Itr fht ciire ol-

laruhrar ltror,. the effect oi'rruiec* rolqhre:r ol r ie fl'ictiol fsctor antl Fressrre drap i: legligi-rle.

-Dircrrs-ri*r Thc eiftct of r*ughness ol ple*u:e dlop is tig*iiicairt inr trnbulelt i-lc'rr,. a5 seert in th: ir{oodi'rhirfi.

EAT 223Thermofluids and Engine

Question 5

A certain part of a cast iron piping of a water distribution system involves a parallel section"

Both the pipes have a diameter of 30cm. the flow is fullyturbulent one of the branches pipe A is

1000m long while the other is 3000m long. lf the flow rate is 0.4m3/s in A, determine the flow

rate in pipe B" Disregard any minor losses and assume the water temperature to be 15"C. Show

that the flow is fully rough and thus the friction factor is independent of Re.

-{ssrrnq}li*rrr tr The flcw ir rteady and inco:nples:ible. 1 The enlrarce ellbrts are legligible. atd thus the tlarv ir ft111;.

tle.,,eloi:ed. 3 The rrritor los:er are negligible. 4 Tirt tlo'is fr1i.r,- nrrbuient auri tlius tlit t'icrioi: firctar is indrpendent of tbeRe1.no1di nunber ito lie leritied).

Praperlies Th* derrsiry a:rd dlrrat{c r.iicoiifi}- of wafer af 15"(' ;rre

rougiureil of e ast ilau pri:e ii c- = 0.{t00:6 nr

,{rlr{t'sis Tlle *r:eruge relocin, fu pipe,{ i:

,. , = i

-:-- u'+ tttr j'

= 5 {:ilr ur :"r .i, :,I.t' + .;r O..i{r ur I : , J

1l;hrn t*t Fip*t ot. parallel i:r a pipi:rg ll'sten the lltad ltrsr frrr e*chpii:e n:ust tre same. tr\ihe;: tlie rnirror l*ise-; i:re disregartlecl. rhe hsad1ot-r ttrr- fuIl;; de.,:eloped flort- in a pipe lf lengrh I arul rliameter -D is

rrlltt

- r

--| ) 'a

\t..ritiligthi:tbrboti:pi1resarrdr+rtilgt1ienreqrraltrrel:1rcrtlr..r,ar:drrcl{il9{trafI.},=I-}3{gi.'.eriiand/":="gir'."s

f -tri I r.l ;.-"r, -.r j_.i = f ,:zE I " =I-, lI:. =,:.6:,),!],!l-,'lf('0tl, ="i.lt,-ur s' D-4 I.g ' " ll" 23 - -\ i, \ ll,uLtur

Th*ri tL* tlsx'rnte in pipe B i:econe;

* a = .i,t. s - LrI)2 i 41trt B = l;{il.--rt m) I r ili-i. j6? ur'sl = 0.?3 1 m

3 ls

Proof thai fl*w is fulty turbulent and thus {rlclicn iaci-pr rs independent of Reynolcis nunber:

Tlr*i.e1ocit1.i"rtpiire8islorr-er.Tli:r'e1ble"ilthe11*q.iiii*-lr.t'.rrbtl1elriiripi1terg'titerliii'i;r1soThe Rr3'rioldr lusrber in pipe F is

- rr!'s D {999. 1 kgrnr3 ji-i.16T nr.s}{{j.-1{r m}

lt ].1-iE;;ltl-r i;z..m.s

v,-hiih ii gieat*i thal 40110. Therfoie" tire t'lo*- ir rrirl:rilent. Tli* relstir'= rouglnre*r oithe pipe ir

^ l ir{r015 ruE D. _={tL}ii!.}5

0"-1[i tr

From l{ood:.'s chart.,r'e aLset .e tira{ for a relatile longlures.s .rf 4.{t0tl$7^ the llori is fu113' tr.rrbtleaf ior Re;.:rrc1t!s tttt*tlretEreat:lfru-rl:bcllr|1lloT1ierefore.drefcruitLlirt1ipipe:irfr]}r..nrr'tlrr}erit.arit1tirrr.ri1reit:rrt*4ifiorthe sanir for bath pipes ii va1iil.

Disntxion Notr thiri dre ilor rate i.u pi;ie .8 is lers tlau the tl*r" r$te n pipr ,1 beceu;e oi th-' la:-ger bises tir.te t: tlte

lalser leneth.

p = 9!]-cr. I hglrrj arrel ir = l. f -i8,: i 0-3 hg.ui.r, Tl:e

Res = {i.g(ill :: I i}d