CE 39 F an McKinny Elmntay Mcanics o Flui Flow in Pis
Rynol Eximnt Rynol Num amina low: Fluid movs in smoot stamlins Tuulnt low: iolnt mixin, luid vlocity at a oint vais andomly wit tim Tansition to tuulnc in a in. i is at t/s, so most i lows a tuulnt < R 4 > 4 amina low Tansition low Tuulnt low amina Tuulnt
Sa Stss in Pis Stady, uniom low in a i: momntum lux is o and ssu distiution acoss i is ydostatic, quiliium xists twn ssu, avity and sa ocs d Fs A ( s A W sin τ ( π s d d sa A s τ ( π s d τ [ ( ] 4 d τ 4 4τ Sinc is constant acoss t coss-sction o t i (ydostatic, and d/>, tn t sa stss will o at t cnt ( and incas linaly to a maximum at t wall. Had loss is du to t sa stss. Alical to it lamina o tuulnt low Now w nd a lationsi o t sa stss in tms o t R and i ounss
acy-wisac Equation (R, (R, ; R;,, Ratin vaials :, (,,,, ( 3 4 F F F F τ τ τ π π π π π π τ M - T - τ M -3 T - M - T - (R, 8 (R, 8 (R, 4 4 F F F τ acy-wisac Eq. Fiction acto
amina Flow in Pis amina low -- Nwton s law o viscosity is valid: d τ dy d dy d d d d d d d d d d C 4 d 4 max d C 4 locity distiution in a i (lamina low is aaolic wit maximum at cnt.
isca in amina Flow d d Q d d d da Q d π π π π 8 8 ( 4 ( ( 4 ( 4 4 4 d A Q 3
Had oss in amina Flow 3 ( 3 3 3 3 s s d d d R 64 / ( R 64 / ( 64( / / 3 3
Nikua s Eximnts In nal, iction acto F(R, Function o R and ounss amina ion 64 R Indndnt o ounss Tuulnt ion Smoot i cuv All cuvs coincid @ ~R3 Rou i on All ou i cuvs lattn out and com indndnt o R lo.5 5.74 3.7 R.9 64 R k / ( R 4 Blausius Blausius OK o smoot i amina Tansition Tuulnt Rou Smoot
Moody iaam
Pi Entanc vloin low Includs ounday lay and co, viscous cts ow inwad om t wall Fully dvlod low Sa o vlocity oil is sam at all oints alon i Pssu Entanc lnt Fully dvlod low ion.6 R /6 4.4R amina low Tuulnt low Entanc ssu do Rion o lina ssu do x
Entanc oss in a Pi In addition to ictional losss, t a mino losss du to Entancs o xits Exansions o contactions Bn, lows, ts, and ot ittins alvs osss nally dtmind y ximnt and tn collatd wit i low caactistics oss coicints a nally ivn as t atio o ad loss to vlocity ad K o K Aut inlt, K ~.5 K loss coicnt K ~. o wll-oundd inlt (i R K ~. aut i outlt K ~.5 aut i inlt
Elow oss in a Pi A iin systm may av many mino losss wic a all colatd to / Sum tm u to a total systm loss o is o t sam diamt m m K m m W, Total ad loss Fictional ad loss m Mino ad loss o ittin m K m Mino ad loss coicint o ittin m
EG & HG o osss in a Pi Entancs, n, and ot low tansitions caus t EG to do an amount qual to t ad loss oducd y t tansition. EG is st at ntanc tan it is downstam o t w t slo is qual t ictional ad loss in t i. T HG also dos saly downstam o an ntanc
Ex(. Givn: iquid in i as 8 kn/m 3. Acclation. cm, 3x -3 N-m/s. Find: Is luid stationay, movin u, o movin down? Wat is t man vlocity? Solution: Eny q. om to m,, 8 8 9 8.5m (movin uwad 3 3 8*(. 5. -3 3* 3x *.4 m / s
Ex (.4 Givn: Oil (S.97, m - l-s/t in in i, Q.5 cs. Find: Pssu do t o oiontal i. Solution: Q A.5 π ( / / 4.46 t / s.97 */ 94 *.46 * ( / R 36(lamina 3 3* -* * 46. 97. si/ t ( /
Ex. (.8 Givn: Kosn (S.94,.48 N-s/m. Hoiontal 5- cm i. Qx -3 m 3 /s. Find: Pssu do m o i. Solution: 3.5 3 3.5 8.45 6..6 t / s 3 * 4 * 5 *.8*6.4 * (/ 3.5.8*.94 *.6 * (.5 / R 93(lamina 5 4 * 3 Q * A.6 * π * (.5/ / 4.3* cs
Ex. (.34 /.6, /,3 m Ns m N Givn: Glycin@ o C lows commcial stl i. Find: Solution: m.4,3 * (. 3(.6((.6 3 3.5(lamina 5.*.6 *. R ( 4 ν
Ex. (.43 Givn: Fiu Find: Estimat t lvation quid in t u svoi to oduc a wat disca o cs in t systm. Wat is t minimum ssu in t ilin and wat is t ssu t? Solution: ( t s t A Q K K K K K K E E 33 * 3..73.75. *.4.5 /.73 4 * /.75 43.5*.;.4 (assumd;.5; π 5 5 9 *.4 *.73* R.59.53 6.4 * (.35 * 3..73 3.5.4.5..7 33 * ν si t K K
Ex. (.68 Givn: Commcial stl i to cay 3 cs o wat at 6oF wit a ad loss o t t o i. Assum i sis a availal in vn sis wn t diamts a xssd in incs (i.., in, in, tc.. Find: iamt. Solution: ν Assum.5 33,984 5 8.6 t.x 5 t / s; ( Q /( π / 4.5* k s.5x 4 t k s 4 Rlativ ounss:.5x. 8.6 Gt tt stimat o R ν Q ( π / 4 ν Q ( π / 4 ν 3 R ( π / 4(8.6.x.,656 5 7.43 t 89in. 5 3.9x 6 Us a 9 in i
Ex. (.8 Givn: T ssu at a wat main is 3 kpa a. Wat si i is ndd to cay wat om t main at a at o.5 m3/s to a actoy tat is 4 m om t main? Assum alvanid-stl i is to usd and tat t ssu quid at t actoy is 6 kpa a at a oint m aov t main connction. Find: Si o i. Solution: 8 Q π 3, 98 4.45m / 5 ( Q /( π / 4 6, 98 Assum. 8 8 / 5 Q π. 4.45 Rlativ ounss: Fiction acto: Us cm i / 5 4 (.5 π 9.8 k s. m.5.5. / 5... m.
Ex. (.83 Givn: T -cm alvanid-stl i is m lon and discas wat into t atmos. T ilin as an on lo valv and 4 tadd lows; 3 m and 5 m. Find: Wat is t disca, and wat is t ssu at A, t midoint o t lin? Solution: ( K K v 4K -cm and assum.5 Q A.94( π / 4(..94 *. R 7x ν 6.3x 4 4 (.5 4 *.9.5. 4 65..94 m / s.74 m 3 / s A A A A A A 5 (K ( *.9 A (.94 98 * ( 9.6 9.8kPa 5.5. Na cavitation ssu, not ood! 5 9.6 m So.5
Ex. (.95 Givn: I t dlu tou t systm sown is cs, wat osow is t um sulyin to t wat? T 4 n av a adius o in and t 6-in i is smoot. Find: Hosow Solution: 3 6 (.5 4K Q.8 t / s A ( π / 4(/.6 t.8* (/ 5 R 4.7x ν 5.x So.35 6 3.6(.5 4 *.9.35 7.6 t Q 55 4.4 7 (/