1. Solutions Manual forFluid Mechanics for Chemical EngineersSecond Edition with Microuidics and CFDJames O.Wilkes_ PRENTICE EL-l.PTR Upper Saddle River,NJ - Boston - Indianapolis - San FranciscoNew York - Toronto - Montreal - London - Munich - Paris - Madrid Capetown ' Sydney - Tokyo 0 Singapore 0 Mexico City

2. The author and publisher have taken care in the preparation of this book,but make no expressed or implied warranty of any kind and assume no responsibility for errors or omissions.No liability is assumed for incidental or consequential damages in connection with or arising out of the use of the information or programs contained herein. Visit us on the Web:www. phptr. comCopyright 2006 Pearson Education,Inc. This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning.Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and isnot permitted.The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes.All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.ISBN 0-13-1482122 Text printed in the United States at 0PM in Lain,Pennsylvania. .First printing,October 2005 3. Table of ContentsPage Chapter 1 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .1Chapter 2 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .41Chapter 3 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ...105Chapter 4 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ...159Chapter 5 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ...216Chapter 6 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..240Chapter 7 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ...303Chapter 8 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ...347Chapter 9 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ...394 Chapter 10 . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . .442 Chapter 11 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ...488Chapter 12 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .528 4. . I l/ (-Vt'+3' Con t/ e-fJi'o4., _(93 X528 1 640 O =4-3 >3 OMB E= . 0-8 X 2*4 '19 E4 _pr3 6. [=3 Mn ECJ COAV#Jon, Q+otv. +cchouq( AccelevicdfovtC9 :Clgl C: -f_1. _h_f ___ /00 S CM -P+S. ((. u14.7 >x I044 8. noI-bR 31 natal / Vt! -cm b~e+C4011 - -5C6touaC 44%A.rth '7L' -' . ... ..__. ___ =0-0060! -Pt-"' "F 1+VO(I4m. e-i. 'c_ 104.41 -}c. {~e_Q =_. .._L =00780 is'7-I-egxbo 5491644 / atom: Hm = 9 ''78 =12-43 %A o-00601? e2aozau membere =p (JD ____ 62-3x I2~-asx I-05*/12 / " I-2 x 0~ooo62'2.'@{: ~ ff. - -I-1- C?A "7? 4&3 5 cP eh. /{-ts "~ 8 '7 '74+o (Of-Vttbtsloul-err) 9. I-6 Pre. m+e (A4: ggubbleA'+H4o. rphJ ? a.dim -1ll Nll gram 44.0!-Cr x &wcH. a. /-e (.5 10"-V- " c5 mwmq,acmu a,convex J'z4%4c-e 7_.43 ? __6/ RP Q q_ Two . ru/ {ac-(JP6 49-! =20'' am rm/ olu-a(,Q. 10. 1.7E 3e+vocl C--A =z____3 =3 M- Z P+e. r.r+z 44- CacHoc'o(_ H 3 __ _ 1 =P =to3>< . :22o/ '0'. ?Or8 _- .9'7l)"oox: -8!mtg 3 IX?3 2 V-/E = 'PA 49 =1.72 xso" 7'-34 ms vgwf 14.511 =*7 PIT =-0. ?.?roof-'-Pg I / Pa , _. I~72:> to oae. rz-Hea {Gt =Z3 V60 =o.3o Jam [43 'O'7322a . , M49 W7 ()1 =%5xO-30! =0-125glow Nd,V11-=4-LA ------ &/ -w~. /Q V{oc7'H& (4, =:l__ -=20 =Q0! a1/ "~ /0,4 030(; v 0'34? 2 (014 0,25A, .0.3/+q/ I'3*Jf. r# gcuu zgeeawe E6 / (3'/0-eC{. 'cIaa. _ (ago/ . Su. b~. f0vuc glow] 6'06 got:/cu-c). L1+ 48. Z-5 Hamcceuf 3~1la/ .'o1 % q S-1-Heq_ -r-G/ A4,l. 4-0-24.45 / gay llg t'.4+3 m. /.r III EHO-pg( 5%/ A / /.). '7oe gt),a. rz, _o. ,. A K p+ac~-vcc ta:woalac A1: +d 5:nPr NL/ .)O+IM44{2 CD __, _ E; l: 'mcI4a. t-e (42 : uQ /13 .131 ll A7- 4)c - c: %; Q:Au. =c'; pA 2C1v.1>, ) = c,/ . 2qz2M. pI)54zM =we+c: ..(_,I :a'. Ko1Jwfa.4ufubsff-luug M. um. l7.. e}. [/ 2 (13-. 57)2-'4--38'75))r322 x (3Q:o'qg? a: >)x 32~2 V . ..________. _T____ A .573-: >"(- ") Ac wk-ca 1 3. . E5 . - 2-7:72-:{-67 Jo 1-2 4 cu,Ac 3,:too . : Chem 014 me % C;W P >1 - - 3. ~ /K69 =3'7?e,-- "67"8"3 "~-'= >< I2 =&-3bxm 3) /3~182 $1/170 / L 3600 Cg'*"""* W'/gf _? :>=0.60 Te:I-352:/0,CD;I / Page 56 C3 =0-62 / C. rocmp: 'o '-v}"4J OK. 60. 2:! /+Tank @'f'0. 'I/ I U13 Ciam,,&a+u~ Maia .""-"'T""" Le/ eL 4+ f= G L4; =J ? (9Z./h4.4.. r.r : b>cLqMee on Acaow rme tank0% =A1- ; _D, fi s:+ AT ('H1_ gw . mm; o eageoc oh1c/v. o+z. .. .1:_. ,aka?4, Except ue Ce-req 1LQ'O wlocck 03 new A-7 ___ 11 so*1x. e aw-.4 (mat-(444 0;, 0; 0-02 0-63 __ _ ,x acfacmo/ g am./50, f =2533 J . ~ 492% I35 % T 57 61. 2-I53+0uI4a'r1 : lV'4wu'JG/6 IQ L. rcu. 'd. r 1/am Q _-algmm k2a(ru4J-v: h:. r, / p2_ = . Peg H3-4nouLC' "" 1}-5-C9&=5.;w 2 Water exitCW-. ce_ ___________ (_, _3="/2.([fl)%dHt-e; )(Mus! -Coxat -. 4a. { Wat:3UQucL an,anal:(RE = 44J10.62:,oA, =O'57-(""}2((: h +41) = -_ A, o.. .j:5_4 Olftg -"I, ?c"oIa( speeoc 1 ac a. (ww6rvr'*% Wine 15: Lg; -4_ ChC| (.e(-6rrr: ,a , Qcu( J'L- .. .x &(l:9~'t+l 5 l'Vl[5t' ~$4414, M: x+u+e Q /Vent Mice_. ._j. . __ 7 (I48 beam) 10 t'VL. ru+ -20 mm +6-f. 0Ce-4c"- 12- fr732 C0nfsuuT u_ / l =L. )q) or L4.) =i $713+ 4-1 L/ BMoc. lL' _; :2+ 193. = . g*+ 19, : B~>A 2 P 2 / 6* / p:''p2='(L'w14%______"e*"""'~ -wulh g" + % _.c Cement) G(game . rg, u eIe; .,L+. ~9.,64-(tat:raceLccI4 e pmxryu)_L Q + :9 ___ _2 (Q-! ' 6)-()1 Pg,$19 :_ [531 ""Z{Z.6x) =Zf+X ax 2 / cL+x)3 (44 4-V) 105. 2L-HH *2: F"$cc =29-">"C9r~ O"- - " Z _.. 1 Ph, C.n44e5' pg : .: o0o2(80.3A-5) ~ 8 50 4? )49 ;5>9ooo: [2_5-5) 1 =2' O/ "32 : _DL.4vM ~l-cr+I/47%;g/ m.. ) J5~/ L"~}("*f &ca"f CF-0} , gQmI*f(f gm HA3?: C I09 113. 3%: Fipelfni.C'o, ua_p. O9L l1>Y-Cited-.Ero, o A11 =2 p(: (DU:__-__ ca. .,Ec, @: *-ms 1% 5, mi:16? -/1/Lcl-(_-pJ~. c:uJ*C diop (-1 Mcuerrglj vf+oror~(, b.tq(_ __ pi-/ l|4~Vbq(-ear 104.) 501 JA4.cLt_ #;at ; /,, ".(. _,qgj huaehanfgr, g : D - ('0 TL;5-11: , Pou)'CJk%1e/ pipe cgtsmhefe . Shea A1,(0, 1.,Q arC. ;(, ,__.I/ - C.-pp 5 =:3 :0 ,6 / ~ ._ new :Fae. ..)-)5 =2/4. :H5.. . $rJLoL pF. gLLC: /K144. 0Ctamel-cf J4.o(&5-Q I'hC! +Ca. ;epL_ 9: dub ($02.,49: wow (gov carom. aw;Jcacm, HO 114. 397two rfegnolds l/ umbe+sJD EoL| 1~t= ,-.Ga- C*c'07ou Cgaacfvl decieqoeo cuf- / Flge /3; he+ 5610!. ) MM] L56 66 0VJ. rl1qa(o(. .)-ca( 9:,41 Cuc)-(qjg 9.;14.25. am /74 / pwerrwe 0(-lop/ (ke%o+e tueecdmr 3:.CL ccfaf % 0-00452x O =5.25" +l'M. r 0.008 --. HI 115. 3'3 E. 4aneou5 F'7L'(; x0L; _ FELQEG-/ E 6; molar MumbefITe:Pu-D =6Z'L">"I0". ;_ -= =7~71XlO4 / & lxo-000672.lE'3}-Ioneou,+rc; -/-ran aohn axeocvw ivzcoi/ eq-C. $$L(m0n'on % awn/ H'6t} g/0(4)L ..'/ .F.= . l.. :7 2'07 y l0-q 7?;-43.= 2 -FF-F L:E = ..- FF-'L.Al? -T 2 'F: =T] Q5: -L 3: "CF"-TZ-o'7>Ho"4 ll 0 o In -I "aO0o60C1444 / rue / fJ+0l4c-ltd,1>+eJm+< a+o, o wowaa 3.45% g e ep++ea~ 5/QCl(. / 0% 4 %I''w% 5%--: ':"T7.. HZ 116. 3'9 ' Pump / '5_l>"'1a. r:. ;331-7. xal-t(e/ l4.d. d.q, , C(OJ41C.g Value,-CK o~Jaue, ,(_ CUmo((&, ;a; ; 5g 4 h>p{'zu. ( %41. e P-p av vazue beam 3g ((1 yuan mam. / cg 1orr. mue,a-l>fao(c. ,{~ on u.04~h-ctzm.cg 6L 356 cmou-+35 4: -=wta. ... r,; L!{Gal :4'>mu(u4 M "me:435: 4+. '; (q,4:)_ 0%, ; 4.9 4 vc4.+m)=5'-761-2-37::3396 a;_ v0{LMk. (fh'LV -: ==0.223 AFB/ J! (Ne)Aiumtw Wk 4 =""_(s*-75.1-2-275*-) =21.54. an/ Maw / aeaca-ex '*"*""- 0-223 52. a cwca(m{ , o.4o (sap) um =2%? //% . . I0-87.1%/ /QW!(at =0.223 :1.4?Pf7,re'-- 2:41../ umLow C. p: p j>=(, .oe5 ac._e_ ;o-oaoz 3> 0.0037546 EL;// ?C_; -oldo Mxumbd) l_Cg==5,1,9 loco p)pe_ 32;2r. >'SCD__ _,v_'_/ _2{; f: V&"P / Z=m_td" a-3.. . 3 That .11 Q2 . : E :I 632 G3. 3C4-(6c( am, o+oveme.4,(~ CI 63-2%I26 130. 3-| '7 Csrtow m 61 C0: c4e, z: e Aquewwt. jo6+?2 lcaf7'oVlA(_%)=43p= o.J= O3e = m>_ 44: =M D 4- 7?T 43 "I37 132. G1I.348-ZUOO;_ W1) X / Lmxzz-2I} Z9 133. _ 0146 Fe 4+ HWar:velooh G:/nu:rt.= 2 . _. 16.;law A 0-zqg H35cg:nos-7 63 / #r"sof r. ro*te4ma( Com/7*! -ff-A /6 tom"= L =(o. oo3xo. >o Mk,___ 2.2x me x 32.2 025 YTQ 1o72x. b'2o2< 103-7 =$33-6 =o_22H[+ lpsm- 2 Z A -it + o-9.2x-A/ (26:-4.- 10,) + 633-6 = = 0 zcwe/1?eq4}au. e. r/ *0 404 P:= J 3:683 + gql/ eytim-:4;I30 134. 3-I61zgwflf10' 2. ___. , P:. C(S ecwq esfmafe _-pt'-J3/>8E?1-8.0a u.S247;_- o-Ezpxaa =/+13 my ' ____"'_"""c. 63Check 014 vaa-ca sSU[L([T0 GCot;Mu((- caea rm;/pt =24,/81-C:above C, /59L 9:3'/ P!>2--34. . /8'52: 1+ (FL* )4 / pl 40 .3 f 132 / P: 24- 6- Let > Lr1 x I5"x32.2xr~e(/ . 2%;[W7 (M?'>-lfcm -2'). ..-E7-(/ Wt1._l)eK. ?]. E ="? C~~I) .1. 4.. me=2m_~: _? _wv21 +721 "WP jam R 2 E >: ;?'4 -"'I2*- "? Cm*I) Zlkm 150. Sheet1Problem 3.25: Comparison of Friction Factor Formulas% deviation is determined from excess of Shacham over Colebrook & White,divided by Colebrook & White. epslD 0.001 1.00E-04 1.00E05 1.00E-06Colebrook 0.01922 0.01227 0.01023 0.01001 0.00999 0.00998 Shacham 0.01919 0.01221 0.01015 0.00993 0.00990 0.00990% deviation -0.1 -0.5 -0.8 -0.8 -0.8 -0.8 1.00E+04 Colebrook 0.01842 0.01077 0.00810 0.00776 0.00773 0.00773 Shacham 0.01841 0.01076 0.00809 0.00776 0.00773 0.00772 % deviation 0.0 -0.1 -0.1 -0.1 0.0 0.0 1.00E+05 Colebrook 0.01791 0.00961 0.00554 0.00463 0.00451 0.00450 Shacham 0.01791 0.00961 0.00555 0.00465 0.00454 0.00453% deviation 0.0 0.0 0.1 0.5 0.7 0.7 1.00E+06 Colebrook 0.01786 0.00948 0.00498 0.00336 0.00297 0.00292 Shacham 0.01786 0.00948 0.00498 0.00336 0.00299 0.00294 % deviation 0.0 0.0 0.0 0.2 0.7 0.8 1.00E+07 Colebrook 0.01785 0.00946 0.00491 0.00304 0.00225 0.00205 Shacham 0.01785 0.00946 0.00491 0.00304 0.00225 0.00207 % deviation 0.0 0.0 0.0 0.0 0.2 0.6 ' 1.00E+08Colebrook 0.01785 0.00946 0.00491 0.00300 0.00205 0.00161 Shacham 0.01785 0.00946 0.00491 0.00300 0.00205 0.00161 % deviation 0.0 0.0 0.0 0.0 0.0 0.2trigger =2 With the iteration option "on, " the trigger cell is initially startfF =0.005 set to 1, so that the initial value of startfF =0.005 is used in the Colebrook & White formula.The trigger cell is then set to another value (such as 2),and the following representative formula quicklv converges to fF.Here,cells C6 and B8 contain eps/ D and Re,respectively. = (-1.737*LN(0.269*C$6 + 1.257/($B8*SQFlT(| F(trig_ger=1, startfF,c9)))))A(-2)Average percentage deviation =0.0089 Maximum ercentae deviation =-0.8C'| a4CL, / Hie 37-10'~c-'9 ~5ld =cg,0(=. e_,{M 24.:24; f4 A""+"*"'*(-'t'2IX2. 4 '5 Z* X 0.08 X0!-BIX 300x32. =45233 w/1106 Laa*h/ me.c at j 159. 3~3:Lammav lm. ) wl Ve++. -ca(Rpe1'1" ctzl4'V(amn-(um zgalaace wamx 0n C / mdef cavc E1 (*r>+ jffL~J]v+* _ Z17-rL. Z' w+*L, Cc.--0___, ,_, __. . u-- = -v- : =+em. + Shear *5-4'/ Ma! -e,"H. :.4: ~21: , p+g. 14 tr -Vfnlc vfia/ colic,aaCVZaf Cgiav.+a4.cee le p+mmcd+o, a din/ F3 (-gagl5'> 160. A =T~. l_. :Dz=7-T____"z=73-5'Cm A9 I' A 179-?5 (5) m:M,o-ammo =64-2, Mce / "" 2.30 xo. oa zama'-4a-/ CL) Max =Z-"M =34.8 cm/5.Cd) Q =ftaH(6_tP of _{J = dz. 8; dz tT'C'v. _y, _ 8). 2,3oxO-Olxlltrd =I4-v d__"_ef/ cu, _; _ 01-2. '77")::3." am(e) 2.,= 2 ~54) =Fxw-6 =36'?-1 2 dz2 Cm F 10 ___ '2 =___; '.i___. _-:o.23o C) F ' 2 L10 ,3; 0oa>