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Welty solutions-manual-1

1. The document contains solutions to problems from a textbook on fundamentals of momentum, heat, and mass transfer. It provides step-by-step working and calculations for problems related to concepts like fluid dynamics, thermodynamics, heat transfer etc. 2. Sample problems solved include calculations of pressure, velocity, density and other fluid properties under varying conditions. Principles of ideal gases, heat transfer, mass transfer and thermodynamics are applied. 3. Worked examples cover topics like fluid flow, heat conduction, mass diffusion, thermodynamics of gases, fluid statics and dynamics, and their applications to engineering problems. Diagrams, graphs and derivations of equations are provided along with the numerical solutions.

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Solutions Manual To Accompany Fundamentals of Momentum, Heat, and Mass Transfer, 4e By: James R. Welty Charles E. Wicks Robert E. Wilson Gregory Rorrer
C.l1APTf:.R , 1.1 n = L/ >( 1020 /i,,;, V::''''; J< ~ R-r = /.32 x 10'" il1/5 A= r(163 ;.,,/- ,:. NA = -'- n OA = 1.04 x IO lg /s 4 P ~p II + dP u1.2 'V = ji X d<j J cv'PCQJb) =f'cv;:[k(cos IsiYlI +2)x + ~('51Yl ICos I)yJ .". 7PCQ)b):::;2,",,-2 [t (~f-2)X +i-(51~ 2 ) 9] 1.3 'VT(.K;j) =To(£.f [-k,Ca5 ~ ccsL, ~) ~ -rt(Sit1 ~ 51nh ~)g J IT(a.).) ::::To £k,[-b.(c.o~1 CO'!>hl)x +t ('5 in ~~h I ) Y] V7(o.) 6)= -r;,e.""~ [l~I~~+ e.-') 5{ -+- (~i." / )G.-l-') 9]2h =Toe-~rC&>-:.1 ( 1+ e.-"2.)'; 2.. L~ -to ~r1 ( I - i:,2.);1~ ::Tc, (O.CJ~:l~; + .1?23 ~) 1.>.1 /(Jt",1j) of 'PROB~~/Yf /-10,,"04t!/l1c.ouS. p~;;J O~ PEo13I..~/IIf 13£ )lO/f!OtS UV't! ocrs/ 12 -:E. ::: [ lof 'S a 'l -=' v z f~ J 1.:5 IS 1.2 WILL IF O~ IF ,)IE: Co/VVcte.S/ON rr'1C70R/ je I IS USe.D, ~ ~ [ csk35 j. I.S ~LOl.J PROP~RT/g s: SrR~S5 / PRE.S5UR.~ ($~ADIE./v~ II~LocrrY. Pi IJID 'PROP£.Rrlz. s : /z./I1?:£RA7U..e£ / D:E,A..)SIT~ PR£S.5 U. REI =':>Pfl:.CII=IC J.IEA0 SPEED of Sou/1/D. I. {, 9 '" ('" I A l" "-e. r:2 ~ r x ex + er ~ e.~ = COS e~.x + sin g e.~ ~ ;:( ~!," e); + I~ IS! e.~ = -sin e ex + GOes. e ~j ..• Q. E. D. A - ~e d e.s e'" e'"__ =-cos <2.;r - ~''( <2.~ de • • • .... :::: - ([.r Q.E. D.
1.8 {L= ~ ~ + ~ ~aX" ax or ax ae ~=~a+~.a.- oy ay dt' (39 de r2= )(:1+Lj:1 ) 9= 1:a.n-1-¥ dr - )( II e eax - (x2 +yt)'2 =r' C:S =cos ~ =- y = - ("'51118:- sine a~ )(2 + y~ ("2 '(' dr=sinG .afr= case ~ I ay t' -sineL --r- ae + case L r" ;;8 1.9 'V = ~ a.x + L i. + a- Q.;: ;)x d~!i 02 =(cos8?r - Si~e~) ax +(5ine.L of- CO~e ~ ' e;;, r- c}9) ~ + ~ Qc;)2 =(ex case +- ~~ Sirl e)~ + y!:- (- e.x Si118 + cZ~ case) 2e + er..a..ae "". V= a.,.~ J .... .a... A ;; dr +- f c2.e (}E:1 + er a2 . 1.10 MASS 01=' SOLID =If Vs II /I FLUID == It If x=p~ Vs =>- Vf =/-x r?s f'sVs +,4 V; Vs -X P 2 = fJ/i. 1'><' +~ ( I-X) /.1/ ¢ =3 )(21.J + 1/gJ. a) 7<1 = (6X'g)x r (3x 2 t- 8!fJ; 'V r/; (3) S) =Clo X f {,? g .... " . e ....~s = cos e (2..)( + 5111 CZ!j ••• 1 ¢ • ~s 15 IN THz.. - 60 0 DIRcECTIO/!/. '1¢"~ =(!biY'q)e.A' -r(3X 2 +lj'JeJ •[cos e cZx + sin.e a:~l fiT THE PO/NT (3.1 5).- V ~ " a.s =(90 4 f 6"7 ~ ) • (cas -(,O ~ + sin-60~) = 1-15 - 5'2.02 = -/3.02 1.12 FOR A PERF2CT CSAS/ P:;O KT M FRo/Yl '?ROB. J./~ fY -= I'm ( I - X) I - "om )( A .... --p -::: fJ", (/- X) /- & >( p~ RI"M
1.13 1p:= A,. sinB (I - -Fi ) a) V'1p:: d 'I' ~ + ~ ~ ~9 ()r r r ae :. -vP =AOSil1e(1 -~) ar~ e WHIC.H REQUIRES -n-tAT *-1V7p/ = ?e Ivlf'/ = 0 ~lvVI =0: - 511'12.e (I-t-~) +C05~(I-~:) = 0 (I) ~ IlIP! =0 : "!>lrleCOSe[C1 +~ f -(1- ~:YJ::o (2) FRo;n (2) 5i"e case . L/a"4 =0 r':4 FoR. a;l 0" r'"0;' sin e cos e=0 . e - 7r•• - 0" _ 2 (3") IAlTO (I) G)=O: 1- a~ :. 0 r2. .. a=f" IhI PasS/SL ~ , :. C/.)AJDIT/ot1JS .4Rs. . e =0; i=a... (3) IS 3 ~ ~ = -jfJv;.'-[~~r] ~ ffE? A- _.J. LJ v: 2.. r2;(l[ Jide fL.2 - 2 r oC L- L 3 if - -~. - ...------------- ,-,15 lAKE R=- i AnA. Wrm s:'&, : 1.01 ?= '3001 (1.01):' 3CCD:; 217 AiM L(o AT Co~~ntNTlEMP,) .?""'/ fOe IO~ ~~$ l,v 9 / A lO'r~EA$E IN PI~ ~o t.l7 DEJJSrry:: 1 m W"'~ m 1'5 MOL&:::u...A12. Wi;(ah'T. ;.tr 2.~Q:;()'-, wt ~ W1~ ~ . ~ (lAwf> n ,:: n ?2SO,,~1 2~,,~ CS).L j>s..l- =2.5'·10" ~(e~ ln 3 ~lc;H AL.TrT'UDc Utrt~ IVf~ G Is CVr~~. n~ L~'(O·~
CHAPTER 2 2./ V'P=PS j dP.... ,.. d~ e~ =-pc:, e.':j ~t...clP = -p<] C' cl':l ~~ = (JSn @ STANDARD CONOlTIONS f' = 1:>/RT FROM ~.15 f1.IR=O.0"7651 I~~ FROM ~. 15 -Po..~ =211h.2 ~ fr2 h- (21/ 6.2 1J.F/f/.2.)(32.1'1i.f 10.... rt/'5:2/bf) - (0=((,51 Ihn1/A-~';('32.114 fr/s':J.) = 2 T/6~9 A: 2.2 FOR A PER FEeT q AS) '"'P=pRT f3=;;(-¥)T ='p'RT =="P 2.3 ~=-dV d'P P V =7 V L"P '. - A ___ 3000?S1 _ l V - f3 - 30"., oc)o-psi - 100 .: 90 VOLUME CHANGE = '0/0 2.l.f MERCURI{ A • If R='Po. tP"" 5(:2"); -PI ='"P.z "P2. = ~ t-PK 5 ( s") ; "?.s ="'P<{ P'i = 'PA +Pw9 (~~)i 'P,", :: '?s Po. -rPM ~(l~")=~+/tI3(2",)+~9(S:) Bl :'?a, -rpw g~~, '12'/- 2" -: tS'·sj :.'"PA =--Po. T 5. ~ 17:5 == s:~ I?S~ 2.5'" 'VP::: peS-a) I.e.."PR e:sSURE G'RADIENT IS IN THE DI'KEcT/ON OF (9 - a); I :5o'aARs ARE ..l- ~ - a.). TH E BALLOO"-l CST'R IN6 WILL ,.. ASSUME THE (~-OJ g t:>1'REGTlON. .'. 'B,AUoO"-l WILL -0. MOVE Fo~WA'K!) 2.6 EQUATING: -p 13EFO~E ANt) D~N6t ACc.:t= Lt:RI"O~ i -p =P5~ 0 :=. P( <j ;-0.) 'jQ, l:ica. == ~ L1 < ~'3To. -.Jo 0 :. MANOM£TC~ LEVEL 60E5 1:::>c)(.4J N. 2.1 MAt£; A~~ ~3A Of2TI-4!;,~JJ. A Is IN 1n.2; 3J~ ~ 04.7-3?K~ g~h/(# h,. 144 .11.7 I tf4.7A ~~ ./'2.2. -= 2.2 ':: 2'.£c; 1ft.
2.6 A 8 Hg I q-= ~ -JOlt.~ 10 I Pc ~~+Yu20a~ 'PD '" /" -Sllff~ I B-~ "J~d(1)-5511;{j-IOgOt"0 Pp= 'iIM I JOII. :O,6JH2-D ~ qf({!5~~~/ ~-~ =: ~(I)- !':>'G24 =%.8fsP 2.9 Air ~.,gt d,j 5'H,.0'"Pa{d4~ +a~~9HJ ~-~::(1-!i1-~)~-(2):02A(2'Z 2- ~- Ps=Z44,7pgf :: 1.70psI 5 ST~JJG troM 16wr Aj ~ ='B..-dl ~j'H2.0 5ru2rtA-q ~ ~ B./ ~ '" 'Pe-~,+dlfd3~~.Jd2Jf~ fuwtr~, ~-?g "'d2iJf~-(d2"d3)Off1p ExPOt;$S"!M4 d IN .r~ .~-~ = SZ.7p'; =0.227 ~J 2JI F -= '? A - '?o..~A ==,oj11 -(fR2 e.G. PH:JO = 1000 I<~/~l) h= 2W1) l<=.3~ F :: S~46 ~~/s~ =- 5"5"'-1 b N - I1c.p. -= vt -t- ~ 1r'R2 ·2.tM C"fr'Rq FOR A Ct~LE J Tlob:= - "'I • v1 - 2M +1rR.~ " "le.. p. - qrr'R2 (~~) = 2.0tl ~
2./2 ASSlJh1ING, ArlY1()SPHERIC AIR. TO 13£HAV'£ I DEALL ~ &- -~Q --lldg - r.) - "RT LET T = a +b~ tJlTH ~/VGN INFORMI1TION, T.: S30 - 2l/ fJ 7; dE. - -g dlj -p - ~5......:30~--2-J.!tl.ly/~ fOP .dE - <3 h (' -2lJd (':J/h) 1; -p - 2i{R 10 5"30- 2~(Y/h) 1n. E =- :ili- /'1 5"'0, ? 2.4R $""30 -p = J O. " "PSI·a. "Po ":: "30.11". H~ .'. h. = q I g 2 ft. 2.13 :r: -. --:'-- --_.-. - 1'lr ='Pa To I'H;1.(J Cj ('-/") +-f'~ 9 (10") PJ: =1':zz: ~ -~ = -L) a (~,'QrL). 'J (10") rH"0 ":J r H9 :: '1.63 psi :. PoIN! A HAS THE HI9HER -P1?~:S5 UR.!. . 6 AIR - ---- -- - D.} ~i=~ = 0 ON TANK Ptrd2 ._ "Pa.tltl. lTd~ _ 2!JO =0 (I) -1l- T @ W'ATER L£VEL INSIDE TANK, "P = P ai", -to PH:1,O ,](h-,:{) (2.) FRoM (t) AND (2)... h- y = 1.27S" Ft. (3) ASSUM£ ISOTHE.R.MAL COM- PRESSION <:)1= AIR IN TH£ TAN- rg~ VrANk =-p[ ~/,qJ P = "3 -p~+no. eo:3 -<j 5 UBST. of ClI) I N (I) G /VcS y= CJ.12f+.- •.. h = I. '3 ~4 q.. b) AIR "':-". -- .-,", .. t i1 !='y = 0 p =P....t- + 2.S'O+-f: 7rd2./J{ @ WATER LEVEL INSIOE TAN}(~ P = 'Pa.fnt .,.. ~H.:20 9 (3-g) F = I q6 (3 -'1) -25"0
"I>y ANALYSIS SIMILAR TO 0..) ~ OBTAI N (3-,)) = 2.? FI. .e o F: Iq6 (:2.1) -250 == 293.6 /bf 2.JS AS THE TANK CONTINU£S TO BE ?U5HED TO qREAT£R DE'P~ THE VOLUME OCcUPIED 'BY THE AIR IJEcR£AS£S AND 77IE 750UYANT FORCE THUS DE- CREASES. 'BOUYANT FORcE =2Solbl DISPLAcED VOLI.JM£ O~ H2 0 = 250 = 1. 01 /f;3 ~o9 !iSSUMINej AIR To -SEHAtI£ IDEALL Sol AND ISOTHERMAL COM?RESS/oN/ ~+m A (3 P. ) In-P(4.01 (j.. f) .::z'C..-fnt f-(-J9 c)(1. 0/) Z:: '15: 'i'l' Ii-. TOP WILL. 8E ('IS":i?~ 4. 01 ff3) 7Tlg;:.) • eo T()P J S ~~ b fI. EELctU J6~ o THE HEI6HT O~ nlE WitTER co- LUMN FROM rHE DIF;::: ElEMENT IS h - Jll-g Q.) FOR A REcTAN6ULAR 6Ar&) d,4== ~'d~ clFw == [ ~ 9(h-4ry) -rPetIfCJ dA d F". -= L6P'S;9'/ilL! + ~ ] alA ~Mo =0 ~ <j(dF"w-d7=A) = 0 (<<{ lj lf9 (h -4t-Cj) - gb~JdA ::0 4 (" CtJ9 hIJ -1)(3 'I'f +;;9!I :L-16¥~JiJ :=0 h = IS: I Y ff: b) FOR A TR.IANc; ULAR GATE.~ dA: (LJrr. -Cj )d'j 2.11 £if(4~_tjl) [G!(h-4+y)-~#Jld~ =0 h = 15: YQ"1 If. STA8LE "posmoN (M =0) Tl??ED 'POsITIO~ eM) M ~ C. '1f''3 Ll){ o.os-d A a - 2 Sa y ,- }(J. ~a dx L,.os = fig L" C.e (0.045"" - /2.) M = -0.0 31 (. :zo~ rad)~J L r 2.11 Q;RESSUR~ 1~ 7 THE 130UYANT FORC£ CAN 13E OBTA'N~D "BY INl"E~RATION OVER ,HE CURVED SURI=AcE.I oR. By THE FOUOWINq "R£ASONIN~: ~F~=O 0LJ =I'IOIJ <3'71R2
2.1'1 F':J = BOUYANT FORcE ON suB- MERGED LO<:i + Q, WHERE Q= 'w'l:lqHT O~ 420 N SHADED 'REGioN. '1IR~) Q = C"R:1. - T IfJ5 F~ = fJJ7r1?~ of" ('R2. - ~)1'9 =,.og~ (J +-4FJ . ~ ,0 [7!'+ I-if] =,f~ 7r (SI/'JCE F~ ='vJ) p~ =~ +J- = J. 06'1 ~ JI 17'1/:2,0 a.) FORCE 'R£'Q'D TO l/F=T BLOC.K FREE O~ BoTTOM; Z F~ = 0 = F -Flo -F.... = F - (ow 3 22. ?S'+-Pa..+...'P'~s'J - (3',. 3'x.S)A: J F= (31c 3')( 1'",,9 22.;s:.' +R+.o. + .5";.g)gc, 10 = 32/1971bf b) FORcE 'REQ'D TO MAINTAIN FREE Pes/noN: 2 F~ = 0 = ~ -(3'x 3' )(,S'),4 9 -r -(3Ix~')[o4 +'Po.nj , h::.S' F:: (3'x3'X-,S"')(A ~••,,) K3'1C 3'JR.+.... :: (ll.';)(-Pyy:;. 6 I~/R:S) +f9R"){2.J'&:.. 2 /~ F =J9'{LfO 16; 2.21 Tb' J- h == <i./5ft. AS'SllMmows : CD~~~ ~rtr"~ &u.- ®HzO Us&!- A~ ~LLT(!)p y 12:= # j liP dF". llpdA e 1- 01. ~ dA:%z:~ eSWledf} llf-.:5'1(h-kbso<+~~) dFlf ~dFa:>5e
h fim"~ ~ (h-~+~)sm~ Z7reSd C( = - (~-~t~ t 2(+aJDC) '2 ~ 'rJH~ Fa=0 ~~ e~0(+2Q Q-fQJz1) '3 SWI,"l.()( ~~~ '5(t" D( '" 'PIcL Q:)~"/'- rJfct 2 n-: 11-rJid" /-+ (1- V%t.)3~- + ----=--:.~ d 2 3DYct ~ E.>c.?At-JDHS<i IN S'tslZrfS5 1_ 2. (/[) .Ii ~ S£ -+ fc ItI;.)rL J 3 D~ L~ (t llf-nZI ~ d:34~ h ~ 0.28/0 rn. 2.22 .J"D 6% ~ =L)9 =tfge Tde. r 0 (A'P_d(A~) =(!,.q~cI~ z: )0 e~'w,e l,:9-,8 -A~ e ~ ::: /-,49 n ~~ tj~ = -,13 in (1- ~ if"): 300}oook{i-.O'fq :. J'P = ILl190 P$; DENSITY RATIO ..e= e.~ff= UW11/ ~ fJ=l.tJ~7~ 9 2.23 "BouVANC V FORCE = I'v=;~ =- 'F dF =:E. "PRoVID(:::.D VOLUME' dT T 'REMAINS C.ONSTANT BoUYANT FORCE VARIES INVERS£L-V WITH TEMP£RATVR£ OF THE /t1R. AT CONSTA-NT VOLUME. 2.2.4 5.~. =I. 0:25 @ If£" rn. ~= I.O:25"!2,gh.. = (I. 02~Y /000'3.. V9. 101m V /8£nf) >>is'' sa.J.... '/ ::: t. ~to X/O /, ~ = /760 kPa... '" ~ a. 2.25 "'- ' Fan ~ -,.----------..----- 0.30 m /J.P"J"20 6l1.k = 999 k19.B Wl (?2')""-.m~ $~ 10'1 ::. 2.4G Pa.. ~ 'D'J::~ Is~ ~TfUSRA;~~ AN)DlUe.t1R; VA~ tbwN~.
Po lsT~~~. ~{sT~~~. )(ls~Dt~~ ~E.~10T~~~TU5 VA:Jr;e .. B,i?H~~:::1?""~l"q~)f~ 'UT2. (1 IZ ~~ ~-~ 2 Ylla3a- ~~6~ == 7O.fo7- 15.~ .. 55.1 pJ 10 T. AI THe. CENTER of THE EARTH} z:.:R Pc :: r;.+n T ffjo ~ NEGLECTINq ~+,." ~ =- P90 R :: ~ 6'1 ·/()10~ .9.107'" 2 ml ~ • 6330./0 3 ", = 352 x/o9 k::, m5~ 2.2'1 :-IT H,.,O 12' p= 2 ~k.!.'3~/1+.3 + MUO 10 ' p= 4 '5(u9~1ftl t "'B t=A -~~ =~'J 12 := 24 j 'Pa -Pa..,"", = 2l/'j -1-40, = 6L(j 'Po" -H..tM. = ,ag ~ PAS -Po..~ =I.l ~ 12 +tE J(f-12) H:z.O lit FoRC.E / UN IT LEI{6rH r: f= f=:: f(p - Pa..n..)a'A ~= C~ 9f df +f~j'2 t(! j(l-l2})dc 12- F'=Pw~( Iq2 kl)-t-~ ~ (s-OJi.'1 F::.2·~ ,/9; +l/'9'S'o = 18,790 Ibf
=fJw9(~6 f20l{O) +-~ j (2.q~3 -20L/O) = 2 'i~ '106 H-'/bf 2 == IS". 3S- ff: 2.30 FREE !BoDY ~~~ (FORM INCLUDED) FORCE=f'~H Am e ~ 2 :3 ~ESSURE FORCE =~<.H(t+~ ZFx- =0 I ,', F:z =~(3e !:L'J. 2 AREA =~(~ Ht~ 4r tJfr,=i( 0.1-1 +-5,'") ZF~:.o Fa =f'9c [2rH t~ - & - .E.c;:J 2 2. ;z.J F. =f'Sc. [2 rH - ~J2 . I , TO FIND L.OCATION at: F =Ptjc.H~ Z ::z I "'EED ,0 KNOW' C.4 PosrnoN AND THEN TAKE MOMENTs. ~7___ f'<3~"!fr~ A 2 ~t-C{5'_3~ Tf'<3.. r.." T, ~'~'I :2 r+9 2- ~ 2! M) ::I'Jc. ~"t S"o..rol. + !] rl A ~h.t T!j " "-~ 1Ir 1+ 7(J. r lJ Ij, -r J NoW ZM" =0, SO MAw -f'~.. ~(2 rt-tl~+f'Sc. (lrH - ~1~ f.2r) -fXJ4!:1-'1. - A J CANCEL to<Jc. :;z. A H'" =z,-l.H + 71:a.r3 - bT(,-3 - 11('3 .::. Z ,:;I. 6 A =f +:. +-Jf:r3 - £7Trl - 1.1...r:! rr "f tf1 "riO. 3 H" 'DISTANCE FROH BoTTOM == t +-A if =~ t- ('[~(-R-) +(~y r~l- ~1T"- 1]J q= *+r[~(R-) - 5,lH(JtY].
CHAPTER L/ 1././ V =IO~ r7x l, AT (2,2)~ {j- =10 ex rJil~j A UNIT VEcTOR IN -304DIREcnON IS ~I e"'_Y3A I - 2' ex -2 ~~ COMPoNeNT IN e. DIRECTION = e· v- (Y3" 1 A ) !J - 2" eN -2 lZ:s .~/ofZx +I'I~) = 5"13 - 7 = 1. 66 fps. l/.2 {} = 10 ~x + 2 x .~'J 0.) ~ = ~ =:Y.. >( 1")( /0 /0 d'J =2>f 10 'J = }{2 .,. C j (2, I) .'. c =~ >(2 _ /0'] +6 =0 Yl )~2J (1,0) )( Q= IT ,.,,3 ::. ~ CONTROL r - - - I VOWME: i~---+-~-r!'L.. _ _ _ _ J 12 FOR C.v. SHOWN; f)c.s.f'(v.nJdA ... k fVdV =0 o V= 'i (I-fi) fp:... )5('.s/,Cv.MdA = )fA/,(v.r1)dA +~~A1P(V-·~)c:lA =f' [112o.ve.. A;l - )oRq(l- n) :2'rrrd~= 0 ~,.. q1r R:2. (f-.,"- -I) 1J2 o.lI'c.., = ~ .. =I 2 $ fps 11 (1.5"~ l/.'1 V;= .of,.,[J'--'-____;::w He.s. f'(v.n)dA::" ))Ai f' (1J·n )dA + »),40 f' (V-. n)cl A = - f)A' fJvdA + (( pvcos30acJA , JJA. = -~/J"Ah +~1.T~s30"A)o =0 ~. =,q, , it - ,/lie - .., .~ V; =A: ,,;;. = 1/6. /9 fps Ao ("D~"30• . Q =Avo = o. S'S-S' fI?,s
=Al 'LJ + 'TrDv-.!:..2. = V-(-n:~1 +1J' 0 L) 2L 2 • ' V V- = ITrO,,/q 'XV;) == V; "irDa r ~ I + "'D ~ 1 = 1.1-1 ~/s L(~~S-)4-G~tl + .••J 6) Q =12.1" cf~ a.) 1)"= Q = 12.1(, == 5.~~ fps A '7r(fft l{. -; ffe.s.,o(o-.n)dA + ~ 5f{~dV ~ 0 fL:$.,a(v.n~ = mout - w'irt = IQ.2 '2 (1Y-)= 0 ?lfl / ••• .2.M=o ~t M:" 70TAL MASS IN TANK IF-" 5:: SAL7 IN TANK AT ANY TIMe" If ,o(fJ'.n)dA =: /9.2(F) - 2(f. 92) ~s. M ~ffL pdll =!flc.v. 13 :. ~ T let. 2 5 - 3. iLl :: 0 dt M ",( • S -,q.:z.t)•• =~(l-e.J;iI M= Z33 I~ I='O"R t = '00 ""i"" S = 15'0 Ibrt .. 0..) F'OR -t: =:> oJO S =I 6 b. 6 Ib"" .. . b) (t.l (S::z __d;.,..s___ Jl; dt =Js 3. ~q - 19!.3 s, I tI t -t = -1:1 £.,.. 3.Zl/ - ~ 5:, 1 I ,Q.4 M '3.!q - IQ.2 5r;;;- , = -~3.S' k 0.39 :;; 6() mt'". /.S'I :. ~:: /;/) rniH.-4.....----- c) IF THE PLutD VOLUME IS CONSTANT; dV/ - dVIde I - cit 2 AI if. = A~ 'Vi 1.1,. : V; ~ = V; (~ r o.:l =A., ( -¥.r~ 11;.:: 2 ( ..;fr)2. = 127 fps 0.2, = 5'(6l/) =320 fpsl. 1/.9 STEADY I=LOW .r. Jfc.tCv.n)dA:.O oR (r d(p-.rft) =0 .pA=c.onsi. JJc.s ) d (evA) = cJA f EY-r.:!..E:::.'0 ~ V-A A "IF ,0 :. Q. £D.
•~. d M +Jr d rn =0 ~ E 0di: nees :. '"to • • '1.1/ Vi ~ l~",-; v.=0 ~LIIP. I"' ·1 • "I-;( 'j fls.pCi/".n)dA -1" ;~av ~O o CONTROL VOLUME IS FIXED TO WAVE FRONT 4MOVES WITH VELOCITY v,.., TO THE R If$HT. -,.0. A~ T~ A (v-m -1I;.J =a :. 112 =Ym ( I -~) '/./2 v =f r-vdA = ifmo.x" SR21T'" rt- ,..lY7 dr '11 R~ 0 L' R'J LET ;z = % de = d YR ( ' I v-= 2~Jo ~(I-zf' de LET q = ,-& J d 7. =-d ~ ".= - 2 vmJ.0 ( 1- Yl J7Y? dYl l/.13 =!1.J.v:(,0 ma;x .·0 V =o. ilt'1I"mc.x ~I '4 [ p(v.¥)dA + ~ rrvpdv= 0 Cos, ~c.~ o 'STEAOy F~w K~(-o-.n)dA =-1'11; (6cO +WtHoRlc. lb.,. 13J+ 2. jl ]!;. .ydy=0 o 3d WlHORe = f 1.1,; (6d) -f>1I; (3d) titHOR 12- =-;:rll; (.3d) . ~ == 21'L b == -2"oL v, b =-v- ~t ) d... == 2 W,side = 2 ifnr., d~ THUs -2,aLv + 21'fobv d.!:J=0 Lv = fob -z.r(y) d~ a.) -u{'f) =!-AVERAGE' A CONSTANT L1.r = 14:vE b ••• "VAVE =L v b b) 1T(ej) = c. ':J + Cz <j2 TO DcTE"RHINE C; AND Col ) USE
80UN DARY CONDITIONS: LJ"(h) = 0) V"~) = V,."o.x 0= C. b + C 2 b~ 11"mo.x = C, b .,. Cz b2. "2 1/ • C :. l/ V",&1L C... =-~ 11'wrCJ.X.. , ) ~ b b2. 11" ~ q V-*~" [t ~ (~t] . b slnce LV =C-Vd~ v~~::: -!:L.::...::v:.--_ _ q Lb[t" -(f)jd~ LET 1 = ~b ) 1).,.,"0.)( = --.:L::...::,1/-,--_ l/ b1'(t-yt'-JcJ~ V"..."'.... =.:2 Lv,,-"' 2 b 4.Ju,
4.16~~r--- - -....:.--, t J J ----t>- 2ern I J - I ,Scm , 2- I I L_~ - - 4crfl....J MAss~ ~:: MAaSnPw 0," tQ, 2JAzl12 ~?AiUJ "). 1~'16~ 1TQ6)2.1~~O-'~ ~ Uj = B.l5" w.~ ~ _____ J ~AsS~ lA ~ MmJtor,.,<lJr 2 ~ ~ ~;(I'Yo~f~-l~3"!j25 ~ V,3=5.15 ~ CV.-; --1 t r ----; t " .~ . f-.: t ::- - - - J O.8mrn. Zern USlN~ llwSEBVRlON (): ~ As W2t1T9Ilu~CM 4.10 ~ U".5 ~ +rsclm. ,,0 dt: c~ IT d';" .. tDJ .j. 5'Qu:.tlc: ~Cs. ~ =-j'A.V=-ywV Vs CDf +QL( -:. ('ltV ® QL : 0 V=G>'tI : 1.91 CM&- i; QL ~ 0." V: ~.'fw.:1.1 ~ A.ZZ ~MowQre Is ~ lr~~sltr ~.12 "''i.=jrd2..o{~(eo-<)dl- o V.e :: ~:,"" Q= '-'4Ii... I> (0 kr ~oh I l;1J,.=fV, =IZC~
4.24 v 17 I @BaTVsc:nt (1f(G,~ ~~ j'21l'L bV~t-r 4: Vec,er ~ v l-~ b ~~Is~ lTtJar=4lT~(~-Ctr; ~f~~4.'2!2 ~ n1.lA7r " f Ilfe2'1fLd"( o :: 5'!'iTL blf~ ~ 0°0 lf~: ~b. 4 b
CHJPrE'R S' 5'.1 ffc.s.p(O.n)dA =0 5:pv,dx :: 2 [p~lfdHJ.:C~dX] #v, =3~ .: ~ ::' ; V, =26."1 fps 5:2 1?l( =fls.VXp(v.n)dA =f>A~2. -~A V;2 =I'A(1.0IV;)"vz -flAv,:1 Tx == -~ =",A V; (I.OZv;.-V,) =-~030S" ~XIO.UJ-A300~X6i8 ft) '32. H l./ IbM ~ lb~ Sa =50IOlbf 5'3 Xl=x = Sfc.s. ~p(v.n)dA ASSlJME VN IT L£ NG-rn f:(p, -~)dy - DRA~ =,Pf1(v;xfc:/x+2fv,·'dx'-f!r.'~ =f'~.~..t + 2V;2. -1/ V;=>J :. ~ "'l1..".:l ( ~,~ 2i I I SJ~CS FROM 5:t~ ~ =3 vI) o -=-(1",)(.,! .,~,)(8·OO ~) =179. gVal P,-'P-;a. =t"(J79.e #- ~f'@.o)~ = 189 p~f=J.31p£; =9.MJ<A:,. J8 ~~ ill r" ~ I.. 25"j'p$ F~ ®~ Q =Al~ = Az. V2 = 3ff% Va =~ = ZS fp.s I=~ = Kc.s:.V~ p(v.n)dA I=x =(pvA),V; cos (-.300) -(0vA),(-l/) =I'Q~ C~)+pQV;.= I·g'''f~ F"'j =(DvAkv;. Sin(-30 e ) =:-SI'Q.15 F~ =271 Ib( ~ i='j =-72.71bf IF BLADE MOVES TO 12~ AT rSf?:; RELATIVE' TO THE BLADE: V; = -40fps ) 1.& = 40 fps AT THE LEAVIN6 S£:CTJON: ... ...lJ = v;. r~l. t-4 blo.cle +V bo..cl~ =(34.~x -~)+40ex -, ... A = -(~.~ eX - ZOe~ (0 I = 77.'6' fps " .r - - - -'"1 ".5"~ I Cov. f - ~---0-J 5.5" Lx ~.,. fdm =0
~= /S7.t ~/s caltlTROL VOUJME MOVES AT V= 4.S- ~ e.x. MEASURE nUID VELOCmES RELATIVE: TO TANK ~9 = FoRCE' O~ FLUID BVTANK ~I='x = 2.. ((( v~M +(( VKdm dI: J))c.v. J)c.~. Bx ==-if(vx M)+(-m)(2. S"7J %) FLUID IN TANk #-lAS 0 VEL/JC.ITlI R~LATIVE TO <::OOROI NATES Bx= (O)dM -m:l.STI=(157.. }~) a:f :s X-{:2.57/~) =-404N -Bx .:: 1<>4N Z~~=~ ((( ~M +a- Vy drn ~~v. -';) - JJc.s. o 11"'1 OF r=WID l~ TAWf< = 0 B'j =-(rn )( -~OT)=(/57.1~r07~ = II(/N ~=-I/Il ~ ""':'CO r-----,-- i EM 3 :<DL ____ J@ Q= Atr= ,,£2 ,A,=O.2SOQ.:a.~ A~ :: 0. IS";po ~~JC =fb:,.yf'(i-·")J~~dV o &= Jo. A,v,:r. +-f':l~ ~~ =,oQ (Vi-V,J=I'Q (~ - ~) =,oQ1. (-k. -:k,) 19 =1-66> Ibf .: THE TENSION IN TIlE ROPE = ~ = 215 lbj: COs30- ~ zt=J(:: ffc.~. vx!'(v.n)dA 5.: P,A, - fi A2 + I='x ==-1A.2 ~~-;: A,1I,.l =;:; Q(Vi-1f.) ~(p. D12 -liD;)+K =1'~2(*~-k) Fx =--1f(P'D,2-P"~~)+~f'Q:a.(k-~ SINCE ATM05PHE'RfC PRessURE CANCELS..... ~ =p.~ -;: 50 posiC) P2 = P;2.~ = 5" p-s1S F - -171(so.lq~XI)-(5'·IL/I{)--L-l x - 7lC .:z3.O#fJ +;f(O.i)(J.94X 9 )(;23.0~-I) :: -5"630 + 392 :. F"x ~ - G238 U,f b FX ~ .[l::J <D ® Fa ::' 60 PSf''l :: ?~.'i psi~ D. =3" :: .:lS"' Q =i()(J ~oJ/mit1 =. iCJ2 R-~s P2, =1'1.7 psi~ O2 ::- t.sll ~ Fx =KG'S. VxpCvon)dA
Jr ("'P.D.:z _ n 0::1.)_r:" _ LJ LJ(i1.{L _J..~ LI 'r S ~ rx -iff' ~ OJ., Fx =f (?I.;r. 9-/11.7 ·2.25")lb f -,;p(1.9L{'Q ~l{ .qr) 'bt FA' =5'02 - 9f.1 =L,J()¥Ibf 5:9 • ~,--;-~~V; ZFx =JL.s.~f>(1/·nkIA +~~ o == P.AI - 'FiA~ ['.5~f'(-v.nJd4=f'~~lr'~SVltAjYi~ p.-~ =;O[V;l- ¥:l-~i1f;?] BY CONSERVATION OF MASS, (( fJ (v.,j)dA :::0 Jlc.s. 1'~'Vi -~(As~ flliVj) =0 ~ :: ~s lIS +~ 15-:: :!'1(iO/ps)t:~'{~ a) ~ =li+ps h) B.-P, =£If(Jtl - :7{1oa)..'.0;(<10)1 ~.I"W ~ -p. =lilT psf == ~76~, lOO ~ -"---::;~ ~ --"',---'~} ';'i:2"'~~JsA :3~ q F= k5.vccs6dm=(-z-oX-i.Jz -::-FaRcE ou F'LUfO)ALso ow PUl~ 20 5.12 (f) c.v. @ ;;---~ F[:o: ::eJl #////77///7/7177////////77//1/ FOR COORDINATES F"IXE"D TO THE CON· TROL VOLUME; ZFJ(&' fl'S~,«v.n)dA+~dV o ZF;c= Fx (( VA',£'(v.n)M =PK1f-}.f) Ga~e]2A)}c.,s. - P [ v--v;,]2. A Fx =fJA(v:Vc )~(C05"e-I) TI4'S IS THE FORCE ON THE C.v. AT THE' WHEELS. FoRCE ON VA NE DUE TO wATER J:LOV,- RK=pA (1T-1JC):t(j-~os~) POWER TRANSFeRRED TO VAllE j P; RxV"e ::.pA1JC (v-lJ"J' ( 1-c.cs~) LET m= 1rc/v- p= "A11'ttt (lJ"-1J"nt)~ ( I-GOS~) FCR "Pmo..,c.J 1:= 0 I-~Ht +3ttt· =0 :. m= I aR ~
ttl::: I as MIN1MUM .~ FOR "P='P~J v-* =~ ~a.) THE VANE I~ AlTACHeO To A VH£El of RADI(IS ... ; NoTE TWA1 ALL MAss HITS CA'RT M«j == I'Av-r[1Tc.. (I-'-DSe)vc::ose-~ ::I'Av-r(/-caseX"t1C-u-) m= VC/v- .) ?= ~A v-3 ( ,- ccse)(m:l.-m) @-o' IAA_ ~ dMot - ) nl - '"'- .: FOR -P-P,..,ClX I clc:N -11 Q.E. D. =< b) 5:13 CONSERVATION ~ MASS ~M +5d~ =0 M =IfX T/,'~ Jd~ ::: -~~ (UNIT CROS~ ~EGT10N) flz i +//"i-/iV; =0 X=Vw, ~=-~ ~(1T"",-~) =fl';-~ (I) . MCt'1ENTUM ~ FJ( =: ~ rif-cJM +rifd.-H "Pa-Pa :::?t(~x&)- V;tf~ =~ ~ l.C ~1f4 =~A (vw -zr) FROM (I») ';;,.02 (~-~s) =A'It,1..[ .:1i-P, -A~1& 2.1 COAISERVA-not( OF MAss! V,A. =~A2 MaM~NTUM : 2F=f-oolm P.A, + ?(A:l-A.)-~~-~AASf> ~~ =/rv;.2A;. -;01{lA, REA'RRAWGINq (P.-~)A, - ~ (A;l-A.) t- p (~-t) -f'9A<1 y =- /Y A, v,-(,;;:-tr,) P.-~ t- (rs - P:2. )(~ -I)r'S~yl. -= jJ1r, (~-v,) ~ = H r4"P ) -v;. =V,i'A1f) A2 = At +.AA _ -AP ....(p-~)AA -~4Yf -;>v,£IJ .A, I As AV-o-+dYJ AP-dP~ A ~ A• .1 (p-aJAA ~o So -dP _pgclY -=..ov-cIv :. dp of-;nrdv- t-~ dY :: 0 CD A1=' 0 TO? ",,:l v; == 12 tvJ/s R== 12i KPa.~ A2.,= .113<1m':&. LIi= ?'I{V tHis 11=1l.{5" J<P~
Q= Av; -= o.3l/"I'4 Ht"l/s m /,Q= 841.1.1 k'~/.s g FJ( =If"V;c a.-H Fr +P.A, -P~A.; CD'5I)-~(v;.cose-y;) Fx =R" -=/,Q("5~e-v;).,.p~cose -BA, R" =(ZCff.1X-S".S'22) +1l/2~o - 9~9. 6 ::: S"OS:S-JJ F'3 - ~A2 s;,,8 =;:JQ. (1{ sine -0) F~ ~"R~ -':jJQv;..s,'r18 ....B.A..1 sine = 31?$ +r:a2 'R~ =H, 3GJS' N· tiAj SEC.TION ® ~ +'P.1 A2 - P3 A3 ::. ~ (Jj-1,.1;.) Fx = ttl (lJi -1Ii)-rf3A:J - P~A.:z. o-A +"R1"m (A3 -A~) - F)(=O o-A =Fx.-RiMtAs + Pc-mtA:z. o-A:: m(Vj-v;,).,.(p~-Rn.,)A3 ~-'P~)A.2 o-fJrof.)=E!' (33ao) t U:~~(:l~t 3!U ~ - SHi. ~ ~(12)· 0--= I Z2/ psi (COMPRESS/Otl) A.UID o;-A, N02lLE~ -SECTlON CD 2Z F)( +P.A,-~~ = 1M (u;. -11,) F'x= mClI:z.-t()-p'A, +P~A:a. o;A. +~A:a""~ +Po..t-.(A.-Aa)-=o 0; A, =-Ii- -O',iA2 -l'o.~ (t,-A.1.) 0; A, = P.A, - BzA.l -m(V2 -11,) - o.iA;l - ?G..~ A. +~ilt'A:z. 0-= L/922 ps; (IE~SION) -~---=-.::..-----, Z F' =rc.~.vdm R= r vdm - ( vd~= Fao~f·E. OUT )n~ FLUID =2 fa3Jf'~2(~)~j t-f'ifo.l3ol .... --;l,V;;2 bd (MOMEN1UM OUTSIDE' R::'2,o~2d..,. 3p~~- 6/,v;,2d :: -r>Vold FoRcE o~ CVLlNDER.: -R=l't{/J S'Jt ~ -~-- tJ;=10fps ~ 0.) AIR: lfw = 1130 fps 1'= O.0023? slc..c.gs./Pf3 A'P= ~ -P. =Pal.{."~ :(.OO:131XIl30)(,q - =:26.KQpsf = O. 116 'i!ps; b) VATER: VW = 11100 fps p:" /.<t3'l "5/W3S./ f+3
~rp= (l,q37X 41100)( 10) = q,} oi'o psf : ~'33 ps; S.!1 3 ~­ VALVE OPEN FoR AN OBSERVER. M() V/~ AT 3M/s} THE SITUATION LOOkS UK£' ~O ~lfw-3 4-V"~-3 ny~ W/HcH IS :nJs.r LIkE! PRaa. 5".13. SINCE Vw ~ 11133 mIs, Vw -3 = IQ30 w.J.s ~ P == r'V",./A'V= (looafl 'l30}(3) = 4287 KPc. 5:20 FOR STEAJ)Y F~W EMz=ffcfxOz)c1ti "THE RADIAL VELOC.TV AT 12 RELATIVE To TH E: IMPe:LLE"R = <51 ~:' &CO~. ( ~)(.~6S"q fP "- K11f ) bas - cy.1 I = 10. ;J.1:l tp!> THE ABSOLUTE" VcLoc.ITV (TAN6EuTJ = Qr;- ~ =82.38-/0.~1;) =-1'J.17fps. t~= 10.21'2. 'I-.-- • 8.2."38' VR~IO.""''l. TORGU E: = r~ 'tflS5. f' VR A T~ .l . ?2./? •.!d- . Io.:u~ {2frsY-'J 12 32.1?II 14{C/ = 2()1/. 7' i+-Ib f 1=bWS< :: WI = 45: J" np 23 to..l1o( =3E:§' =.?03" oc == 3So ;l<l.11 a) e. = 125"0 AXIAL. L04l) ~ F c }c:s.vdm ~:= J. 71 cfs v= <S2.M V': (i·?fX I'lei) = 2 't?(. fps ~('&-I) vb) LOAD = (t.?lX6'IX2 I. 1') : TT J~ '3:1. J74{ , I------··-=r [ t ~--Lo=- r 1.2in I ---I .'---'"L..- _ _ I c.v. - - - - y ~ M~ =M~ TCR'<UE ON ~PRJNI<LE~ I3Y SHAFT: {{ I ; x~1 ~ p(v.y,JJA=2(pAv't-r;lJ)~."5. M, = -2l'Av2 rfj = -2.('2.~1)'Tf( ~f(C(OO)!s. <jc. =-1. ~ U:)f-ff 5:13 T=J(rxv)d.t:. =-"'R(lt'si~ 1= Mf -w~)'p2Al.fr Mf =2AfJ lIr R (vr 'Sit1ol. - wR)
s~ ~ ) L ~ ~ t II I x i-- 3' •+' /" ----1 XM2 = ff~s('-xV~ -~o)l'(v.A)dA :: sq r(-I La(v)-t dr 3 =-~v:l.t [rP5]~=7'V~t(36) V ~ /') g L. t = 4-;~= .::l.. I.:t = c~/ -. bt' .: M~ =595"8 ft -lbf , I + t f I I IVsr _______ ~-v. I I L 2F =1k<iyp(vo n)dA +;t}[2pdV FaR caQR'DI NATE F=1X'G'£) TO cAR I,." )(- DIRECTlotJ Z Fx = l; r( V;r ,LXO.n)dA=pAj 11 (-'1>C'5 .. . . -f'Ac V~ (-ve.) &~)fc.v. V)C pdV=:. ('(Ae Vs :-Aj~')(O) :.FK::f'[Ac.V;Vc -Aj1f2.] I)J y- DIREC.T/ON l:F~ -= F'j f~c.s.V'j p(-(J·;')dA :: 6oA~ vsX-~) ;- CfJAi Vi X0) ~ fcr v. IJdV=O dl: )J)c.v. Cj r :. F!j =,0Ac. vs:z. . FORCE OF FLUID ON CAR" R=-~ 24- . -mitt =~out plfh =pv-(o. +b) :. b-o-. =hcosO(.J b+o.. =h b = h( 1+ cascX) 2. . 0. -= h (I - cos ex.) :2 ZF"~ ::- fV'j dm F:pv2. h sin ~ b) XMr :: )(0 X O)z dWi F"~l =~ 1!f'Va -~ V";,vb .:: pv2 hsiYloc.R= ~,Pv.Ji:lf'V.:l. ,,_ I , (o.':l-b~) .{ - 2 h ~l"""'- =J:lI(.Y-2coso(-f ~ ?f-2cOSc(~ 1I 2 h sino(. f= 11 cotcX 2
H2 = h~ +2 v-:1 n/9 H -= Yh~+(2V~hY9 b) USING CONTRoL VOLUME-lI) ~Fx= f(t:.J(xl'(O-.J1)dA f~V=i' o ZFx= P.A, -~Az. -""R=YnAV}( 1=1h - P:lL -1< ~ phYa(~-V.) R= Pah -~L-,ohv.2('X-I) F'ROM HYDRO"STAT/C:~ p=:~ ~i"c:X 1. ) «='f) 1.=f' 1,. =~ -P. -=1'<j11 :z L5 R= ? (h2 -L:a)-f'h~(1J[ -I) 529 Q,~j)()ny V.h( =Vz h-z- M.o~UJ-.1 ~h.I~n.Z= ~Al)~ ?"'Sohjz ,~ =5'0h,h Wt,AlilC :z Jv, hi(V2 -V,) ~ ~.-i~~" ~V.hJ (V2-V,) ~GNnw(rr V2. 2~h/h~ dn~ (ft>~:) =V;~h, (~,-h~ 2 ~1... ~I-Ya. h.:th, h~- 2v,~=0 ~~h2 ~l = ~ (~-"("'-~f -02 gh, ~ ~U1i).)vrrY Vz=1~'~~ {1~~V;~k,)
5."3D r - - -, USD..r:;T~ l~ ,; I ~L~j. ; f:~~1I t : I M=s>Ah Vz - n: m, '"gAV: -~AIi L_k' Y ~ + *dt<A, :.0 c.v. . . ~ gA n--sAtt:rD ~(JJtff1 ls SAr{~USD tv1~ LUrr14 tA$ + Lf(f " ~ -t ~lJ~dM ~~~5 _Asas ~lQAL -~~~+sA%ih~)fh2 ~u:r Is 'kz -~ 5.3l USWG-rut;. c~v. Af!CM5 Wrrf4 II To TH-g ~(~Ha>w) LM~ :: Ccrxu)t>e dM j J ' l: m01n~ V~ ~ := ZL19 +t.;~ ,A: y~ +l:L =O.442 W~"L TAk:l1J<l ~ ~ 6 W~Tb>TW6~ -3'P2 A4T:3VSAV - 3'4~l ~T = B.S T :: 40.3 R-~bF 5,~ r - - - - - --, 2 v,----+- _+ L- e.v-)J - - - - -- - -t Hg roo.TH& C.V. AfDIE L~: ~~d~ ~+~A,-~At%~(V2-VI) fj~ V2 ~ ~Sf;{2~ Of ~J~~~JD ~.~~~ '9,-fz :Tf4Js~ k ~ o:=>&T~~~* ~ Is (Ll~ ~ As g~~) Pc+Jwa(L4-t)=~tS'-t+~tz- ~-~ :z ~~(J~fJw) =71.~~ ZPa.-
~ 'J' Q -:::.A,V, 'Z 'IT (.08)5 =0.02.51 mi4- rh: gQ :z 2'5_15 tzrs V2 :r V, ~~J'" (2.8 M,i ~ 2 m(V2-~)+~-~)A, ~ 2 19<O ~ 3«) "2 55coN 5.??J SUSCE ~S~ 15 Cbv~ WLW = ~CUT=S<4Xt)LO st~ tno..q =eo] s/~ mOOT ::I :25'0)fJ-dY o =2J152fa-cps~'(}:IY () ~2glJ2[Z-~] ~: lf2 = ~ 1!- :z 55.0 ~~ 4'[-8 2..7
CHAPTER b I--~ CD I I I.Z..,.= 22 -2 ---, IT ' P,=:/S-'"~L -t-_J ~:: 175"KR.. 0, =.25Itt D:z=alS'2 ~ WORK ,.- ~S(et!)d.;,+ ~ rrC..:;{dV o J~S. ~~- :. -1r= (et~J ~ -(erl), m =~[, ~~-u.2. R ';"I :l lU,,-U, +2"- + ~'i +~(~-i')J S/ijCE 12 =- T. U2 .: U, ,/ • m =f'Q =1025·.'2(= 21S.2Sk1ls V, =Q =4.278 M/!) AI V'- =Q = 1/.S7~ m;~ A'l P, ~ IOl/3Jdt-· IS",HjAf- '3~'!?I;) oJ ~ :M.92 il1 ~ J ='i/~ 32 b Po. SU&STITUTION YIELDs ~$W '2C cH =~J1916 AI.., = 35.9 KLJ 5 MIUUS SI~}J I NDICATES WORK INTO FLUID. FlUID APPEA'Rs TO BE H 0 A ;z. ,I SSllME' NO 'PHAsE CHAf-IGE; THEN 11 - LJ V-l) '2.-r,) .1.- I n- de.( T U ~ :z homl~1 u =CvT <H: dot n W d <- = (no - u) WI IN ~t C", II =(Cp To -Cv ~Es.)0Av ),N dt flV ~= (§; To -1R)CAv)'N V V To :::. ~N 1" V,./ 2Cp ::: S30 ti'I()J~{J. 35ST:1') 'B.p.. (:)X. 21(){ 32.Jr'() f.l.lhf/'os"l{t(xl()~j =- >31.01 ~R ~ = (1.1{ ·5'31.0{ -5"30)71(~tOlo) ~t ~ 10 ::: 2"'.io/ = 61!J "E'5 6.1
6.'I sa _J'fAl .:: ((ore. +~)(0 ·il)dA de cit )lC.~_ r~ ((f 4dV ~t»>f.v.-'o JL.ie~ +-'%)I'(v.n)dA =0 . tri. +t(I+~ =f+~t~~ r} U:z. - (..(. = P. -~ == Cv .1T to AT :: ?,-J=i fJCv c --I ~ v Ib,.,eF =IO·lq" = 0.029'7°F '2.'1(IX??l) 6s - ~~s = ~c~+-~)f'(O'n)dA [£Js =gQ. 6"5"0 =qo~000 ff.~tf tit .K2 o ~ (e.T~)o(v.n)dA =/Avf>1- _~l. ~~. 2 +.! ('Po-~) +- ~ (l:~ -'jA) +C~lf' 0 j Ps =-aws/dt- t'ii tell' -,-LJa (!.jA-~ ) AV 2 Tf- J B 6.6 =(-2010 t 3 g5"0 +-3CJ 25" -I- q~7) == G702 psf"" =~6. S"psi"" CD D-IO" ,7 ®li=LiO~ 1?= -6ps'I~ 29 - [lJs = M~f'Pl. -~q~ + 111:I._l{t+- ~~l de [- (->9 .2 'j IJ =(lXr.:J.l/).trnO+b)/I{I(.r, t 53.7-:2'.0 +51 ~L-62.1./ 9'" t;(32.J~'I) j - dW.s =2?iS-I Ff -If". dol: 5 =: 5"D.6 hp 6.1 ~_ _ _ __ CD • ® (fW-u----==---- Ah:: 2.5'em. P. -B =25"",. 10/, 3:2S i=h./a;fns 102 10. 33 mH;.ola.+m == 2l(5'.;; I=b. v/' = .3.& = :2 ·2'15':2 = ~02 ~ P h22 s~ V.:. 20. 0 I+t/s Q = Av= 7TG3)2fl-O) =I.t/I? mJs-q- == 5'0.0 ft3/S
-~w= I.:U~ I.'1l1m3 202 ",~ de M~' 5* ·2 SS = 346 "" oR .3Yb KW =0.465 hp 6.i ENERGY EQUATION - STE.ADV ,..:" hOI + 1IM31103 = Wt:z ho:{ A'S p=c/ v,AI(CvT. + ~~ t~) t V3 113 (C",73 + ~3~ t ~3) = ~ A; (CvTz +V.l 2 r ~ ) 2 ,.0 AS T, =- 7;) p, ="P3 e=vT, l' ~rv,A, f V:.A.3) t A, v,3 t"A!.vf ,u 2 : 2 =V:zA2 (Cv7i t ;'2 +-;) FRoM CONTINUITY; V, A, + tI, A3 = v2,.A:z J 112 =V. -r 1r,~ ~A2 ~V (T;1 -T.) +P=;P,]= ~,~ lft~ +A3tJjV;~ _ ~ Vl.1&2. 2 :2 CAN ELIMINATE Z6. Cv (72 -T,) = P,-'f;i + V. .!:1,.2 +AJV]V3~ ,.0 1f:2 A;:~.:l _ V.14 T So Cv(-r; -T,) = P. -P:a. + I 1I,; r' I t A3~ 2 A,V, + A-!lI3 V:::)" l M( It 11:):1._~-_~ --v. 1+ 3 3 A3 ~ tA,v..4 ;;. I A,'if 6.9 MOMENTUM: f>. -~ )A. = p~2A, -1'1f,'lA, P,-~ = p -,0 t!i'4 A3 ccs.G + ~2[43~ ~-2 • VI - 2 b, c.osB I ... Ihv3 A. A,V, « p(et~)(v.n)dA=O Yc.'S. ,- lL ~ V ':1 ve, -:4 +U13 - £.lit t "Ps -~ :::a 0 2 ;z> VA ::= Q = 3f1o/s =3.B2 fI'/s AA 701(19-):1 Us = Q =~ tI~ ='-IlI.4 =15.28 fl;ts Ag /fg ~ -~ = Vs:l. -'{12. + c.{~ -U A I' Z PA -~ - 10','" + .liSP. 109 -:2 (3J. J =?'I)
~-""B3 = 2./S' Q. of flt.id fCj ~ = Z f1- + 2.IS A of flt.ic:I = 4.15 w- at flu.lcl. ...-I:t!.{ 6.JO ----=-t VA: 2.1{'5'"Y ~:l:: lI.JI V4 2 "Us =3.gj V 1:!§..'-= 1.:3 V2 2 FaR TI-I~ COlJTRoL VOLUME SHCWN; ~ -~ -{if::f{(er~>,(V.n)cM o 0 t. 0 t +~~C.S.pdV ~t o 'C.v. ~ -'PH + VA :l.- Vl.'2.. t ~ (l1A - ':i1. ) ::. 0 fJ .L (IO./l/L/ Ibf/f+2 ) +y2(1.11-"7.3) 6:2.'1 lh""/f+3 ~G + "32. r;L/ (-;"1 -:! 0 y2= 1'/2.3 y =13.5" ~ 6./1 ~LUIO WEltiHT 31 Z~r = rvi! dtH ;:r ( p(O. Vi) V~dAc.s. -F -Lv' +PA(A =-111 VzlA +~(o) USE GAGE PRESSURE ~ R~5Um FROM 6.10 r: := -t.J of- PA/A + mVz fA w:: p Q VOLUME -= 6:l.l./nr~~.s +'lI) =1/1. / /hi ( ~S-7" j.'1 !/rIA = IIlAz :S'1.51(2.7r'12 '-b-) t4 t-1T. 1~ -; lIi IA :: 3Z.6Q fps F:: -111./ r 10 '!!.1.+ 62.'{[,3S'X3r.., I.{ 52.lrl( F=1399 16[ ON FLUID FoRCE oAt LID IS /39'K Ihr 1 b) THF FORCE ON THE LID IS THE INTF6RAL 01= THE' PRFS- SURE OVe;K THE' AREA O~THE LID. WHILE "'BE-RNOULLIS EQ UAT7 0 N Gtves lis P=PCVEL.) viE Do NOT KNOw THE VELO- ern' VARIATION ALON6 THE' LID. CD ® 6.12 Q=6~ AIR ~'S :lCLCOHOL fJ=· ~J.I:tQ "P.-~ =0.1 WI <l.lcohol :: n L/•'l~Pc. A.="'U'(6)2 =.2'83..,.,~ L/ VI = ~/A, = 6",,'!./~/'j.'83 ",.,:1 =21.22 "]If; f + ¥l.+tj rl =, -t lj2+ ~ ~2.
- -')A;:l· p'-g =7gJ.f. 86 N/rn2 = 6LfO.2~ P 1.226 ~/m3 6'10. 2 = ~~r-J (2;2)~r-~ ~t=3."ZLfI Az= .510A, =a./II'1ml. ~ =. tl29 n1 6.13 -- V. ::L_ VJ. 'j"') l. 1+ i2.-p,= 0 2 P V, = 5:1 fps I U;1 = U.S" ~ 11-p. = -2.0'15' Fl- of H2 o,.oj = -2.a45 " H;20 ( I' fig0 ' 13.b "H;1a) = -0. /5"05' ' H-S -: -/.1r' Hj MANOMET~R 'READING' 'S GREATER AT (J) 6.JlI h ~4---~.. '~---------- d .. ." CD :.': .....~~- AIR USE: SfRNOVLLI £QUATION BfJ1JE'EN A) SUR~AC£ (5)*0 BEFORE AIR IS INTRODtJc.e:D (ST'A. fa) Ps .,. YJ.~ +S~5 = 'P.s ~ V'B~+ '3 i!,.B P 2 P 2 ~2. =<j d - '118 -"Pa.+It1 Z f'"~.o a) B£11J£EN STATION lA (AFTER AIR IS INTRODUCED) E @I 'R ,,2 :l ~ +.!2 -t <j l,2 == ?A + V,A t SZ,.A PM 2 PM2 ~ = 'Pa.+m ~ V,2:: II,A I Z~ -2'A =htd .1. '"RA - Po..i," CONSERVATION OF MASS .. . . .mA,R +WI H~o == ~~I)( ~AIR +fH~o A11113 = PM1r A16. tMH:z.o » ...nAIR (O£J.Js,T'{ 'RATOa:.' IO!) .: ~= 2 V2 (Q.fIXI.K)('-P;r]J ~ - 5'. 9~ IHls 6J~ -h- 6' ·1 1(- ~"-!jf/=f{c5.(e t ~)f'(v.n)JA 31
IAJllfRE K, = 2 A P J K,. = :2~ P t: -~ ~~K' +K~(Yo-2)'fs-(KI+K1YO~ ~AT = Gbf = 40.2~ '5~ K2A-r ~ ft .,fP=(5"-3)09:- 46. '6 ~ t}l. 't(,=(2Xlf~.~)(r~.'Xq)(3:;.JflI) 30 zfP' . (. KS") (.1S-)(12)(~2.") = J. S4 ~"'J<:l.('1o-:2B~=~CJ.i+2c~p~12.21£ [I<, fK,. ~y=[3D2.Z +.2~(S~=2l/.99 ~ .: r= -~o.;J.S(~.J? -:2¢,9'1) :::: 109. S- S :: 1.125"',..,;,.. b) "'P. =B -FrS" = 136./3 ~ 'F?z ~1'o -~~ =(1.21 ){24)1.=3'1'l.<fift,.. .2 ~?=B -? ='3Ql,1I1- /36./3 = :J/~. 3S- Po.. AH = A"P = :2IJ."35P.. o.16~oj (O.1~jJOOO~/m3'Xq·f1~ I 6ft APPLY CoNSERVATION Or: MASS ~ + d~ =0TO TANK: ~M f"t c.s. M =Tlo2.hp 4 ~M ='1l"O:1.f' dh (c1m= 'i/d:2..pvc ;it ~ at' )c.'i. LI '7IDf dh +-r-r#dlp ~ =0 i.J at 7( 4h d 4 ...I t-Uc-O~t- 0" - APPLY' 'BERNOULLJ ('QVATION = AJ BITtJ£EN SURFACE i 8I ~ - 'i1t'AC = - lie. 4_'3 H ,a :2 "'S.) "BETtJEEN '5VR~AcE' ~ C Pc ='Ps =~T~} Vc.2 =2 <j L .: 'Ps -i?s = -(L +11) :: -It! Ff f'9 Vc :: ,I;2.qL = 25: 3~ f'ps
Q =Av =trd:2.Vc. = O.I3i! '(:t3/ 5 ~ ~ +..£ Vc: :0 0 dt: 0'" Vc -: y2'jL - (ho -h) ho=I1@t=o LET 11-h, =z 4h = d~ I dt dl: dZ! d'l...,r dl .,. D~ V2'j L (I +z) =0 -3 - ( dr :: -d':1.Vl~L (' dt )oYlf2A. D:l Jo ~~. @ t=o h". 1,. ,/B t =T ho-S, =3' 2L '/,- 24. . = -::1..~'{JaL T; -3 o 0:1. J T- JL D~ ( ) - d.1 Y;2c.3l I - ..;I - 3//.. = 105"1/ s == '30.9 /H;". 6J185~=/21;..7f.ps~ T:l/o-p PAr... =p~j"~J(1O.?.3 I~ "=2051.11!1l. ~} fl.2 fJ=:E ::. :205"1./";') =.OO~ 39;< slu, RT (,115" ~()O it! PAlM + ~2t7}2._:E t 020P f> ;( -,0 .2 AP =(- 00~3'P'l!5912- #l1/()o) = 1.3(,6psf =O.tXBSpsI3 P= :J.05"I.lr.r/.3" =2052:5 ?sf :: 14.2Cpsi 6.19 Vox- =~. Cbs 30- ; VD<J = VJ' 'S,' 11 30 .". ~. :5.'25'"15 Q = VJ' A. ::. 4.42.10""" m?s HEAl> = 'j + ~."J. .19 =.6+1.6' A Br;:T1JEEJ.J CD f ® : =2.2.1 1ft c ~~, + v;i r ]( = '3 <12 +- V;z'" t- 'PI oP.2 .~ :z;p Vi = Y;2'3 (tj,-~hJ = 35". q fps Q= A;z V:z. =0.733 .f13/s a.) VA :: Va=Vc. =Vt:> =A.l U - ~ A ~ -4' ="/.9rS -Fps b) BETWeEN CD *A : ?A =-"B+TAt 1-,.0<3 (~I -<:1.1) -,0 Yd.2- , ::z = 2'1.12 pSI '5LMILA~Lc,lJ ~ =11> = '2;:;.12 p'S~ 'Pc: = 1£#, IS- P~'t 6.21
A =".193 fI'J. ~ v= ~ -= 6.5S fps ,+g: +':11 <j -= "P.1 t lfl"+~2 (),p- P () 11.= -f:1.Q - V?_ -b(3.l.1'~(/) - (US)). I' J 2"- --r =-t.1,.'L ~: p.::-(62.'1 1~)(f.".2. AJ~) =: -2.i,7ps;~ ~lf ,,~'" / STATION : AT SURFACE O~ 1-1-,0 P. ::'P~", ) ), -= 0 ~ '1,:: 0 STATION : AT PUMP IN LET ':h = q' I ~ ='P.... ~rAl +0 +0 = '('+ Et t 1I~:t -1-4' ~ ~ 2", v:z.":Z.. _ BT.t -B- - "8:JLI,/U'/.7-.2'O.) ~ - p~ 62.'1 -~ = :2S:~ V:l.= ~().¥tpS ~ A='iT:Ja: :2'7.1 ~"2 l./ Q= All ="7.Fo ct5 c..I Q:: (7.loX(0)( J;;r)= ~sol ;;W~ 6.23 I=RoM DATA OP PRoBLEM S::ZOj VElCXny LEAVJN6 IMPEUER J 'lIr =I".~:z. fps I Vt; = 10.22 fp$ J w r: : 1,.:2. fps .,.-- t10.2:2 .fps L.._ _ _ _ _ _ _ '7:2 -rps 35 HEAD:. v~ -= S:21"O = Z2.S-f}- .2~ 6'1.Q ~'P= 11'112 =5'279psf =3'.~i ~I{ THRUST - Q V I V - AnJs hp -- Q Ah • Til RUST -.. Q. {i;i; _ ~ .• hp Q AIt yAh .: HIGH VOLUME', LoW PREcs.S()~E' PUMP. b.'2~ 1>= S'Ops,'3 D: Il I" CD A=CZT'/., ~2. V, =3.6'l,f,,!o Q::. 1.9 cfs S.<i. - 0.'0 hL = 'B-~ + v, :2, _ Va.J. P:J :lj =(1'141)(45") ,'I -"1211/ +(61.'IJ.O. "S) 6 't. 4 = 130 - II :2 ':: J g ft. 6.2' FROM 6.~ ~ V 8 = ~cl- -P,~ - ~,.", :z. f' tt~0 PIA - P,mM = tj(h+cl) ,oM So "PIa -1?1A =P+I:a,o <3 d - f.~B:z.f'~0 -~ <j (h+d)
ACROSS SECTION ONEJ THE VEL- OCITY CHANq£S BY A FACTOR OF ABOUT 2. UNLESS THE: MOM£NTUft1 OF THE AIR IS SUF- FICIeNTLV LARGE -ro ACC[LERATE THE FLO~ THERE WILL 'BE· A PRESSURE: DROP, A CHECK OF AIR VELOCITV "REQUIRED YIELDS SUPERSONIC AIR SPEEQ, THUS WE MAv N£~L£CT THE AIR MOMENTUM. t AmP. AIR : v,Jj~~ l. BEFORE AIR ~4a-t-~-l rl~ ZFl: = )Vz drM fiB -11...)A =m(v2 -V,B) =~A~ (V2 - ~ '4),a~o "Prs-"PlA =-~2.(I_g ) . fJu,p TOGE.THER WITH BERNOULLI EQVA. ~ vt(J -~o)= CJd~oU-tJI i-~)] I Ll 2. v.l.- - 1M J.. 2~ ~,. = c;;!d PH~O r,-~(t ~dn p,... II - A4 ) 2~o .,..---:--~-----:- '6 ~ 9.iIXI.8~X'-1!) :s 3.113 IM/s I-~ A q2 % REOlXTION. /'.2'1 tM ='pAh ::f' 7:;r'l.(hfho) ~ =p'TIJt dh d-t .~ dt ~t :: ~fi1 vC(At =/l![t.:J.";29h ~ :: -d 20 .bur = -d~ i ~Cjh t)2- D~ Ch~dh =(~-d~ ~dt 2~ Jo D~ ~ :n~I;,:: -~ vSS t -= :2(J-m~-b.S&3 t: -(-G.st>3X/5)2. - /''-.L7- ~T sec i~X-s'J.r~i{) ( ;Y;:2.t . = /l0.~ Ift;K I~ ~~ A p'~-_....J , 1FIlJf!EN A ~ E } -r V.A 2 of- ~ 2!A = ~ f Ve;.2. + «j rE 2. 2 Pz. 2 -PE :"Pc: -I;' ~ L2 I ~ =V ~ = <:JL2 t "Pc _ Fa ~ L~ -rJ!." _ UA:l. Ii Ii If 2"2
50 ~--Pc = -Va~, Ii :2 "PA --Pc. = ~ L2, (1- P.) t Jl..2. ~ 7J 2 ASSUM INq Va ~ 0 =~ ~ THEN Pa =-Pc =P" ~ =~ L:z. (~ -0 6.2<1 FROM 6.2g' ~ -Pc; :: -(! Va:4 , ':r ""p. - p =,.g U:l +9L2 (~-f.') -~ ~~A C:2 :. I :l 2 CONT/N VITC/: p. 43 ::l) ~ :: ~ VI 12 _ .'.e. AHEATER AsrAo< Vg':l,. : a:l)lJll. ~ LI. l. =JL: - R:1. ;4 ~~ I ~-Pc. :: -A(~rz~l :1( f?j 'R.1. 'R "PA-"Pc ~ ~ }Ll. t~ L-'J.(~-f.) -IiVl 2 ~ ACROss f.fFATER (PRESSURE ORaP) ~ F« s rVx drn Vs-f--i-UA -P1 1---0. ?s ~--' <j (P-s-"PA)K=I'fi'Va (VA -Us)I .. 'P~-?A =t!' JL(V -U ~)c: ~'lf_A) 2 'R R 1< It -;<:1. l Po COMBINING WITH 'BER tJOULL, EQUA. Ii "L~(I_ ~L) = -p,r8.)2~l. _ ..121~ 1(.1. ~ 2"lp' 1<1 '2 '3 L:z. C~ -~ )f t1 V1 2"R2. v:L(1. - ~~ of-.!. t; ~-t" ti -A ) "R 'R"'Pa 1'Ra. If 2 :zRl. = <jL:a (p. ;l! ) v 2 ~ 2tj L :z. (P./,p:z. -I) ~.3{) 1+ I-~~ "'R~ USINe; C. V. AtdOUJ-ll> ~ u,..s. e+Py::: ~. At-~ "8tV !::: 9D(J J l)~::: LfoUr So ~~~ d~IY'::; Uot.:rr t-~~ .: AU "" coAl"" dA~ CU--=C'f=4~DD S/~'IS AT:79.<a(~ l~'" ~ ~ s: 4~r AT~O.~5P~
6>.'31 tJ~ur;a-£U~ TW*~C»A f -OFT~ 'JJC1DM~ AICZ-,1 ~AP T~~ ~TC46 V~~L. ~~ '<'lA5t-DS A~= M~ ~ A'P:z 1?~ 9An. . T~ ~CJJLL' ~~ We~ ~t5N J~ Iw> TS(!; ~AP '(~ L:?, n 'L, ~~=. ~+l)~ s> Y 2- TUO$ o:L ~:z AP ~ (y. .z7(,]w>Z - : i t Ie $ Y J> ~ /~ ~27~2. T~ J7lL)W ~ l~ M=~Q) Il-=- u: ·~2~ .~«r' ~rr Q:: 76.7·Z4·"2. 1 49.4 ~'%' [00 M., ~ <st.76 b~1s 9ol»~ -~. '" 1i+~~)~(e~~)J 38 ".. "2- h :: lJi-u;. + h-h£. - l 2. 23 lr:~JJ(XJU...( ~. is VAL-fP hL.=D. Urgscg w~ Mu~ S~<n nL/6,Twcs <:;'(/E!;~ ~ ~y Be; l.del1FG~ h2 ;, ~(Jt~B-l) 13:: 8~2.. ; - ;Jh, ~B~S IF'h~211,.~~ ~{s ~ ~ ZUi (1.f./J-fB) F SOB<M(nm).J~ 1#T<2 © ~'" 2 +~_L -(~ t'll -4 (0 26 2B o~ ~LA>S ht.. :zoD JOe ~ A~ h1.>D FOe 5>8-
0.33 GJerr(].,f~ NbPrF16.D &fo.O.JLL{ ~ ~$CC c. £!-t Y2,."1.~ls;- =R: + ~~4hL ?J 2(1 J78 2(j k)Zl.c) ~ ~?::~~ J ~zO 25-2:c :::Z H LJ:'1.. '4 ~ +hL=H= 367 ~ 2(5 t (] W~ ~ 2 '0/ (JeZ 9.32f;-f~ q 2 Al& ::: f;.CE6·ro L cfs ~.'34- LSvg:; fu (;.() ~ FOe AC. v. &J:I03Wc:fr~ ~p -?JA= ~ ?-?~% Ail? at g ~ =~ fp'lM:~tR Q-z fr:) Z 3 Yrm:l.~ ~ Q4-%a) $·re Qf/?;;: (1).44·1.25~ ~ ~'FV }/0cur;I2 % ~ :z' fBI U~fJfl .. ~ s fO'~ E".Y~:r~::.4.1{,·10 !!!c..F.".... 59 USl~~t~ ~~Aw9~A ~ J..(~I/l-=. a.+w-tS ~ 20 ~ 20 ~:~=: ~"~%2WV ~~=-2:5VW=L~VW e ~ (%~vw 1')P~ b.% Lcr V-=A~Br:V(r) V(Io) =0 2 A+f>G :0 A:;z -~ro I V=B(r-ra) V(~-)2 wdh ::z -etr{ -~) ., ~ V(r)zu.rl r- G 2- (.-_~ ( 10
2 &T~JJ~ AJJ.t> Z I ~ ,.t.5....t$ '% nL-~ ~ +o;'l.-,of ~z. S(3 20 ~ ~ ~ 2 1< u: zl) r. --"t -z Ua --I;> I S 2- 0: 2 ~ 2+hL%~ J kl-~D}lo~l£, t52% @.::: (4,0 Mt M::yAUC :. Ill§) ~ ~@ h~'%()J ~ L1:2~ A~A~ } 1.6 ~ z L(O~ ~ I'!L"3~ }.b ~ ~V~tfz 0"2.'" ~ '" .g,291'V1i; 10/),:6,(£ ~ '~ hL~~J~t:'6 I-I~V: LY2}%i~"lJ~ h 1. 1- t...2.~% 3th <J Z%, ~% cfI/~f~) U2..:Z l3~ ~ M, z Lce6lz~ ~.3B II ~~L'-r ~-----.-<-- It- (sT/.(lS~ z;>, ~ As I~l'iiG I ~ ~ ~ '-~ ~~d)) ~,~ l7·S9 ~ &.. ~@ / -!2.%2~J :0 ~zJ2~(!)z~t86~
C1-lAPTEQ 7 7. I ~'lS{~ ~? Aa; ~lN6D ~ ~£x. I . T OF? ~e I A~ Z6, ) ~ & .0177G::O 80 ICO .{){)70L .cor28 .r.m I .Dloi .W'S i eo z~ Foe WAn3f2 C(IV '} Q.~::: 11.32. 2D-1DJ ~ /~ ::.' 1 ;::. :> 7 '-'32 PI+O O.~ ·10'" . ~~~:Z70% 4l 7.W t6e. An2- Q'" 0 QI40 :::}d32. _ LIS:> .10-5 Q32 /4M - (,34::).IC-5 QIM) ~O.~2 41'32 ~b~z-(3~~! 7.4 z =N c = No. OJ=' MOLECULES 4 CROSSING A PLANE W=MOLECULE'S / UN IT VOL£)M~ I t<s mole CONTAINS 6.0;25" • /02J, MOLECULES .? HAs A VOLUME O~ 22.4 ml 6.025". IOU. MOLECULES 2;;.~ W3 =2.6Z·/0 2S mol = 7.6"3'1023 mol m 3 fP - -/Zc - 7r RT =15'0'& fps ~ =? ''8' . /0;).3 • IS-O'S 21 = :2. 1'7 'IO~' mol tP,~ 7.5 7' =.,i/(d~. dr )R V; =1Tm~)(D -(~)J =2VAVEE-(~)J d1,fx =-1./ "lJAvE Y' dr ~ r; ::. -~."lA 1.TAVE = - 1920~ tf = -.~~3 i/:"/R'a @ tCo·p
1.'7 "IV:::: 2,,"1/".2 ~ E¥' + ,.37 J<Z Raj 1,.('iv)= 2-;2v-2-..... f'+3(fj] 4. ('T'v1_- 0 J .r - I d... J ~ - Y"3 APPLY ~/RST LA,! of THERMO tfQ _ 6"LJ= (( (e.t~+~«r ~V dt dt - Jk.?I'"'-U ;eJ~ ~AU VISCOUS lJORK ~ = £lJe- d-c dt [!de :: (Tvl dA dt J ~~~ IlTJ. b - ~ r'-'Irll1V cu"olo.~ - , ..... r v1OUtct'" bouJ'do¥"~ :: 0 T =","!bl = p. rw (LINEAR PROAL.£) d':i t:. GAP . ~O'~TANce :. i~ ='rvA =0'~4'XrwX27rrh) ~ = s:S"?52 l!.:!- =5.S''lW 1.1 j = <fQ= kw2 dt ~=J<tJ,4 I 42. <6 = k w} "7 =2 CcJ, 2- ~2 = 1/ <1,. ~ INCREk5E :. <t2. - ttl _100 <b, = '300 ~a 19 ~ = 2. ~6 q3 -/06 -IMT ,252"" T:. J"15K tr = 3. 611 A M =21 ..0."" = I.lq 42 NTRO<:iEN £Ah<. =cU.S' ~ =I.ql .~ -O,a = 1.I<1J{2 (UIYEAR INTER?) M =II. S1./75' ./()-6 Pc.·s = 1I.5'5",P f>a·s ?JO ® L-I_ _ _>- 3.1 'o/S CD I >- Lf ~s CHOoSE: Cov. MQVlNq WITH SHIP I ~ F= ~ V d", STEADY r=101J c:.s. -§ Ftk;d =~x -11" 0!.A.t5;2~'" C" _ )oX wrrn RESPECT TO Co'! MOVIN6 AT II!!! ~ Po" ;: 0 F~ = -Pix = -V;; m:z -(-.q H1/s) Ir( lal ~/s) F'fluid =qO ~'" =qO N ~ J=rl • I - -F_L'n~CI - ~IIP1 l='5hlp 1 = qON IN THE' Wt;'GATlVE X DIRECTION
III ~ iJ) ~ r ~7 L_ / a.) dUX » aU; a'j ax " [J ---:I I I J ....- 2-0IMENSIONAL (;(~y) FLO..! Vi! =0 OZz =0 av 0;)J{z = -.. 12-)(=0 =?;,z av~ __ o __ ~ ;?<j ---- "TZy = 0 = '<1r AXIAL STRAIN RATE =li"",;i lfJ((}(rAK)4t-u;,lX')..dT: =~ ~K+O AX4t ~t 45.r~ a 43 VOLUN£ CI-IANlii E RATE =Ii..,i!- AAKle+"t - A.1)t'~ 4¥+ 0 AAX ..di: At-+O =lit1li-r '1r (>ff6X)AT: - I"r ()()At= dl4 AJ(~o A>f .1t ax 41: ..0 FOR 3-DM: BOrn AXIAL STRAIN RATE AND VOLUME CHAN4E RATE ARE EXPRE SSED AS a~ t d 1.1~ + JV2 (5EE p~oa ct.3) ax ;;9 dZ . . 7.14 r- z plo.ne. Z
B-2 PLAN~ V"-8 -PLAN~ r " .61: =~~O rVrlGt6B -Vr Ie Ar~O t )"'11$ + r(~1,,+6,. - ~J,.)l ~r J =..!.. C?Vr -r r l..(~) r;Ie dr-~r • -,.J rr IT d~ f- r d (Ve)l.. 're = 1/9,. =ptr ;;e ar r IJ ?J5 H~1T 1 ~ 1 t i •'j/t ~h f LL1 --1 E l-- E=.oIGMt -1 0 t- RESISTINCi FORCE' =f:z F2 =STdA = fcr1l'Ddh=rJrDh 'I=,P dv- = ::y: elY ~ .. F = n v-7tDh =.aV'.jl'ltDh.•• Z --E ,-- E. F;i' = 1000 C.osX3:t ./O-3)/olS-J7f l"lo"" ·.S~2 (3./t) = {C07a, fJ "lib Fr. = W FROM PREVIOUS PROBLEM Fz ::;; v"'}:: 7TDh .I ALSo" Lv' =;79 E :. jJ ,/:u7rD h = I')'t~i e 1.T:: m9 £ =b8tJ·9.1/-;o-r pif7rDh a5"OU1XIO~~.~ ".. = o. 7f:>6 nils dA: ....d¢'dL dL =~ sin 01..
M= .M~ ,..3d~dr l A1ij,1f h SIf1C1C 0 0 .: M=1T'~ w D.y 32 h '51"'''' lvzO~ (?t-~)~:'Trl)L%(J) 4P;<" 41"'= 21.7 rsf4L D 7.2. , ~% 0·76 ·ID- 144'5 -, jLl2():Z: D.~~..(0 ., Xe~:a-5l%
CHAPTER g t.1 -£ = 32"uv. Q cJx 02 v'1f!i 4:: ~Q dx 7T IfI Q. =KD.' Q2::: K ~i K = (-:&Jr . dxjmp. 02 =20. Q4 ::: 16Q. ~ CHANqE = Q.2. -Q• . 100 Q, =1500 ~ INCREASE. K.20RlG/NAI STARr 4O~Km=-_=EN=O:.- '~Km Nat 22Km I ® ®~-------@- -dP - -.1P dX - T ORIGINAL: ,;, ::: KD" (-:~) -t1lf.3 = LI.) ~ K041 Nat: (£) =rHH -A'f.2= LI'l~ L 1'2 K1)'1 J K[)'I f..I1.P) =. t1N/a..,1 -.dl,?3 = L.2.3 mN t L J·3 KO"* 2K04f SINCE - 11"P..310l0 = -41P..1/Na.J-Alii Lu ma _ L..:a. ';'H + L.:1-3 mN K D'f - K[)'12K ()'I 46 13 CONSlO£R THE CYLINDRICAL SH£ll ELEMENT ~I__-L ar ., THE SAME ANAL VSI5 AS IN SEC. S.I OF THE TEXT LEADS TO; 4..(rTJ = rAP a) dr L LIT R ::: OUTSIDE D KR= INSIDED (K.(,I) ) def'Y) = ) t? rdr r"T;: t&""P r~ + C, 2L ,., = -;« dv = .1'Pr + C, dr 2 L. r Jdv= -.1P (rdr - Sfd,.. :2L.,.u J A r V = -.A!:.,...1. _e,k r +co2 I./)-' L ;U "B.C. v=o @ r ="R J r. KR C. & ~ R~(J-I<~) 4 L .t.... VK ~ = 4"PR:l _ 4 PR2.(I_~) k'R ~L. ~L AYK :. V:: ~-Pl?:l.[i- rl._ (I-KaJ.tr1.] 'IAL R~ t.. '1K r g.Lf i(rlrx) _rdP = 0 dr dx
'Tf.)( =~ dVt :: ~ l: + c. dr dx 2 ... V.{:: -L. 4E r2 t S. .t.-cr + C;z lfA dx oM B.C. Vx • O@ r co.Q. , ~ =V@ r =d :L ;z C, = -A r; -L.. dJ>( 11 k~ LV+ J6,.u dK D~_da~ d . C2.= -2-dP ~_ C, kl2. ~A dX 'I .M :z F :: fA = rC1id .1) .: F::. 17"d,uf}:L (V+ ..L. 2,!:d£..~ l! 16,M «x d (D~-cF») + d &J~dx FOR CONCENTRIC FLOW IN THE. e DIRECTION J Vr =0) Vg = F(r) 50 Ire = A r~(Ve) d... ,..-; Pte Ar41i! X Fe :II 0 I P~ ::. ple.+c16 ••• 7r ~eAZ'lr+t.r -,(,48621,. =0 SO THAT Tr = COt.lSTANT OR )l ri .4..(~) = C J d(lfG) =~ 4r dr r" r A (2- INTEGRATION YIELDS: ~=c, ... -£ 47 lic. Va '1:1 0 @ yo =""'ROc.TT£R 0= e,Ro-S& M Va =(JRu'Nf~ @ r= 'RuIHER :. w'Ri= C,R; -..£ A C =# CiRca c, = wI<: R,-'Rc ~ =G)~ r _ w-"RiRo Ri -"Ro I<' -'"Ro =w"Ri"Ro (r _1::)1(0 -Rl 'Ro = c...J~i ( I - r"fRo ) I-K~~ ALINEAR PROFILE .' OR 8.6 1P.,; 207KR.·I:==::;j========@ - . 0.63501 <D #:: 1/10 X/O-& ~; =. 0165"1<1 ~ms JJ= 5"3.0 Ib"JR' ='l'l'i. <t5lJ ~/,"3 a.) INVISCID.; USE BERNOULLI EQN. P. + V.Y+ ~ = B + ~~+. ~ P elf: '0/ I 7 T / < P,-~ :: £11' ~ =y2pP J m=,aAv==w;o'"f2jJ.AP Q= Av =1J]).'-Jj~P 1./ --r b) VISCOUS" LAMlNARJ -!!P ="32,.u it· -dP = ~p dx 02. J dx L- v: AP D2. T 32...u
m= pAri =~7rO~ 41P 02. =1TD;..oilP 'I L 32r' lli Lp =1J.2 GOVERNING EQUATION JS !L (~)( )- JfP -= 0 dy dx FOR N£WTONIAN FLUIDS IN LAMINAR FLO~ -;;x-=fol d ~ dy • V - -'- d? tj~ 1- C, u t C;z •. x -:J"u d}( Z;"J ae. @ INT£R~ACf (@ y=0) I) Vr =V:zz: 2) '~r = ~XIr ~I dVg -=,I-{Jl d Uxrr dy d~ 1.1 g:p = ;11 d:l.~ dX dlf Ix =...L ~ 92.1" c1 Y + ~ 2"a elx M B.c. Vx =0 @ y=O UK =V @ ~=h j~t)7 J 7 J;II c, =A ( v- 2:!: dP) ., .2"u. dx C~=O FOR ~>') =D =0 " d Vx ) =0 ) Y d Y 4=0 c, =0 :. dP _ 2).( V dX' - h~ CONTUJUITY: dP +~ (Plh) =0 dt ax MOMENTUM: dVK +Vt JI!¥ =:1 aP at ax fJ ax 5 til T'ieM 'f' +S5'e", @ 1
BERNOUlLf f='ROM S TO I P5 + ~ + <3 i!s = P. + ~ + Q r p 2 P 2 -J' ~ =9.di!' - !t P 2 l-IAGEN-POlSEUILLE EQN. FROM 1-2 (NEGLE.CTlNG, MOM£NTUM) Fa -~ = 32-" 11." =11 L D2 L 32 .Ltv, :L :: f (9AZ _ Va::1.) 0'1 L ; u Q= 1rD~Li," ~ = </Q q ) 7rD~ 1) = 1iDl/ [~t.r - ~] 121 G. L 11" 2 DA# ?12 tv P941X4!:1A~ APPLY MOMENTUM THEOREM TO THE ILLUSTRATED (LfMENT ~J=x =0 It-J THE UMIT dT ......pg -= 0 d~ 2 ~= -pg dy~ ,Lf. a.) "BOUN DA1W CON DITIONS: @ <1 = 0 , Vx = -V (I) @ I:} = h , 1=0 .: ~:~Ih =0 (2) 49 v)( =~ +CJ. Y -,.0'3 y~ :2p 'B.C. (J) C, = -V B.c. (2) C2 =: ~ A b) v.. =-V-t ~~~'TJ(~J{~J] c) Q= "'evA= -ihfv+ alr~ - ~ h'"<:I"l cl~ 2~ h J Q=Uh-P9h"! +~3 :2.u 6.,u = vh _,.o:rh 3 :3).( 3./3 0 = Ve Cr) ~ ~= ~Ve 4!' ~ +Ve(r)~ dt dr dt FOR FLUID dr=o:. dO': VeCr)d~ at di dt d~ =~ X' ~. w= Ve ~2 dt } r ~ = ~(-~) de r :. d I I --U :2. ,.. - - e fl..,. dt FLUID -;:-
8.~ ~b"/ ./ --- (NO PRESSURS CHANGE IN e DIRECTION ). g.J!; CONSIDER "PASSAGE AS A STRIP CONSIDER FREE BODY OF 8.£MENT Y n-I -AX·/, Iy-t~ z.~ =0 pi&'-I-I:';LF1A'(.1 (NO MOMENTUM IX - ~- X+~ FLUX) Tty'.AX" )( (PX -1'lX-rAX)AY +- Ci'f:S+.6'1-1ifj)6X =0 . DIVIDE BY AX Ay f TAKE LIMIT E' =d'P = f'B-"B.. _ to? C1<j ~x L - T NoW '1=..udv 50 Ad2v= Ll"P d~ d~:1 L SOLUTION IS V=C, +S'i +A?y:2 2pL 50 BOUNDARY CONDITIONS; @ '1 =0 V=R52 .0. c, ="R~ @ y =h V= 0 :. C2=R2-APh h 2)lL THUS V=1?.l2(I-t)+ ~~"rr~r-*l FLOW RATE Q=i"'vd~= h (I ld~)= l<n.h_ A"Ph 3 o ..b 2 12p.L HENCE AP= J~f L [~h - ~ EFFICJENCY: (il~) '1.= "POWJ:R OUT = I' 62 P) -POWER'N llR(L (-10)) To IS SHEAR STRESS ON FLUID AT THE INNER WALL, -r;; 'S SHEAR STRESS ON THE INIJER WALL. 70 =.",a &1 =~~1l_ API, - dy Ilj=o 11 2L THUSJ 12~(R.o.h _ Q ~= G. 113 2 1 .a~r;u1?.Q. +!1.!!'~ Ql L h Zt~z-1 ~ = 12~ (1?~h _Q) Sl.RjJ [¥+ tr~h -Q)] "(= EE.. ~~h -Q) "R.Q.n [L.JRSlh - 6G.]
SHOWN BELOW' ARE THE' VELO- CITY PROFILES FOR 3 CASES; ~ =-1 IS MAX. Ei=1=IClENCY 'RSlh 3 ~ = 1 IS MAX. FLoW' @ ZERo "'R.Slh 2 AI=> I· .6 .tt .2 <1 h Q=O ruu, . -:(1 -.'f ~2 0 .2 .1 .6 .Y 1.0 V -RQ 8.10 ~QJTk"6~ ls- (1~ ~== 2J (V--P~PJ6 t::) A}.JA~~ Of!" ~ta.c U 1m=; ~ A~~Y~mt;; ?~~ 51Ax::l5TI-tG IJs:r 5
B,17 1 V ~ ~~ -- --~~I- l'A'S S'~ Tul: A1 1-rl' r'rlrt.. " L_ _. 1_ - _ L _I !VET ~lC4L . I I t { j ~'T~ f1..vx.- t ; Ar l I"S~ SO Lf::tD i: W'+- 27f f( fA.t- -1'cr"r'l{ Lxi r.O rt.(r r ~~ II 2. S(j 111( Are 4Fra--rA~w::tlKG LMtTAs Ar~o J<A r --t d (rT):O U dr to ry ~ dU;lcir (. "" /'..-.. :. ~y'G i !1'""'~~o.lJL.Lb ~! AL,J ,j~-,~_ VV'~~~. 'jCJ, t 1.~ £L r%. "2 a~~ U'2, / dr- AT ,-"z Q{ h 40;% ~ / dr v t.4US pra::z ~ ~e~n):'r) 1~004~ ~w Wrr'i q(Q)~ ~v:zr7 Ufo % 2t(c~1h).~+~O-4) 52 8.B k- % QA-VL.-/ ~ z LTIM)Z 1. tr z ,,(e{~ik6+~}1-e(~,~) ~ ~ 21v ~z ~
'1.1 CHAPTER q e~ c1r r (I) + &~~!.:dV =0 [c~o.n)dA ~ PVr(~iI'"A(:;)lr"~H' -l'vr(~r~e)lr +f'l9(~r~Z)/GtA6 -pVe(JlrAi)le +pV~(r~~r)Jz+4& -p*(r"6BJlf)J z L~ fJdV = E.. p(rAGtirJlZ) de JJ c.v. at 5lJ8STITUTE INTO (I)I D'V'D~ -sy (r A,edf'A Z~ TItEIJ TAKE' LIMIT As Afj 6e~ A~ - 0 !.S-(rV,.) +..!.. ;>Vs + dV2 =0 r (' Y' d9 ac q ,. I" ,.. ~ .2 V =Vx ~;c T ~ ~ t Vz fC.~ t'7_~ fj dn ;}".. y - ~ 1t.)C + ~ "''.1 t aZ eJ (0· V) = Vx!x(il( .e;r)+tI~~(~.~) + Vi!~( ez -€i!} NOTE: ei' e~ :: 0 IF i.;I~ =, IF i. = i :. (fi·V):: Vll'~ t V~~ + Vi! ~ 53 (0· 7) TELLS TH E ~ATE Ol=' CHA~bE "DVC TO MOTION. ~D3 , 2 t CONSIDER 2- DIM. PLOW CHANGE'S IN VOLUME =(1'2'XW) -I - ( i2 )('32) ./ 12 =AX~ 32 =Ay 1'21 = A X t [V)(J<tAXJ y) -Vx(X,'iU& 3'2 1 =4<:!+[V'1(X+U)y-tAY) - ~( X+AX J y)1 At Q2x 3:2.) = AX ~y 0':2') (3~ ;).') =JlXJl~ +[V~ (X +t.~ ~i-A'1)- V~(x+lI.)(J~l~x~t i-[V1(XtAX,y) -Vx (X,!j)J~~~t -1-[ ]At" TIME RATE or: CHANGE OF VOLUME AT A -POINT =lim ~ V t~}+o AX'A~ .1l1t ~t :. t=1.UIO VOL. CHANGE =dV~ +dV", d 'j G;)X ='I-v "BUT v·0=0 FROM CO)ffIt-iUITY.
42= ~o + d r dO + de ;;0 dt ~ di dr" dt de ~ = ~V~ t 1" aVe p- + v. aedr d r ,- ~ r -e r W -T Ve~ie dr ~ -= ~ ~ +aj~ +Vt"det"+ Ye~ dB ae I'" ae ~ ae ~'-' ,.. ~-:= :;}er ~ = ee~ = 0 dr ~e ar dr (}e,. = - exslY'e t ~ case =es()6 SIM'LA~L'" 9€e, =0, dee =-er, d(' ';)8 HENCEI i' ~ = ;;Vr i(" -t dVe e dr dr ar Q A : = (~ - Ve)~r i-~~ t-V0 ~ FoR Q.? To BE 'D V; ~ = Vr dt bt dt de =w =Ve d+: r .•.-:g2 ::. ~ -rIV('dVr- -t!!dV,. _~~ I.. ~~. dr r ~ rtr ~v. ~VB r V9JVg t vr Ve)~_ 'l r Jr r;;Je r ""'S ct.S USUJ6 THE n",COMPRESS'BLE Fo'RM OJ:: "THE NAVIE'R-CST~ES EQlJS; D v=§- V1=>+ vV2 y Dt" P a.) FOR SlWALL V; ALL TE'RMS OF ~( %f + 0 +vv) ARE SMALL 'RELAnVE' TO THE' orHE~S ?RESENT. l,) F"OR V SMALL. I3UT V LJm6EJ. TH£ "P'Rot>CJG"T at=' SMAll V AUt:> 2~ ORDER OF l-AR~E :; MAI{"BE SI6~IF1C.AklT COM1=>AR~D TO THE REMA/NltJ~ 7eRM5. ~ =~ - 1. V'P + J V:2 0 Dt P ifT Vx~~T ~~ ='3x -;~ () 0 () :2 :;}~v. 'V Vx =~ = 1 2P ~'1~ ,.u 'dX ~=J..~Cj+-Cdlj j.J. ~ I +v'V':Z~ ~ =-L Q)P ':12 +e, <j t C:2 2)-' ~X B.C. @ C:j =:tL ~ Yx ,0 ~=O C2 =-..L ~ L'J. ~"" ~J( :. Vx =..L BP (u';l_L;2) ;:?~ ~ .J
'V. V= 1.£.(w"R 2 )=W'R:ld (,) - 0 r Oler r- --y:- de r - :. CONTINUITY IS SATISF/E!:>. 'i.j Vp=:¥! +~£t' = - V~ Dt ~ d<j ~~ o = -V;(R, e9j~)= Pc ve-~~ ~ p AT ~= 100)000 tt-) V= 20) 000 fps: I2£ =~~ 000 s+-/s Po e.-1I.91S" DC- 22., 000 ff: a = ~ (O.OI06)~ = a ()o96 Po s 55 +'i]-()J~:)t 'J.~ VVx ) ,.o[;~)( +~ dVt! + V'j dV", + VzdVi?l ~x ay ~i'J =P9x - ~p - d I2 IJ/~ +;~+-~~ ax cfll3'=;lX' dCj 9r')J +.£...(,ud~) of- C1 (.u a~)+~ 1Md~) ax ~)( ay (}X ~l ~ W i-!x(M~)t~(Md~)+;0~) tJOTF: JHElJ 'V-v=0 } A 15 CONSTAt-lT "TERMS ' ~ ~ (; ).{V- v) f '7. (M¥X) AR£ 0 AND TERM ". (~'il Vx ) 'BEcoMES ).).'0'2 V.x. '1./2 GIVEN: f ~(rVr) +~ ~: =0 0.) f~ Ve=OJ ~(('v,..) = 0 .: r"'Vr (e) =Fee) J Vr =F{e) r b) IF Vr =OJ ~Ve.:: 0 -;;8 Ve =fCr)
9./3 FoR THE INCOMPREsSIBLE LAMINAR CASE) OV ".. rli:) J 2- Dt"=g-7+ V 11 FOR 9 NEtSU6~LE') "D V== -yp ... Jv:2vDt I' VECTOR "'PRoPERTIES DETE'R- f.lUAIm .'BY V EVP wHIC.HI ~ ARE IN"ITRDFPENDENT; i.e. CAUSE i EFFECT., .: MLJST LIE IN SAME -PLAN~ La') IN ABSENC.E O~ V/SCO()S FORCE'S Dv _ -V? -- -I:>t .fJ Dv ~E'7E?M'NE'D 0"1 -JP~ Dt J HAS Pes/TIVE SENSE 6lVEN , "BV -VP OR DIRECTIoN Ot=' DE'CREASIN6 -PRESSURE -b) SIMILARLY" ANY FLUiD.... '5TA11C OR MOVINq.... HAS nils SAME' 'N~WENCS e WILL MOtIF oRI TEN'D To MoVE IN THE DtR~CTION 01= D~CRf'AS/N<S 'PRE'SSVRE • c) 9.1l/ FoR I-DIM STEADY FLOW; Vx = VX' (X") V'1 == Vz = 0 NEGLECTINg 9) pVx ~ =-pof" 4. [1.lp~tf"J.{itx dx (jX <.it [~ 0.)( J oJ( 9J5" COI>JT/NUITV: ~ t :x(p'lx) =0 MOMENTUM: p(~ +V)C ~Va~: :tf l'cu ax) ax 9.1" Usu:4TwG; .c ~(()kJ A~ ~rTtVG 'O:wAl ~ L1?~20 AND ~:: t<r) EC( E -~ y.!WS z direction (a"- .~ v. ~ ai)PWc+ v7ar +~+v,-r; ~ [1a (av,) 1¥or2 , ~2'J=- +pg,+/J- -- r- +, + z r ar ar r 0 9..17 A5$OM,W~ IN ~t&ea ~WJ(bm(}.J()rrY ~ Yt6t.PS rU"C :::.~~ l.J~GLS ~2~=O ~ E-4 TI!5U'S r direction rt' av, v.%t' i ¥Z)' 0 ~~p +v,-+- - +v, t ar r 0 r z iap il 1 il 1 a , 2 • i,=--+P8r+/J-[-(--( ,))+,a7{_~~+ij;,]ar ar r ar r Iii? ryao Pz
Tw~&~ ~ (P~3lYi)~Jqr or 2- 0 ~IB 2 Sf.t1(.oTw @ % -lfe e,., ~ dt r tre :zfCr) ~ trrz~ -z0. U-sUKt ~-6"~/~ T~ TJ.tt5~ .-sTt«5 Lgr W~~(Dg ~Tf4tS E"nli£r-«»JS ~. , direction ( av, av, v. av, v/+v av,)-+v-+---- z p al ' a, , aIJ, az ap [a(1 a ) 1 iv,_2 av.+iv,] = --+pg.+/L - - -(rv,) +,.-=aIJ ? iJIJ a?a, a, , iJ, , 9.{9 ~ £;- 5"'(fS.DS IJ direction (iJv.+.LV'+~~+~+Vz av,;( Pat /fiJ, "iJIJ /, Tz) laP [iJ (1 iJ ) ~ 2~+1z!J= -- -+pg.+/L - - -iJ(ro.) +,. () +? IJ z .1 iJ(} a, , r , ~ ~ &~ ~ %(je~O W~ ~ % peJi e..(n~at or:1 ~ ~)) 9_a? A~<.we: ~y t1..ow" ~~~~J ~[.L d. (r LJ~)l -:.D dr r dr 'J ~ .LQ...(rtJe}=:~ ra-r ~~ 'tJe ~ ~I fur ..... Cz- Ar Q. LYe ~ 2.12.-.1 /tr l4 L1~ I4..a~ lJe".!fe~n,t(Q:Q2Q~OJ~~. r(' )..J?~~,
CHAPTER 10 10.2 b...;;.~ ~r t3 ~ tt~t Wi! = ~ (0( +,s) cAt. 2 : lirK ifQ.r1-'1(rv81rtAt"-r~I...) At...O r Ar At: .At .,. to..n-I (V...le+A8 -Vr!e).Ai Jr'Ai9 IN THE' LIMIT,' TAN ~=Z G.;Z =li~ .J{rVgl r+Ar - r~rr) ~}....~ Ar t.z - Vr 18+6.9 - V...19 rAe 5e =1 ~ (rVe) - 1. ~r ;;r r C1e Wz = ~V9+!(h _dVc)." Q.£D. ar r' I) ;]9 JO.3 d '1'= -~dx +vxd~ == -(VQOsirtoc)dx +(~cosoc~ 0/= -Voo(sirlol.)X + ~(coso<)~ +V'o Ja'i V·O=1~(rvr)r..L~V9 =0 r ar (' ;;6 LET r Vr = ~lP ( r'~ 8) ()8 V'.O = J..r~ (tl) + 9Vsl.= 0 r Lar 'as O'6J ~ (9'1' tv.J-0 . I = -.g]J!- - 9 - •• viii ~ ~y- -ar :. Vr =~ ~: } Ve = -!f :. Q. E. D. la~ rb 5 3 5 2- 1 -:: -- X. - xY B.... S~ lJ":z V0/J {bsnJ.J<XTY &l (s v..Gzo DJZ Vf-:'O Ust~ ~ 2'1 + P.l ~O ~' ayJ/ 0)6 - '0X ::30{) lL 2 ~ := Cl!P. :z 5~Z x ~ ar
/O.b IN CO~E d"P _ "v~ i.e. w--p'IW " - - -tr-- - ()t Dv:-V:l.C,. Of: r dt' r V= Vmruc i "00 ?l~)-"P(o}: P UM~{"Rrd(' =e.lJttt 2 1(2. Jo 2 I1?ROTATIONAL: (r ~ R) 'P + U2 : 'Poe, p 2 P J '1= Vt'H'"R r PoO - PCR) -= IZ u..,.2- 2 THU5.1 "'Pot::) -1(0J -=,tJ Jw?· So :. U 2 =~fP =- ~ VtM=126f~ ,.0 .002<f a.) MAX. WIN]) YfLOOTV =126 t?S b) OSIN6 ""BERNOULLI 1=>00 -1=> =!!~2: I'~~(~t-=IOpsf pUm2=3~ .... ~ : "$l =J.q 'R2 20 f.:: 13=1.5' SO T/rvtE % (31'.5: 131.5= /.5'6 5 V l? c.) IN CoRE B -=P-r ~J.=r:jP'; fJ V2. = P1'".r: -= :3~ r-t Ra "R~ "Po =(2116-3i ) +-g~~ Po = 211' -3'l (I - t'.t/R~) VARIATION = '3"'8 'Psf 59 10.7 VI' = '/oe CoS e ( - ~~) ALONG STA6NATlON STREAMllfltS e=-~ ~ Vr- = -Jo,o ( l- ~) b) ~lf' = -2 tLo a.a 9Vrl _ -2lbo ~r --;:-3) ar: c:a. - T 10.9 "Pi" pU2 = CONSTANT 2 I~ ~ -=+>00" V2 =Vo02. HENCEJ Voa I -= vel:: 2 b,si)19 sl~e =.5 .". e%!30; ! ISO O 10./0 a) <p =V... L [(::f-s:tJ o=V rp =VX' €)( -r V~ e.~ VlI == ~ -= :3 U ( 2_u2)=a;;)( ---e >f -' ;)u L-~ J V'j -= BaS_ -6 Lbo )(9 -:: - ~cp ~~ - L-:t ~x 'IJ-= g ~ ( ,.,2~ _~) 1- f(X) L2 :3 '"= 3 VoC) X.l. 5 t- '1(~) La
WHEN '-P=O j '1=0 OR <j =!".J3x ----l-----":~~x 4/::0 b) ¢= u,,¥! Vx =- t} ¢ = u., 'j -= ~ ax T ~g ~= ~ =~X' = -~ afj 1: ax ¥= ~ u 2 +f(:xl ' 'P= -.lx, )(.1 +~(u) 2L :l I) - 21. .J WHEN 'V=O j '1 = :t X ~ '1'=0 ------~+H~----X c) ¢; = Vca L 1M ( )(2 +~~) 2 Vx = VaiL 2x _ d lJl 2"" )(2.+'j2. - Olg VCj = VooL ~ --21 2 X~2. - - ~x 'I'= ~ ~o.."-f(.!i)+f(x) 2. x x IV =- ~L ~~ to..,-'(~) T <3(<j) :. 'IJ= Vd)L[tcl~tl(t)-io.n-I(~~ W~£N ~=O .) x 10.11 Cf= 2r35ln~ J ~ e:J~ '# 0 ~:D(Se~fc 3 Vf(:)TUQ) LQ 'f~~ (6r9A~04~ +~~) ~ ~ ,2:r~ 1~ ASQ-ULtS 2s~~ 8/~ r ;'PLar '(' lO.t2- t-0 -= lftD r$ln9 + QS 2i 6'(OeFlAJlTr61J r~OJ ~ If'! ~>o f:ao Is-W& lwe. 8=6 .e:Tltl; ~v,;; ( Ax,$'. ~ li_~O (f"~ ~ G:;irrTo L~) I OIJl; GB"~ Yzee ~ 2~ Q. St,0 '( Zilttl r~2IilMit(.a e-+o ~w.e)
10./3 ~VRCE AT ORI61N !.p= Wte p2Tr m== SOURC.£ STREN6TH FREE sTR EAM tp =Vc:o y TOGETHfR tV= Va) g t- ~e 211"1' Vr =! ~tp =VcO C05e +..ttL ,.. ae :.27Y'r ~~ r'sine Or' =0 @ $=11 AT a=71 r= ~ _ Q. zrrPl.4x,- 2'ii~ lall.{ As ~iP = pDv Dt =pBftV(~2)-o. (V'xv~ /WD FLOW 15 STEADY AND lR'RoTA- TJONAL I Vp = -Pl (~) OR v?= -p vVv BUT AT STAGNATION PolNT v=o HENCE vP=o 10./5' LIFT FoRCE : F~ d,cj = d 1= ~iV1e = CR '..1 -~ t ." mosiYede1~lae . t'ov ~10'.e) '"' (ir F~= Jo (1=>~-BYR'5IYed8 FROM BERNOULLI EQUATION 61 -p +tpv::t = CONS.TANT 'Poe t' f p uc%)~ = -p i- f pV2 O~ TUE HUT v= 2 (/a:I 'SI'rtlt :. P="Poo t-! PVoD~[t-l{'5;",~e] F~= ro£t'lleo2E-l/~;n~~+45;~ 'R~'rle de F~= 2 f' 14'Rr'LSin~e-~iYl~Iv~ (;) de F~= 2.Rp~ [j- - 2'5," 2eoJ ~~ =0 WHE'N 10.16 ~~TIDkJ 1blJ:r'S tLc~ S~ Bv QacLe.5.
tf= - Ie( ~ r ) ue =~ l.J~6,lJ Z'ti 21Tr Ol2(qw 15 Itr krtk:. .~ ~ f(1,o) ~ K ~ K. Z'ir(2a) 4~a. ~ Lfe(-.:tJ0)'"-I(, e~ 4tT<l A~ If(a,O): -1 e47f(l. tf s;'~ 'f -= +~1r VO#!J'Q(. ~ -t:t. 2.'iT G2. f h. -.1~___~--L I ~5~ )6 Sr.tq.u..trl~'G/Xj <1- lfa>rsut6 + ~ 2'rr 0. _g..~AnClJ -g,AJT O=-~D ¥1~s (Jr: ~2D lJ: =..Lo~ _l.(~ + I.[r~ r r W r 2IT ~ Y 0: ~ - LJtp := - If. ~v.tb e:> or c:IO ~10 e~1T) ra:sn =k=- Q. n~ S, Ar ~~JJA17o.~ VDlAF )("Z -~ -= - l.~ :::- D.02~j.t-... '(:() Z'i1 tTll) Z'il9 b. &py lJ~(Gl~ Sr~N.crm ~1...Ll& l.5 ~-:! I5QDrStnTI + Q1I -z ~ 2it Z . ~vs ~ ~ ~ rSUA<9 +-~ 211 WH~ e:1t~ rSUA8=y:z.. i?.J~ -~)~ $.0.007"1
C. A.7 Lt~s?~6. ~ ALLTf«; h.olV b~AT (,)0" W~ Q=~(2h) h:z ~ = I.q z D.Cf>33W 2o-lt) 2-S d~ tv1Axl),AJ.,W) ~ ~ '0,22. .EIlMM~ '" V Ple) ZE,=O d ,.GlT, p. ' GT 11 O-I:tr- ~1'P5Ilt8d9 =0 o 1/:~TM +~J(~:-U1-~ LJ:-2'tsm,.g « Iff"'~D ~M~~')p.jlf2Ijfs2eJ9 I~T ~ (~. -~A1t''D+.2. O{y"z.. V .,J' ,j (, J ,LV ~Oza 1.257~N T ~ 10. IzN
CHAPTER" fI.r 1) (1..) cv ( 'Ii;) 11.2 p (MIL') Q (L~/tJ H ( L) n 9 (L/t2) "P (MLYt3) i =rt- r =- Z- 3 =S" CORE ($ROUP (p I "OJ w) 1l;=t1 (8Y INSPECT/ON) 11; =fQ, DbCJc H . V D P (LIt) (L) (MIL') t= 5"-'3: 2 ~=~ CORE GROtJP (D, V, p) n; =Dc4. Vb fC,)J.; 71i=Ai _ 1- r;rvjJ - 1Rc 7T;.=DQ, VbpC: e ; rrr; =L I> 11.'3 ~'P (M/Li-a) D (L) P (M IL3) Q (L3/-t) w (I It.) )A (MILt) t: 6-3=3 CO"RE 6 Ra./P (P.I 'OJ w) r;r; = pa.. DbWC.~""p ; 11:= A'P I fJDV 112-= p q Db w G Q j ~=~ 'O'3w 17; =f' a.. Db W c,,.a ; 77;= ~ PDaW I/.¥ T tC4 tjI L ~ BV GEOMETRIC SIMILAR/TV: d =.J2. v= J.3 V .I L 7rcl2J =..L 'Tl'D'2.L 1)~_ 31 _ 3d i/ 3 '4 d2 - L - 13" :. ~:: (3)~ :: J.I./l/2'" a.) BY 'DIME:.N SIONAL ANALYSIs: ~ ='DQ.wb pC 'P I= La. (Vc)b (MIL~t MJ:~ -c3 '-t=-5'" b:. -3 c=-IJ :. 7(, = _:Po.--_ ,ow3 D5" FaR DYNAMIC SIMILA'RITY: '"P ( --P Ip4.)3"C~ model - ,aW3 D6 proh1:'jpt ~=[~ ·?f·jff.r3 I 3-$'~ =(3.3-~/"3j3 = 3-2/q :. l.)p:. O. 'T13........t - - - - - 1:,)
11.5" MODEl "PRoTOTVPE D D ,,1> V V 20 knots p p p ).t A M F /Olbf F A 1)2 (bD)2 FOR DYNAMIC 51 MILARITY ; ~'" =1~;p ) Dvpl == DVfJ(,u rtf A- ? ~:: Vp(~ .fI;. .¥t)= 6vp , I I .: v~ .= I 20 Krto-t5 a.) ALSO FOR DYNAMIC 5IMlLARm' £u.~ =EtA?· ELA-I - fAIpU2 m - ; V" ? r?:: F,.. (}t.%.ti)= F~ I 3b J.ri. :. Fp = IOlhF /I.' VAR tABLE C~o.x 0( S M L p 9 1< Cmo.x 0( f3 M L fJ 9 1< M O o I 0 I L 2 0 0 0 I -3 , t O O 0 0 0 -2 0 .: ~ = '3 -.....- - - - - - b ) l= n-r' = Z-3=S .: No. OF" DIMENSIONLESS G'Roups ::- 5' -~.------- 'iT; -= 0<, 112 =/3 'IT3 =M0. LJ., ~ c C¥MX I =M~ Lb (LlP')c ML)lt ~ a. =-1 J 10= -/ I C = -/ 1TS = C I'Mtl.X ML~ 1lq = ~Q.Lb~cf ; 71S = twf' Lb~c 'R ~ 11~ =1::1- 175 ="R-c.) L 11.'1 IRe = L V J, = I '2..&, ~L .10-5' ,..,4-1) "llIa.,.... . oJ 70 5 @ 2iOK (~'1.6°F) a.)~ASE'D O~ LEN~TH ~ = (r:s.'1X22.2)(/OS)=9.21_'cP J.'3~76 b) "BASED OW ANTE NNA DIAM. Re. =6.1/ ./0-3(2.2.2 )(102- 1.3¥?6 = I~ ;16" (1.97./0'1) /1.1 JI. =COIJSTANT ~L '/::a. U 4 .."., - p ---'-m Lp
(~) =~; =0.1 --. 1"", =_31 b V-p MODel SPEeD =31. 6 dlo OF S?E'ro O~ FULL SCALE SHIP. 11.9 RJR SIMILARITV ReM =~FULL. SCALE T£MERATUR£ NOT GIVEN,! ASSUME 'H2 o = 10°C JH,.o = I. 3x/o-6 W1~ 'MR =2t;OC JAlR ~ ,.":>(105' ~ =2.'1'l>C10-6 wsl ~ LV I -LvI .u. -,I J LJ - IT .. ,..- vF.s. ~ F.s. ~ h~ .J LVF,s. m Um= 1l,·2.4Cf·/o-6 .q :: 122.3~ /.3 ·10-" 5 F"l. = .0262 hF.S. 11.10 NAV/ER- STOKES EQUATION; Dv = Q_ vP + )) "12 V 'Dt ..J P NONDIME'NSJONALl2JNG; VC)C)2 DO ~ ,.. P' I ;2 r7"~ - - #' = S - VoO v r" L Dt ~L;:"'P~-- 2 + J Voo2 V'.,. 0:/1 La DO~_ 9L v¥p* J v~ o~- - -- +- Dt* U~2 L~ ~ = ..!.. - V~1l'~ ~~ fj>Jf: Dt Fr 1t?e. 11.11 SYM80l.. PIMEWSION MASS TX COEF. K Lie 'DIffUSION CQEF. D Lo/t DISK DIAM. d L ANGULAR VEL a.. /t DENSITV p M/L3 Visc.osrrv » MILt K D d 0.. P M M U 0 0 0 I -:)L 2 I 0 -3 t -I 0 -I 0 -) r:'3.1 V1=b, i.= 6-3=3 77;= d/o..~pnk; ~ = K cia: ~=..D. cl2 a <"i73 = olAa.Vp~. rrr;=~ =_,J f'd~o. my I'" (K.. I J;L )lReJ) =0 .. a.),. da. d 4 o. VAR II 0. AND/oR d Tl-IEij ~oR FIXED VALUES oT: ~ 'RoT I:>Af;1Q. vs. ~a... b)
IU2 SYMBoL PIMEW510N FLOW RATE" Q. DIAMETER 'P 5HA~SPEE.D N VISCOSITV A 5U<F. TENSION 0- DENSITV P o 0 I 0 o -/ L?/t L I-t MILt: M/t2 MIL:!. r =3, r'l =b J L= b - 3 =3 CORE" GRo()~ -= P N1) G 11, = pa ~10DC Q ----=-ir, ="ft:>:' '112.= p~NbbC,L{ _11'2= pND~ "M 113 =p~NbDcO"" .-113 =pffiD3 11./3 tt L -t M-rn M 0 0 'D- L D 0 I 0 P - m/L3 p , -3 0 9 - l/t2 9 0 -2 (7- fVlt:1 r:r 0 -2 BV INSPECTION 67 Jl.1L( M L t V 0 0 -l L 0 a 1) 0 0 P -3 0 T I -2 11"; =L/D ~ =~"J.pD2, T :. nD'W =t ( LID) O'R V L Yf -= f (LID) II.IS" ~YM. PIM. POWER P M L2/t3 DIAMETEJ< 1> L RPM w It: VOLUME Q L~/t DENSTY P M/L3 I'ISc.oslTY M MILt r=3 Y::.6 L=6-'3=3 " J CORE (fRDt)? : "'P"DP ~ =-P"''D1o pc. W ~=-pa.DIIapc Q ~.1:... II. =pD~4i 'IT = ~ 2 P <;(3 tLl6 FOR DYNAMIC SI MlLA'RIT'I,I) ~ ~ :.lRe. Fa L...L ScALE :. tFlM == UF.S. LF.s. JM .- r Jt=:'5 • VM =60~(~)F.10~ =2LfO r)'ph 2. 10-5
/I. 11 AS5UMIN:S /NVISCID EQUATiONS) ~ DO = -tiP +PS Dt MAKIN6 EQUATION DIMENSION- LEss: V := +(~ )t ~ I ~) t£o L L ~2. OR JL = f(>< t~) 'f;L L"J L ~)5IZE" = 2 "" =.005~6 ~ "360 VELOClTV 1r _ J~ ~-~ Vm: ~~IA60 =. 422 ~/5 b) TIME- t: Uoc = canst. a'R 1:- 1:. L '1.0 t*- _ Lwt ~ - Lw.j.Le. -.l- f; - L P Vry. - r; LW' - J1. <i tltt:: ..!1:. 1,,. = 3~ Hti..,. If.t:t II.JZ IRe. mode.l -==~ 'Pl'oto~f:e. I'M =ArM. vp L? A PP VIM L.W ? OR '"Pw -M =1)401 )1"", vp Lp ~ Tp ,up v-,.., Lm 11./9 I=R =~~) r = &. mode.! ~(( SCAle V :2.sr""/s L O.lfl n !2. '15" ~ N 45'0 rpwt v"" =~ lM =O.qc;q V 671~'V L I J::S. =.~ ''5 F.S. F.e;. b) TH-~05T: EM =E~.s. ~~a ) Fr:s. =F)I p v~ F'.~ Af'S pv:Lto PrM FF.S. :: 2'lS (,. ql./)(-..-L )2(:2.ct5'12N j.q'l .'10<} ~- .~I j FF.s. =SZJ '300 N ToRQUE: Q --= FL :. QF:s. = QM(F"•.v LF.~ FMA LM QF.S. % 20 (5'~30D) (-:2.({~) :ailS . £/1 ) ~ 25',5"/1 Nm
1.20 IN he$r~NT(,~/~ Is W~ g W=-7f+)AV?ll~ -I) f.!1t$(~ l£~ o-~ ~ u-/~;t~ v;,-l/L Ou;~AtJC r "- - ilt: QY.E.. ~~z~~+31~~-l) J L/I/ n.+-" «.~(5c::Z)W' C 7D o!.-Il·.. l~ T~ GrO D="THE ~ vrry ~}./To mt. hpzn~ -rt~t ls I.Z I E 0'tcfr2-J I (L) S (M/k1 ) t (T) TIJ~ Is ~ 9IMENSt:)N~"5S q~u? L.. t=.t -~rS We.~ 1,. f'S.,. lz.EtIs @ ~ug 4r ~ Z. tzEt cit S "8r4 12_ ~ /:4.i"2 5 It ~ ~H.&) L. z ('?/~ m~ d:4:~t~ A- Yr~/z,~~---~-",-~~-~ 69 1.2'2. a (/vA:) )1- (J.vLT) J lM/L~) V (Lfr) d(L) V(L) __ ._ /_ f. r7 •.,r;:?.y< ~ I ~ ~~ ~ ~L.-~Lb..JI'" v.uy ~~~ ,let::5~, ~tVt~ l~(O~) I tv5 ~~AJ dJ Oy'1) YD ) .J-i~~ / X> 3~ ~~ il-g W~$ D) ~) Vf() ~7 {JD~V 7, 1ilu:; J JIrD = ,~/ :lEi. )Gli'l 'I /«- 'j'V") 1_'25 5StEW VA2L~.. A?(r!Lz.) ?(~-t!LZ.) Q( L'L/t ; L (L) Q(L) r2(L), "' net-I) T~lJST~ ~LD £Sf; 4~~ VIA {~(D(;; WE UA~o 0/. 2i ~ ') /0 . _ A . .-7 L e6JLt ~r j J;.. ~N h:X7C~ ~ Q6.111;, , i.MrGrow ~TAl.V~Q - ~Qh
CHAPTER 12 122 "DRAG = ~ pv2AR C]:) SO Df =.!.pV2~C-r 2 ~L>-t =~(.0023"Y1!rfa)(293.33/"(itof 21100 (.011)(.75') Ibf =202b~)(~O~p~} Ibf a) WHEN p=. 000 'T3? ~IUlj5/r;p. V= 500 ""P'1 Of ::' 3Q21./ I~t ( 5232 hp) b) WHE~ P=A, (SEA L.EVEL) V= 200 mpk Df = 202b llof (IO~ hp) /2.3 SPHERE IS SIz.E OFAGOLFBALL 1ReC.RT1CAl. == 2·lOS" AlR @ 20°C J= }.1/9·/0-5' mys ~D= 2./o'ii" V= :;'105..;2,l/ / D If=:J.·/o'!i . f.'19·/0-~ = 70. 9S Wf/S l/2·/0-3 12.l/ GOLFBALL SIZE SpHERE 1)= ~ pV2 PI ~=.l(.OO23?~JJr([;g"'AJ 2. 4 12 =J.?bb . 10-S'"Cn V2 Ibof v= 1ReJ __1R.e.(.ISq)cIO-?) 15 l.bS /1'- = 1.'5"61R~ 103 Vfp~ 1<e CD Dlbf So ?5' 100 12S 1,0 115' 200 225" 2S() 2"15 3CO 325 350 lfOO J.{3~ ?l5"0 .1.11 .021 611, ?'19 .If? . Xb,505 .lft .0'03 108, J3J .11"1 .130 J 29,759 .lIb . ,'Z3 1'T30/0()I) •liS' . '311 21"/262- .'10 .li~2 25'9, ")15 ;"3 . lin ,-ZI/I'I2 .2 ·373 302" ':;{/4 . I .21& 31f6, 02.1 .08 .220 100 200 300 '100 .J -h:>s 12S" ~ TRANSITION c::: 2:/05' ~x =~ J X = JJRe.TRAf.ls V V X =1.l.Iq -/0-;; .2.·/os =0.099 vYt '30 12.6 F/UD V~ @ [[)5E OF B.L.
v~ =~ (Jxl.OO)~('It'-of)'1.=5 OR ~ =2~ (IO-8.2?92)= 0.1" ~ v;Re;c @T= loo"F JAiR =O.ll·163 HIs lRe.)C = x,VtlO:: X"'. gg =~O/S76 x" v 2· .Il) '10.3 x" .s J 2 :3 'IRE-x 2/)J2~ 'IO,S":; '61,031 121,5'11 X" 2 v~ -Ff/s 0.5"32 0.376 O.U6 0.211 12.7 NO, "BERNOULLI's EQUATION IS NOT VALJD IN A'"REGlON OF SEPARATED FL"OlJ. 12.9 Vx = C, +~ f:j + <:3 y~ +C"f ~3 Va- "BOUNDARY CONDlnoNS: (I) V)( f)} =0 C, =0 (2) V't( (F) =VxF (3) av~ (d) =0 ;/':1 (q) VA' ~~ T ~ dVx == -JP +..M~ dX" ~ c::tx 9lj:l @ '1=0 .. v)( =V~=O :. ;)2Vx/ =..L 4P = - I PVooa'4 ~ ':S.2 'j=O ~ d x ;a cJ.x ... - ,FROM 13ERNOULLI EQVAnONV :. ~ 2 VXI = -/00 cJ. Va1 d~.2 ~ =0 ~ d.X. ~$ = C2 (i) t C3 (iY-t C~{Jt FROM (2) FROM (3 ) }=RoM (~) 1= C2.+ C !>+C,{ 0= Cz +2C3 +3C'i -F2 dvao = 2C3 J ~X _-. Vx =- ~..1 _1 (~)3 V1(S 2 $ ;a E' +£2~(~ _2(Y)!f!!~) 4J dx lJ 0 It}/ /2.10 Ix = a. sin bg Vx=o @'jzO 1J Vx = Ve:%) @ ~= 6" v~= a.S;r1bE ~VX =0 @ f1=d ~~ o =Co-sbd:. bF='% :. a = '.100
.: 8"-= ttxo.lS.... ----------0.) ~ 12.1/ VJ.= 2 V~ ~ Vx =VE Sir11T!i = 2VQlX SlYlltl;& :2E it u p=~o - 2pt&,2 SIr12B =~-2"oVC: ~ ~ = -L/PVaJ 2 x dX 0..'2. - d"d'P =To + ~.(dpV/'0.'1 dx· ux Jo -Veri)~ pvxd~ ~ = II d vx == 7r)J. Voa>: o r ~ ~::o a. d ~ (" EPv)(~&~ == ~p v"'~t (dX '2. ax )0 0.2 dx)o ,_ eos'Ti::5Lr dg - 2- =21' Voo:2 d (JX'J.) 0.2 c& Vs ct)~pV" d~ = 41' Voo 2 X cI rax"SiYl7i~ d~ 0..2 dx Jo :::zE ::: ~p Vco-:J. >< i.. (d"x) '110..2 dx COLLecrrt-lq 'iE'RMSj 4p"&1{~x) =qreU ~ ')( + 2I'Voa2d(&~ Q.:1 a. t 0. :z olJC - zpv«!..?)( d- (bx) 7rc..'" &x "fret$)( =11A VQ:l'X T ~,I)Val"Xo a.E ?~ - YJllof-$X + d clr~p vco~)C,...!PV~ ~ '1ic..::1 -ax[ a.~ ~o..:i.J IN LIMIT AS )(-+0; dS~ 0 a)(
12.12 11771/11111/11//777/7/7 ;( X'+dX XF~(( VXpCO·n1tAt~i(<<~~dV Jlc.s. oti).4C.v.""" g~=PJ"I)( -RtI)(t"AX -tP}X+.4X +r1x (J1X -J/x)-1;AX -----:2-- tAX f1.s.vxpev.~)dA -= L[pVx:ld'1xtAX -LipV/d~x - VOJ(~:fVx ~~IXtAX - tdpvxd'j}x -V'joAX) , REARRANGING f D1VIDINq "BY AX: -'PX+AX -'P'~ JIXtAX 1" (Pi XtAX ~X 2 -1' pI -XI1)(tAX -~IX)-T~+ I)(. AX 0 2 == j:pv/dYXtAX - S:pV/dljx ~x -veo i!pVx d~I)(TAX - fa!'~d,:!~ +Voo~o IN THE LIMIT AS dX-O -a ~= To +I(,,~. +ale ~~pV:c!~ _ /, 4.(c3 P~~ CD ~)o REPlAC1NQ J'f =1x(JVCXI~ 12.13 FOR THIS "REGIME) 1<&<:103 1I?e.= Dv @ 60G F J:zlL{t·IO-S"~2. J - J S "Re. =oba Y; ~ =I J '1'::0.001/6 ~5 ~=as '1'== .1"3 Wo/sI .: 0.0016 ~5 ~ V < . "3 ~/s AIR. @ ~o·1= V=1.5"9 ·10-41 er%; R~ = (O.'2/12)(OZ) = Q220 1.S''l·/o-4/ FROM 'F16. 12.2 I CD ~ 1.:2 -Ft>: /'3 '0. .2 )(1.2)(O.O?6lfXIT):J.. l~ 2· 32.11Lf =.SOII"'f- .: Ft> = .S'Ollhr ~ ~ J; ....~..-------- ~ b) VX:' aSlvt 6j "B.c. V.,.(lJ =-Vx[ ~ =51r1rtr;:i ~:x (S} =0 VXd 2~ .:J
b) FOR ACIRCULAR CYLINDER " 'LWHERE Vx$ = 2 VQ') 51 ( 0. } VxJe2._ 0.'11j)( 5" ~ T - V)(~ 0 V,,$ s:Sir15(~)d~) =¢=fSY~~ d~ _ - Si1'I ~ cas~ _! co.; ~(Z+Slrt2~) 5 ,s =.! - J. cos. ~ {2. +S;r'l~~)-SiY1cos~ 15 ,~ 5 =~ ~ - G?s ~(gtq5in2~ t3sin~~] ~Gl2= o.'1f[1-cas~('irl5in:li T3~in'l~li ,) (2XI5) sin' x s;Y~ a: 0.. et.=: o.47)~-casl (~tL('Sil! +3~j,,«*~ ~ VOl> Sil"l6~ a. c) VxJ;2 2 Va, sin ~ As x-o dR. x«a. j 74 = 2'19 /s 6)IRe = IQ.l ::: VD J U = (IQ:1X ISq'IO-~) = .IS fps I/l/~ THIS INDICATES THAT THE EXPRESSiON t5 VALID OVER A WIDE 'RANGE O~ VElOCITIES (AT v= .ISfpsJ IT IS Nor VALID) 12.1'E D -= CoA ,oVco2. 2. 2 =.S-(2. '29XI. 22G)(30) :2 = 631.1'0 N
POWER = 30m (631.10)= 1095"o.QV s =25". '1l1p FoR b 'hI/s HEADWIND 1D = .S-(2.2~)(1.22b)C36)2. 2- ='109. 6'1 N PoWER :. 30 !t1 (qoq. 6'i ") s =2721''1 W = 36.b hp FOR 6 Y)1/s TAILLJ1ND lD= .5'(2.2'1)(,.2.2')(24)2- 2. ;;: "I(j/. 2. 'HJ 'PoWER -= 30 ~ (L104.2Q ~) :::: 1212<1 W =16.3hp 12./9 L= CL ~ pv2 A ;;: a4(1.22'}(~4.7)2('2.2'i) ~ ::: 1122 N = 2~.2 bf 12.:20 D'RA6 =~ P V2 Co A~ FOR EQLJAL DRA~ AT TIlE SAME S"PE ED <;A6R= Ct,AI~ATE Ct)A~ = .5"(2.2<1 ,..2) -= 1.''lS"M~ CD APlATE = .01 .'iTt> 2. ["iRe. >0'4] '1 .: I> -= l.20J ~ 12.2.1 JI)::: Co A t pV4 = =1.I1(irlb)i (.oo23nXI7(,)2 12.22 3 W=VV= t~VCoAJ2 fo" ::O.CXJ2(9i9 5(~/fP' ?ttO~ =6.ll'2207 a -, ~ ~ W=~ .2b'R·ttJ (lOZ."1).?i(25.i3J £!2:) : 19.~ Yp b W= gEE ~:: 15.70 tr 5>0 IZ.Z3 T ~ F 6 -? "l <.:Ay =UJ 'v -p"? O.{{i8·fO ~ CL. ~:: '{Q:: 139.3 '2.~IiL 7 D,I~-{6-3 ~ =2f)2, auI ~%0.4 b_1kt~~=~ SN'LC't> A12- <'Mi='0 - ??~u..~~(··_/~.) - . __C)...... ~if JD:: o-lZ8I.16(1~.33}i"-ID7 2. i44 ID :? 0 .42 l~f C. LAMiJJAe ~LA$J2. (As D'5d..~ krYtr; END 'at: ~ 12.2).
It.2.4 :} J}~ 0.16.1 ·/0 ~~ .S'T4rlTtN~ AT ~ -r7.5·'cfI Va 92J~ frs 2- 1Dz~~V ~~~== V 2 0/$,@ ~.J64 V CD 7.5 10 15 2.{) Z5 .2 gz.lB ~ 12'Z.9( A6 'B4.% .47 2'45.82 .44 307.l7 .10 ilk / ;' Slt1(X)Thl / (~12.4) 1/ I f / I 11> .072- .1014 .(~ .128 .16k,7 lb 1b 1~.2S '2.. lFT:Z~fV ct~ .. C~~! I V~44.7~ L=: 5('2~(44,7)1.Q) (2.29) -z f. 8CIE tJ (W~ (~a::of-!)J If.2~ W:S~ Ot; = o. 52~'b L= W~ ~gV'2,A~CL Ae2 ~.B{ 1~1. / C,-:% O. 224 ~l)5 gQ ~ Ll42 V .Qz{5LO~:: 240 @at/s ~Too kApID.lIJ.t ~TQE.. Is O.372s.}J~ lY Qw~~ Is 88.5. 122'7 S~ U-Y(k',D)iG ..Tm; NAVl6Q- -~~ ~ At- T~ lJtu 1- JL ~ :d?-tJ(Uf~/ 8y1 .r~d)( iJ( Y20
~A~3 I~..' ls- lYm % M5W WIND~ ~~·~W~5PmD 12e2kjJ.a:me~y 12e=~ 2 128 % (~+Vt~~+tft.lf:' z ~ ~(lfa>-t-~~tr:(trm~V) -1."-- - 4- ~ ~ l5~L +- lSi,t. T~(p ~~t~tJ...V)+ l(~~J".. ~') Tug Clt~ ~ TD V (S t.~,.~(V~2'(JtDV) lW~dN fu ~mLt; DJZ ~vt;_~~T~ KWl5Tl~ ~tt &-r~ T~~R.u~ ~Nor-~. '~:2. NOTb.T~-rUi; Buz. ~ Nor 'Stow ~1Z.L~ )J ~ 155 77 I= ~fJ~~~jh/(Ja> TI-lOS ZI?e :%.lJ~.lY~~~'~'L """ O:(1~3r) I.,O.I (Iae~2:91t0e i~~ 15.3 2CJl3A:z 044~ ·{o'2. cPs -1. V~d.>* ~ ~-k2 =- 14524 ftko.44It3!t~ ~ v.~ os O~C:1~ _(O.-t; !t~ V45 ~ '~57 _O-s .ft~ a.~" ~7ft(z)(r4S2)~14('87 t!>.~i .0-t; I ak.1?O ~ 4}ffi) b~ £ z 17_ (§;:S 7m~ rlD I.S7/ )
x 1Re.x dLJ~ ~~ G4't1 0 0 0 0 . I 2·1()5 .111 0.321 .5" .2«19 I. Jt' I .352 2.0'3 2 .'1Ql 3.SQ' 'I TRAHsmON Pol NT ~=2'ltfi f.JAR I 2. X, me~ 13.S' ~L = Lv =(Y2)(LlO} = -:l~ ZOO J} .Isq .,0-3 0.) TlJRBULENT FLOW Cfx -= O.OS?6 (';f2(x)0.7. efL =J. (LCL ax=O.o!;".f' (L -0.2 L..Jo TX L(Tr2)0)( c;{x = 0.07-2 == 0.006"07 JO.l/51 D'RA6" =2(bJPv2A Cfl: FOR 2 SIDES =(O.~2373XI600XI.5)CfL = s.;r4L =0.0392 lb. b) LAMINAR FLOW eft.= (~~Y2 = 0.00375 DRAG = 5. ?CfL. :::=.0.0214 lb. I = J+n FOR TURBULENT FLOJ~ d' _ O.3'g1 X - (""Rc).2 ~---x IF Y);: 1./ 13"'7 v= Q == .~b =0. 3'1 Hot/s .7 A l((.u;)4. T CALCULATE ~t f Vt ~ -2 r: J J~1';;'= a022 5'f V;< ma.x --~-- VXmAX ~~ FOR THE Y7~ POWER LALJ v= o:Z{? Vmo.x ("PRoB. '-1.12) :. VW~ :- O. £f 16 t1/s ~h1o..x == t:J. 07!JWI J ':::110- b Hil)S ~ H~o L J )-V _ I 'vxmc..x ~tl1Q.X' - I3.2ct :..jJ;. = O.'{It, ~.022!;= o.ori'll!! p 13.2' s a) LAMlNAR SUBLA YE"R ~+= ~ijJ ~ ::: 5 J ~ = tj+)1 = 0.292 n1m ~,",(p
b) 'BUF"J:"ffi LAVI:R 30 > y+ >S' .: ~~)C =I.?SI./ Mtti AY =1.~'2. ~tH c) CORE 1'5"-I.?£" = 73.25'"......... 13.&' MOMENTUM ,- pV2 ENERGY ,,-.JPv3 @1i?e -= IO~ .&-=~·S-Jk)CO.2, 6L l-s i~~~S-J =2. '3'1 v= V«)f(~) MoMENTUM =pVoo 2 f2.(-rJ MOMENTUM nuX' = f 2(iJP ~2 ENER§V ~LUX = f3~) Y2f1~3 LAMINAR; M = sin2.(i 1J)p Veo2 L E =SiY13j~1r)~pV~3 -CL 2 ~ ~It{~ rrt) ..M- ~L &1- Z pVoo2. 0 0 0 .1 .J5'b .021./1/ .3 · 'I5S' .~ol .5 · ?O1' • SOO .1 · Zq .195 .q .qq .t/f E ~pV~ 0 .OO3E .Oqq .355" .?aK .'i7 1.0 l. 00 J.00 /.00 79 ~ M ~ q PV~'2. ~f'V~3 0 0 0 .~:z • CJ()l/ .2S1 .ofq .1./92 .3f1S- .126 .5S3 .4112 ./68 .601 • ~6b .2.10 .6QO • 5/2 .:25:2 .61~ .5SQ ON 6RAPH: ) MoM-LAM 3) MoM-TURB 2) ENER6.Y-LAM q) ENER6'1-TlJRB J.o .X .6 .q .2 OL-~~~--~~---­ () .2 .'1 .6 .8" /.0 M £-LpV•.2 ,~pVco3. r3.Q "'ORA6 =CfL ~pv2A -2SIDE5 A = T·l/O·2= SbOfP- D= ~(.OO20qqX205)2(S60)CfL = 2~" JEq .eft. Ibf- "IRe. = vL - 205·? - 'Z IL/O 000 1) - 3~6'1'IO-7 - J .I • D02.0~ 0.) LAMINJ¥R CfL =1.32X' = 0. OOL/65' ~ D= 11.26 Ibl b) TURBULE'NT O.OS'1& cfj( = (vx/lJf2
4L:: 0.072 :: O.Oo2QQ ~.2 L 13.10 ~)< =0" COM"PA'RE' C" ~ CfX a) LAMlNAR ~:: S"x fi& TURBULENT s:" _ •3?6 ~ '1" - 1Re.X •2 C;-_ .3=1€,'ii"".).3 LJ ':UJ ~ - ~ If"e :: -"T7 b) LAMINAR Cfx= ~tt TURBULENT CfJ( =.OS''7~ 'iRe)( .2 Cfr _ .05'76 ~.3= S:'17 ef£. - .66'1 1"3.11 Tl1R13ULENT: o _ o. 3~ C _ o.on. X - "Re".2 tt. - ~L..4. 1Re - V.L L-7 T= 2oDC, J=IO-b ~}§ 'IRe 2D. = Lj./OT D= fPV2 Cf A =~ ·IOOO·JIC)O''1·200 =1I./0'7Cf N efL = .00137 D:::r 5"l./, 'l2S" N 6'=.31(;, ·20 =O-W3)')f -IL/.3cm ~.2 Bo eft = 0.0000664 D= 265"6 N $:. 5".2,0 =. S'/O-2~ ::" . 5"em fl/·/oJ 13.12 0.) J"~=1,(1- ~.&)cl'j = ~s:(1- ~) d(~) LET ~ = t{ J~ (. ~1 I ~ = )0 ~ -(1J d~ = 1- lti;- I +YI = $ V1 (rt+lX(lt2) . c) 2 +.E! = 2 +(21X"H'2) e (~)CV) == 2 + ~ Vl
13.1£1 J; =V, I cl Vxd"i 2) 2 de P 'X d;"t2te et-Vxcr G& O.022S Vd f. I n )~ V)C~ (mIXr1t2)B = vx~ d lJxJ"(2+3"e +- v~ de ,dx 11 j dx MULTfPL Y eY ekI AND NOTE eX! de = %Je 5N ;L deSfil + e5~(2 +3,,') d v'x~ 5' dx 14 n} clx =0.0225 fr~+I~(Y1tiJ~ (~J~ rS./~ LET eS-lt = U EQUATIoN 15 OF J="oRM ~ + 'PC)() U =QU() ( l) WHERE ~} = ~(2t-3"dIAtVxi Li Yl"} r).y. Q(x): ~O.022S ~. IhQ~ "tl)(m-2)j tvxiJ Ux~ MAy VARY WITH X EQUATIONO) J5 KNOWN AS A L1N~AR FIRST ORDER DIFFERENTIA L EQUATION T-IE SOLUTION 5 u= eSA{ = e- fPr.x)clx5~(x>e ~P(lt}dxc(x < WHeAl vxr.s CONSTANT ?CX) = 0 U =Q x -t C..I c= ul){=o I~J" TM£:A<XS»tE1;> A~ tSb ~Tm:.. VIcM~IM~ S1tn>~ ~~ &t~ ~b-r~~ ~v,lk(~~~ ~DtS~~<1~ hJ 8~£·
'3.I8VlC'''(~yJ=~O) t ~~./Lx ~Vx'L 7'l1!...2 d2.Vx'/.f+ ~ y + X~ 2 + ;;y2. 0 Z "T ~VX'I X~· •• ~J(d~ 0 SiNCE AS V-Q ~/~a .. .~ v/(X, '!J) "../c, ~ T C,.~4 t-C3~ ~ ;;;V' I~ 'j=o etc. ~/ (x,~) :>'j tb,.«:j:l. +~)(~ ;}V'; 1 e.te. ~4j ~eO FRoM CONTINUITY ;)V'/+;;Vtj' =0 ;;x d~ So~ C~<j+ •.. +b, +2b2'1+b,3X",=O COMPARING COEFFICIENTS OF X-/X/ ¢ ~' TERMS.. WE OBTAIN bJ=o} ~=0.l C 3 +2b2 =0 HENCE ~:'(XICj J= ~ y +Sy2 + C3XY t- V~I ()(,<1) = -C3 '{2 ... U ... I / - -c C '{3 - c., c.. y~ )( v'j - 3 I ... 4 TAKINc$ TIME AV£RAQ£ VX ..V~ .. =-Cg C, '1.3 t- HIQ.H E'R OR DE/{ TERMS ~OR MIXlN6 L{;N6TH " THEORy fx'V~/ ~ ~2. ~VX =VM (~)Vn -'-oCj ;t"R ~ AS ~~o ~Vx~(;x, c;1~ As Y=>"R ~ vx ~ v"" ~'1 ttl< BZ.
CHAPTER ~ ru V =~ = '0 ~'~~o.J ·~s ~ (o~~'f ff)2 =l.fK tps RQ. = )V = V.l2'1/il)(I.Ii) =2 q 5" JJ 8 -Io-S' LAMINAR AP _ ,- - 2 r f L V2 . £. = 6 -- -"L - )~ - ) 't P 1) ~ :: 0.0542 A?:: 2 (.OSq:;J~ (1.II)2(SV 0.0'2 32.2 = 66-=1 tbf a q.b3 ps~ R-'2. l'i.2 ~D~.111 2 AP -= 5"ps', Gl)ESS LAMINAR FLOlJ g = '32.f<2 OR ~;p _ L.. 32Jv AL '[)2 ~f - D-r c V=A'P S .Q.D fj'j2 L ~ =lS".I&ttf ~..J. ~IO~ 13.2~ 5'? 32 ~o 2'Y f""ps ~ =~ = 13.2'1'. lOS:: l'3.fC1 Y 12·1 .: LAMI NA'R J:"LOW~ Q. =AV=1l'D2 y;== aOOO?22 CfS 'i c:J oR Q =2. 60 ff~n1in,= "lettS ~~ (i)~N.'3 _________ Ar 2c?O~ ;::-250-" 'D= .b2~ ~ 2 S3 ~ == ~o...~ J "P2 :. 300 <'?~ Q == O. 56 w.~ S J= 4.~)(IO-b Ml2.J!:> P=2'10 ~ /~3. ~ - ~ =(Pow£R) 1t cH o =~V +ffCe.-rfrM.ito P:: ~ [/2.2 +3.. 't 42 +uz p J 2 2 -Or+~dt,+U.,~ p= ~.;.[~¥,+?j;;+~-i:'lf"J 1L = 2 tf .b.}L2 o ~ ff =ff (1Re) %) 1Rt!. == VI) - Q. 4 ~ 25'S 000 -;) - 'iro"'J " e =.OOOlS fl., E:. ,oooo~'{ %=-3.bl~lo[~ +(3~D)~] =: '(,./3 $i :: .003'Z1.{ V = I.f5 G ~/s r2=O,~!; J ~ h1.:: 2(.003~)(2i'O"O'l)(.~s"I)=1:l17 .62 ~ r>::2, -'P. .= 3'00, 000 -/~ ()OO ~ as.;z~ ,o~ -aIO ,9. 'lo~ ~~ =~p~ ::. if.XV1·¥;lO'.Sb ~ 4441 ?= 4'141 (25',2 -250 r/2/":1) ::: '/,413 I 30b . IJ, "'1/5 = ~~ 13 KW DR.. 6"'Q,! hp
GIVEN "PIPE J A'P -- .fPV 2 - f iA~ P FoR l=ULL'l' iU~ULE"NT J:'LOW, f -= fUNCTlON O~ e/O ON LY THUS ~?_ ~2- P THE t)EA 'BEHIND WATE~ CAL IB'RATION IS A'P. :: ~,~B ~?2 w.~ P. So t..~2 =A'PIIo.O (~02.J p..... wHa,o ;:;0% .:1'D _ '2 (~~ 6:2.'1 - ,'" ~"nc;' 1°2 .- ~ 2t.3J ?o - 7. T..cr -' 1~.5 I 3.20 KM , ~= 6."1 '/0-6 jlM2/s p.: ZOo I K~ I ""~ v='.1~/5 D=.l"~ e =. 000 ,5 ff- L:: 32q DOO~ 'D e = ~~3 / ~e.:= llbJ Doo ~ = 13,Q"? ~ = .005'12 ~ = l/t~1~ p~ t> ~~ ::: ~(.OO51:2)(32q ~) (l.I):2. : ,-:rl J~Y()7 • :: 5".1 M ~ = M~L:: Z'D11L(.'1/)2(1.1) S"~1.1{ ~ ~ =lq41 KW W.G ~'P.: A"P, +- A~ + 6 'ij I) A? MAltv' n> 'P'~E V 2. ~ "i:) J 2- ~+~=rpt~ :z. ,a T t#o A'P. -= lp:z. p ~ 2) 6."PFRtc.notJ A~ =ZK~~+t(f.f~~~ P 2 t;= ~PlZK or 'It! -'cJ '3) A~NOZ2~ :2 u.. ~ PI" _ VEX,T .:.L-+ r - - 2 T2. AP == V i-xfT _vp:2 == ~~(V£~IT- i"p ~ ~ 2 Vp:1 I) C.ONTINUlTV / Al>Vp -= AlOiZ ~VE)OT :. A~::: .?2.(Ap'2_rp -"2 AN:2 I} ADDIN6 T06ETHER ~:: Vp:l fi'"t"2( : Llf b +Ap -0jJ 2 t: :f 0 Aw?' .'J K:= !/ f! L~ ID 2K =;; -a:; t 3.1 +1.5 == 155 t)/e. == ·'=1¥:J,·5'fOb) = I~ ~y '" 1'1.5;<) USIi v= 1.570 /0-5. Vp2 == 1Cfl1 lSp ~ 9.iripc' 35.CY2 +I0:2'-10fr} r FC)R 'DIe. = 1.2.SZt)lR.c ~ 36 12") ~;J ~- ::: }8.35 I fF= .005~1 U:: 9.81 fps lRe. ::::3~09(/~Vp e4
:. Q =Av =~~i~l~.Ul=.~cfs - 13.~ 6?M ~.1 AP=hI. : 2 tf 1: )2 P D ~ := (4.'15"'1'4'1) = 3304+2/S~ fJ 62.'4/32.114 hL = 2 i" 2S0fjli/6OJ 2 = 31ls" .£± D &D~ DS §.. := ~ -::: O. lOS"," DS 31:2S lR~ =Dv =- D(ui/bo) V 4 '10-" (1TD)t~) :::: Li 75' ., oS D ASSUME ft = .003... D5" =.02 "gt.{ ~ =3.i".2 x lOS ASS(),tt£ fr = DS= .0'3:1.'1 ~= '3."72 ·/O~ ~p = '1K V~ P9 .2~ D =0. t.f91 Fe ff =.OOl'{ 5" .003'1;- D = o. S"OI-l fI- tf= .OO'S<l1 ASSUME "PZ = PATM = lor kPo. v2 ::. ~2 = 16 Q2. A2 11:2. 1)" CK 85 _pA?=2K 16 (i?2 71"'''' Dc{ Q~ 2 'Ir~ D~~ P 712 135' 32 K; 32 (s)SK OPEN ~ CLOSED '12 CLOSED "3,A a.os ED ."3 Q ,"5 .2 "!I .1 K .JS .KS ~.q 20 Q .2lff .125 .055 .02.s'i Yz ~'1 OPEN MODIFIED 'BERNOULLI ffiUATION BETWEEN I fZ 'P. ~ v.~ ={'= ?2 1" y{+ 22 t- hL p§ -. 29 T i'; fXj 2~ o V. 2. L ~ ~::. ~.,..Z2 +Llff -;;1. f'3 2g 0 ;;z.~ = Zz. +- :1 (1+ 4~ L) 2~ C Q::. Soo tS?~ ::. 1.1l c..fs v= Q : 5.b?~5 'D = 3333 A e. 'i<.e = ~ = So 6:t ',S ·,a~= 1.D3·1()~ II I.'t ' - r.:;oo F l % :.1'5'.136 ff =.00 '(q -1'2, = '3' .f ~:l.(it 'I". O~'1' ~) ~:2~ .S
-P:a. = "S.S I' ~ '"Pz =-~/q ?sf~ :: -'S~ 'P'$.~~ IL(./O ?>fTWEEN I E2 4f"OIA UNE '2" 1)IA LINE I <j('12 -~,)of-V:22_v.2+ 'P:a.-P,::: 0 2 to -20~ T '1/2. + 1'z -?..rrM -="2 P BETWEEN 2.f3 ~(~~ - t;i2.)-t v·i -V2.. 1'3 -P:a. .J.hL=o 2 P 2. a" V3 - V2 +"PATM -'Pa t- hL =0 2 P ADDING : -20~ + V32. +hL =0 2 V"3 =A:a V2. = t4 ~ Aa nL = ( IS • O.? +-J) V 2 ... 2 t; DL V 2 ~ 2 ELBOWS (ENTRANCE ::r~+ 2f JJi"lv2 Lz f Q/,2J == (2.25' of- 6"QOf;}v1 -6'4~ r(2.15"t 6QO)V2. =0 ASSUME f ::: 0.006 • V2. =6£1l4 = 1,2q.5'7 2.i5 r'i.1'1 V::::. IL'31 fps 1Re..::: 0/.2 (U. 3t) '.22 'IO-S' 1Re. = '3.1'10 5 fj:. = .OO~£ -~y V2.= ~~~+3.J :::/l0.S" /: 10.Lf~1Ps ~= 2."l·/o5 tf -: .o~t; Ok FlOW 'RATE = 1F(t fl.1,0.<f9 == o. q,S c f's "'.11 UESTIMATE: VELOCITY USING &RNOULL'''s EQUATION v 2 =2 q An v~ 25' fps (A11 =10') 1UI5 IS A MAX. WITH NO LOSSES USINq hL = K3L.l == V2 DUE TO A 2 2- SUDOEN OPENIN6 AT ENTRANCE (SEE (;c. Ii -p.79) v2 =SAh V= Fl.i-t'P5 2) GtJE"SS v= 10 fps WITH WATER @ ~OoF ~-=b10c0 I ~ tf =.004'1 :1 f' 2. v1 v:1 a~ =Zh + Y.. ='h L ~ +_ +-J I L Z t5'2. 2 .2 ::11(2 + t4 fr~) .!: :: 2~6 '[) (FULLY DE:VELOPEO) 'i~~ =5".<-11 D v-= 't 32 fps (CLOSE EfJOUtiH) Q =AV =1fL~q)C'1.32) =.0 5J cfs =,q.'H, G'PM PRESSURE AT "PoJNT'B ASSUME Z-R O~PIPE BEFORE B Z. + ~ +1r. = HL -+ Yi+;'+ ~ l 2.; Pj ~ 14 I PS ZPRO ON SlJ1<F'ACE' ~ = -'4 - vi -hL =-1./-Y'"~+4t;.!:.) P3 ~~ .2sl" fc : -'1- J.3S'O(3.n)::- -q_2~ ff P"B = -4 'f>'51'~
V= Q = ~ '~'1 :::: 225fps A ~,~ De = i A~£A = 2 '21 -.:: Z''''=."6t1 l' '32 ~ = q~J 3~O ~ -= •0«'5 ff ~=L'333 ~ :: . 005;Z q I1P = p~ "T k v:z. Dc.2. :l.. =.oO:2.3~· tJ ..005'21. 22 (22.S) W3 2 :' ,~?7? }:)sf =,ocHq II U~O '2II H~O -= 62.Q ;:>s.f Iq.l'S CAST IRON e. = .ooo~5 9: Q= 3·/0' ~Qj/do.~ =4.6417 cfs %T ='PoWER COST +Ulrr/AL COST YR ~V'K5 + _DfI (INITIAL caSi) $ - 'PoW£'R COST + .II (INITIAL YR. - CO'!>T) F'OWfR COST: ~ , it'60hrP KW"'r lj("' ?eWER = P. '::iL[ht.+112]25':l5.KW .g(5S{)} 311/3 ~ =.oOl6QS ~GL t/l'~ KW PoW£R t =1.03q~ (~ Ib;Xhl fl75) == 301. OS OlLt 175") ~,. 10" PIPE: V= Q =~,5JO R-/~ A IRe. =(5'1'X~·S)) = 4,3 ~/OS l.b5 ~ 10-5 87 ~ = '1'gO, •.!- = JLI. O~61 ft =.oOSog , ff hL.=4G b V~ =q·2·5"270·'bG22~ o ~ D:;2Srrr2 1)'1 hL =22" Q62.!i = 2QO.3 OS jl = '30L05" (2QO.'3+ 175') ~r +.JI.(~gO'2'll.lf) =S 153 '321 /<:!t'""/ 12" "PIPE v= ~ = 5.9/0 ~/s A ~= ~.~7f·lo5' .~ =1/16 / 'iff::1'I.2!)3 +~ = .OOQ92. hi. = 22962 off :=. It~. 03' !)S" ~r =~oI.05"(.J.n.o3) -+- .11 4(5"2'80.2'1'1.7) =If, IO~ 787 1<1" "'P I'P~ v= <:) = Ll.31..[2 fps A 1Re. -= 3.07' -/05 'D - l"~" .l- - ItJ 4~ fr=.OO~X'Je: - ;)T oJ " 'f.t;: - 1. I r hL =5"/.10 $/ :: 30J.OS(:226.IO) /~r + .{J-CS2"'!o·2 ·'b.n) = ~ B7,&82 /~r .", Iq" -PJ'P~ HOST ECONOMicAL 6" I (C Lf•24"
0..) SOO<3~W= ~ :: I.ll~ cfs ~(7.1/6) =G2. A:.1rD~ A, = O.JQb3 ff2 l{ A2.,=O.lq 61 Ff2 v= 5'.b~.fpS (IN ALL 'PIPES) b) I~ ~ Io..~t loofl~!::: .00171 n ~ = 5~ J= 1.22 'IO-~e. 'Re =~= O.S(:;.6Z) =2.33 'IO~ J (.22 '/O-~ J1'ff =13.1'3 fr.:: .005'8 A'P = Llff ~ ~~ ~=1-f'V:1=3/.'3~ t = 200 A?= l./{.oot;1)(~ooK31.3) ::: I'iS.2 ,?sf 41P :. 1~5".J. p-;.f ;::: J.0041' psi t-HOOlE 200' e =O.OO;2.~1 1:> J:? - ~I fo 'U'l_ =1.6l! ·/oSe- ~ ..L :: 1:2. SCI t,.= .00 6 :3 " ~f L. :: 21"3 t,.'P ='-I~OOb'3(:'X.2! ~X'3I."3) t> =22Spsf =1.S'Tp~i C) TOTAL ~p= l.ooY +I.S? +-I.ool' = 3. Sg-ps;. 1..-.2 ... CAST I1<ON ;SO~ • lAP: ~ .ob7 COMMERCIAL ST~EL A"P =p Lf t+ J:. ~~=10 3 IS-O· 2 v"-If 1:>2 D .:. ~.'OS' V2.+ f =2-' -lOS D 'IRe = Vb =I06 VD 'T a.)D=.2M "~+f=·l<{ l<e. =2 '10 5 V e = .000 !"S"6' 'D/e. =??:z I ~ = 1~.:213./ ff=.005"73 'iRe =>c:o .: V => '.O~ ·/Ol» Of< Q.= 0.163 m3/s b) V2 t.f-':: .0'16 q 'iRe. = b~OOOV e = .000 IS"H "l1'e =1£165 I~ =13. 53<{ ++=>.00 'S~b ~e- ~ 00 FoR ~= .DOSO V=> 3..23 ""'/5 'IRe. :;> aU~JO()O ~ = .Oo4~5 V= '3. 2;2q ~5 1Ke.= ~S/OOO OK, v~ '3.Cb WlJs Q -= O.O/erg »13/5 J~lb ~=~~ L£ fj !)~ - /1 r L Q,'J. - "1"t"~ D 2g (~"D2)'J. =32 ~.h.. Q~ ~.2. '3 pS 1Re. : VP = qG.. II rrr'D 0 ASSUM PTIONS I)RUB6ER HOSE IS SMODTH "D"RAWN TUBING IS o'*' 2) NO OTI-I£R LOSS ES IN HOSE JbooF =I. 22 'lO-s Ftys ~:e. '11'2 p"5 =ff Q2. P 32. L
=f;Ql. =1. 36:2><IO-~ DS" i<e = ~ = 12.5":2.'°5 Gl 7b~ p a.) "'D :=. Y:2 'I ~Q':I.= 2.301 -/O-b 'iRE! =2."S0'/" 0' Q. fASSUME -= .OOSJ 'iRe. = 5"32.10 fCALL. = .005/1 .: Q. == .02. J:2:2 c::. fs =- I. 2 =t~ c f~ .;. -= I. '32S U:JrK/s b) u= ~c./' ffQ:J = Fl.4"6·10-1:. iRe.. =I."6Q _/06Q fASSUME =. OOt.(4t;; Q =.Ob.26 ~ 1R~ ::: IOq" b I q +CALL = .00 1I~). :. Q== .06:2.<f0 cfrs = '3. 77'iI cfW1 ~ = 3.'1215 tlo""'5 11I.1? A r - _ (I) 89 ~ + V¢+eA =~ +~+Z'g -rhl.. ~ ~ ~ 719' EQUAL Pi! -~ =ZA -L'a -hL (2) ,09 ~ = h3 (3) ,.os ..../ V2. h3 - ~J +f'A -t- ~ = ~ - 2-B - hL 1./:1. L - +- YlL = E, -zB -11.3 ~ 2. =- 60 1M %::. 2.2.,., ~( I t 'I tf ~) =30... 1..3=l!'... ~ .ff~ = q(. ooct)XQ = 3.65"7 .3S v'l. _ 30 - --- v=IJ. .b'8 Kifs ~ <f.bS; Q= 1.2l W1 3/s -......I t - - - - - b) ~ =.2S"0 off ::;:> .OO?I " => t!.~S'1 /MIs 'Re. =:~s ·?bSI =3.03 '/0'" 10" . Q::: O. Z3:2 IN3/S I I'/./f T "~~ 1
AP ="?.l-~ = ffj(- ~l. +Ac) =fJ~ ft' €vl +Pc)Ai! v= Q = qO *3/5 =4.S'i "'/5 A 7r( S..,p. 2j ,6i=> =10 "'f8~. :>. (</.Si)>'4 T (q:fif?X6h"Z M4j =lO'!.f'"?I:2.'1~ t b5f:7.:?] ~ = V"D = (4. ~Xs) =1.''If"tI T 1.3'( 1< 10-5' (ASSUM~ Tft2.0 -:::IOOC) tve.: Iq 6is -L - -3b I f)·9 tl. I - ~~l f.fi - . OS,aU·'lfl-IO" {J.1·J9~I~J J ::: IX .32./ tf =.OO29Z A-p = 10 3 t6'112l{' . OOl9Z +{,£"r1.~ = ,. 35'8 '/03 K1=b.. 14.9 fi!oM ~UbWlI1·'3/tr,:I.~~ THe; 'Cb 4'rk:W ~1'a.oa;e Ie; 1P=Sl,JV~~~?e-P....?e-Z}hJ U L2~ s>~ '-!t;RE ~ to;;T,,~ fAILS" v~ AJJL)~Pta; kr~ Aa .2. -rt;I2M-6y-~ '1, V.t '. t "" V~" (~JiQ,Y/-A~!) 20 2. ~, L T = -2.03~ lie.-90-::(S-)IOS ~ QS.S ~ )lej glOd -c~-2a 111 - 2fD. 0 W" nj..=hL,~ hL'2- W~~ 1)=(),'ZM/ (): (.<69.)~ ~ "2~QVI ~r'h:O.a:v~ ff ~O. ~ ,~bL,~ ~ 17S.<ff", WIIEQc 0:0.42"" lJ:r 4.CAl "I ~ ='377,~g(I e~-;! 0.00:) 09 f z 0.00371J / tL.l-= 291.95 1P:r[-t.03"Z5.5-Z:D+ 14(J}.~ ::: 4tW(24L7)=55l3 ~W AT 25%'~ Dv5rz.. lUes 0,~2."", VrP5.
14.~ J Eo:; O.QX)(5 e£.,.o.OCO~ gf5f~ s ~ I Qz~t;~ tof , ,-/ 0 1. I ~+~+~t· i"~T~~1 ~- P,tJ:Vl ~ 4 - V~ trl SCi '2(3 tY VIz V1 =~ = G_;4Cot~ Ck1. ~ ZS~8~) L~=ZO.ll TuQ6ULbVr ~ HotJ/ J3~ H~ 4.7. ~6)-t<f) K v,'t.. f) 1- Sd •~ +i!," ~ t ~ -tz?,l-kL ~~ ~ ..R 1- ~i=-lO-~-hL rIG ~.7~ HJLL~ ~~~T~$ ~ .e.~ -:: O. et:>42~ ~~ kL:? O.2{S1 ~-v J 2 ~ = -0.81 ~ -2. %~~ J<:! 91 1«5 V,I.." ~ (J,3.?A-G) 1.f4t, ~ "% (759.3/(( + eo.~.v1) ~ ~-z 4DJ <C42 V't ~ --t. ~ if)OLe VI }~u::: ~) C?~ ~-f - ~G~ -f.v :O.~ ~ ~ 37.~ ~/ ~z (;52% ·f(f t1?::o.ro3e49 SkDw ~ t1"20,<XB8.5J V, :%-3£0.~ J ~:z 4B9( ·(rf t1 :;:0.00385 D~ :D VI? %.GA ~~ Q -:z 7.0T5cfs Q ~ 3(7S ~P)/
14.22- ~14.~ 4P"y?'f(Arr~h+It]gG' 20 ~ A~ V ~ ZI( '" (1.3 ~ (0(.7) ~ ~ (' I- A1... tfO 25711'5; ij.,19.';2 lUU5 -z. ~~ ~::2~[et>.Z7~4.~ 1Q~ :z ~,2 z O.()dr.t;; 92.47 z~~5% 92. }4.f~ WJ2lT~~LLl(~) ~~~~~J)Ulr (~~Pe ~ ?~~) ~'--= ~~-~e)- ut~ t30r AI" l~ hI- "''rtf ~ LYV~ ~ t i. ~ t,.:c-l),~~ of 4L' 1,.: {plf, 23 kJow Q=ALJi, ~ :: O.73~/~ T~<& (U ~(073){ T. -= .'3- 2Q:L:= 0 BT/5" f 4 S§; (,(013) , .18 ~ ~T~14.2. Wrnl ~L~~~ft ~ -tt.J tf ~ (O/~ (~ LA~ VAllJfSS. 1"-1 T4flf-J5 14.Z ~ ~ 2LY~) ~ug tne. f; ,:::(J~~?7g) ~ ~ I~ ~ 2~ ~~ ~.2C ~<: ~7.39 f:eTf4t1S~ LetD~( _S~ l1> ~ ~g z3()S J Wb ~y ~~c~ Fbz-ntts ~G Clu & ~.
14.25 T~ H.a.u '" ~ 1t:4~~) ~ ~ =240 1 No ~AeE;CI FIDM fiG; ~4~ 7. 93
~t _~ '7 G- 'bD F 7 ~~ h f2~ 1-~L • v4S6 ~ -r +~+- 0, 'tF2 O.(Ylg G,QS OlO2.. '::::<- .•.-~~.-~,---- O!81~ T IA~ + %2+ 0,14 l.9'6, lbtuIPtt- {"'T.t.. ~(a,) 'PjIq G.) Ze= '):2,,4- .~ ~~ f,()j,m. b) 3rl= ~14 *~IJ{04 H c~ 4eO# ~/1~ ~ :; 1,94, ~ lrl 3 '-. .?Sla~ ~ /,. "' 6.~M ../ '-.. Q,(P'Y; CiI/I I 1 / ' / ' / , · r/ ?40~ f , / ' / / ///~; ~~s t:: ~Y'=-t;1H:J ,( -<_. ",-.' ~... +S CD f1~""1 @® / 1 -+ ~C;;; !A't~~~ (zOJ0)'=~7Xl(l ~{):o '4.{)~o:;: (4~J(.1) ':1 o,')..g.. ~ l -:.. 0;:::; Ol 100 = <Ot07~~ ~t (l.~'X.J) £'7..;:" 0 ~000~S :. C48 X04' 4~·,'7 Z R.. -= co {l '" I ~ ~ ';l,A,()-'l-~S == C)0Go W 0,1<.0 ')000:;: ~~Tl ~~-:r'Z. ; -r~-13 ~ <. 12.7.. .~ T3-?715 {Zo H~~. ·~:~~U~1j3 S f~.M p{({~00S ~.0&~EM e~ --~o+V'l ~. ?·t:v ~Ct;la'~;i- ~ (;, Ct.)l + L/O,o<oC) '" u, ~.' 1"" le1/9 L.
SA 19"sc. '1-- 7;4.() .f)J,S f)•." - ...-(' "/ . I~-~____~__ ~T ~tf- V'I QI01'L '}oY7";'. ~o-· ';J,S1-'-..S_'·_ OIIIl11 + 14,4·" L L-:;- 0 f O~'I(O v0. -,.. _--- --------.---- f ...~-k~t~ c. U,)S W/lMo,?~S v../~/Jeo~JM') l~9 ::: 0-0?17 INIW~ = b.T/R tq'-;;: Jo'LS (t!S)~ 40s ~ TM~ -:= ~~-' 40'0 ~ 445 ~
SJ fj I ?CO ' IS,IS ~ L 01t; ~L-=: 2.f-= l4GY':'Y4)0l0.1'O~1- ~~ 3.{o ~/w ~-6I.-tCil~ ~b{ ~ ~SS­ ~C:l~M, ~~ ~ k~~'5Os: ~ ~l-x';bot. ~fl6~ Rf6b~ b.Tkt~ 1,Qo -.= ~l3A '-/w) ~3 = _ +-__ - I ~l I~,~ 1~A' ?-/~i~ ~~. tI= IJA,s W ~;f.. IJb.l, lftJ/;;1* '. R,~ "" 0r'~~-= O,~YZ3.)% t, :=: ~f"Ir = OroolOS ?Ti~1 ~ 1. -:;; b (:/"1-. ~ 0 dSirG1- ~l ~,'j.
g,,( letJJGG'~~ y~L~~- -:;: CoI,1. b ~~~ __ ~~,~ U~ If~~P'~S ~ttlt~ r;40~1.. leW" ~~)(r;X~J."IiXil,'-~ ~=1£~)(On~,~- SA-~J -.. sSll~ ~1J/~ ~= '1:1L,,9; ~ %(]).TV "".]& 91 ~ ~ ~ ~ ~/L
,S/)D %00 W-= fl'~D~!J(H~_. !s- ~" L. 01(:{;( h.~t~ ~ S)(f1V,£ "c~~.q+GAt~4-r,;'-1 _ 1Jr~s0~4~O.Illf(.)~1-S,<fJ , %( l'~.~M.- ~y ~-, '," r-- c56~ e.. c 1o~ f.
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~lP-Wl h,JS.Jl-A't~ I ~ e.- I fuA)~~'L.5 J /J w; t).TtL L l,'j t- fZ-XO ~l) = 0,(0;(0 ~/W t).liL ltJl' -l<S0l:f'1.CN ~ ('01 .- L~.:_I_r~~1ILtS;+ _I F7a~lJ ~iL[ 11,3 l1-Yo 0(1'7 = ..L rC;,LcfiX~ t _I +~V'~It~,l'( 1d-1'L l 2..f~ Ot~ J K= ~UJ= ~w6/4 LKUj:=: 4'h~ ... ~'~~kL ", S'J.'flX0.I~~ot ~':~,1=1).,1.91- ~1 T~M" ~ &~', '('0" 011'""1 M NS()~"T~J ~5: ¥O-~ -= Od11- od1:>l ~ O,()} M -= 4tM 100
~~ eo ((P,? leOti N C:-tL~ ~~~t€Si (c.} ~+~~~o ~+t~~)~ a( &2T =- 0 -£EJ'2- -"'" c~+C1.- Be I 1~~C7-
<6I '2.. ~. f) N ~)UdN) k=- .0-~r ~~ ~- (~cU'N-t-~?)~) LV T"l- 6J.;., 01('~fL) --~(z.o-a.l) &1 o , ~" ~{~~L)1[~-I,6i+i~1(T.:r~
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{11)$ c/t?t'IVC7liue,) dtyp,) t?!uaU O. d<f ) 5~JVf? hY-'<:p rt 6~ rj:StJlv~t''' fUl1chc;'n Of? If'(ce/ {f~tJjsheet '.. CD.::: 0. I 9b===- Problem 24.28 Excel Spreadsheet tp df(tp)/dtp 0.02 1.90E+00 0.03 1.54E+00 0.04 1.29E+00 0.05 1.10E+00 0.06 9.34E-01 0.07 7.97E-01 O.os 6.7SE-01 0.09 5.72E-01 0.10 4.7SE-01 0.11 3.93E-01 0.12 3.17E-01 0.13 2.47E-01 0.14 1.S4E-01 0.15 1.26E-01 0.16 7.2SE-02 0.17 2.42E-02 0.18 ·2.02E·02 0.19 -6.09E-02 0.20 -9.S2E-02 0.21 -1.32E-01 0.22 -1.63E-01 0.23 -1.91 E-01 0.24 -2.17E-01 0.25 -2.40E-01 2.00 1.50 er "0 1.00 --..!t :c 0.50 , 0.00 '", I ' "..... "----·0.50 .. 0.00 0.10 0.20 0.30 0.40 IP_ 0.50 2+.2, 9 '-f50zgrne (SfeClBS A).- (V}tt ::: /"(;IOtJ fl(y )'YlCJ / e dsA -= 11 I), J1 m 0;,1i 0 ~ /,o4x/a'(I'rl:L1s ~ C!afaICl$e (spec/e5 /3): H8 :::. .;2S'g CltJtJ 9{jmo/e ds) e :. /tJ, 41 nm 1")<::1 -1 ,I vlJ-f/;P = 1,/() ;.t.IO em ;)./5 . -r;dns{Jorf fafle el1 ;l1ft18 trltJ/ecv/t!'s ~r't'l/cf.k cJ>P'r6?S i O'lli !Jf/UldaldieI" I(..S" Cl )1/l;Ije ytJ c.1 d//lw;~~r' JJrtl~e~s, - . 0.60 (jJ1t ~ d.5A :::. 4)~ nm dfO v-e. dpc;yo e rpf3 ~ ~ ::::: /(1, 11 nm d<fore d(to ye 1 1 5()Zc;rnej srfec;I85 A r;(CPfl)::: (I'" Pf~J:;' f;..., (Cf(4) :r.. / - 1.../1l1 ~ -f j. 09 fJ,/dJ 6- - 0.9,5'lit l'f;e effecf/flg o~f/z;6"!(/;f,1G ~e~ D:'HzO r;{%) fjJiftt ) C -' !! i CJ m j>!.rl / n9 tile ':Iirv 0,'-::' ) i/ If • /' / 1;_,.<:' )'4{)r] ;"Il/ 11 Ii ;!;k' ;,:J IJj, ,., . vC/'" ;/ i:~ ,#... -, /11 -ftFrlJ/,( d/' '/d:Jc<nj 1.5'
the rt:1(7,1- df4; /1tll7~;'edr efth::1INJ~ /5 C,C;iJd/I'Jc"',:/as./~t /If£"::? If .r,,/ver Ij Mileht'J/1 0 ~ liJeros-oil; E)(~e/ ro Ob/all1 df!..[f~ li~~~"1 I ------_ IProblem 24.9 Excel Spreadsheet Solute Lysozyme (A) Catalase (8) dpore = DOA-H20 I DOS-H20 = 21,3D <PB = F1(<pA) = F1{<pA) = D'se= cx= Mol. Solute Molecular Wt. Diameter Diffusion ds Coefficient (nm) (cm2 /s) 14,100 4.12 1.04E-06 250,000 10.44 4.10E-07 14.3 nm 0.394 0.729 0.074 0.080 0.006 15.00 <PA= F1(<pA) = F1(<PA) = D'Ae= 0.288 0.507 0.443 0.225 D -t) -7 ,/ 'AS ~ 3".1t, x /0 emf'S dS A ::::: /:1..,31 nm' () oAe .::: ~-If.2 (/ 17(~) Ii(tf!t) dfdvc> ~ ItJlJ n fJ') 41 ::: dSA """-=- 12,gf{nM:::; t),I'2ilcf IJ cirp{)re Me nfI1 "2.. F,(1h):: (t - ~)~ (1- (), J23?) :::: ~,1617 r;,(~) == / -;z,/04fh f- :Z,P'! ~3'-0, r5'tit~r =/-:;',/04 @, l:J.3t)-f,1.,(1/ (011:85/) 3 -d, '10'(rJ.I-:2.3 &,)S';:;:;. 0.. 1-'/3 ~07 =J, 1" xlofoi7~rl)(a 743) ::= I,Cj7K(O'eiYJ~)
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:2d.l1- ___ ~m--~ ,,--JO,I5'm- -, -, - --(j.()5'fY/ -~ FrofYl :L&-13 01+(3 :::. OJ{)5 CMY.s C.:: j, 77 >< 10-s;"LJL.; Clh.:J [!orr/-Ytij 1./0 leime NAc1Y'r~ 2. J -'" N~c1t'r1::; O. cff.H:: C 'st(r?'''' ) ::--u . rill;.. /s cons}4nf di!:. '~Az .J Ill; o ,) 1! -Nft.;; NAt":; -c D/18ifftl(J,j~l!!~E:) NAt =- -Nl6.c as ~&,13 ~~~ P,J N..2; 71r') ~1:. := - C 46njj~~ ~ 0 c1,d, r=-lr1lf'b ~ I:::. 0 • r:~, 615""111"::" l6tJW/:: b<J @l:: :rt70 J'r:::: SenF:' ~rt(5~/.7.) f 7,5- 171';-'- 5'1:/0-3 , ~ -J I ' r(em).::: -5x/d ~ + "15 =:, - i: f 15()r~ ~(}O :2.. r;2= (It>tJtJ -l-) /I)(/02f )N'fi- (4Xta4)1500 dt ;:. c. Vftfj fifo, /P - /J,;) o (J'5d~ - 2;)2 J tfoo ,) ~ (4 x104) L~.c- a ;::, c ~rC(!>. 5) ~ l4'1.I0 4 )C;tf)) ~ c11trprr{rJIS) jA/ft~ (3,77y: (O~rruktOtto! fJ1fry'~J5)~ en-is S J< IEl2 '" l- a'!) 4><10 ~ = .If,~" )( 10-7mole/5 = = 2~,/5'
Wtt(h ~J = c ()fJt3 1m C~) JiI;.:. C Of1l3 (Od9!) c:::: f.. .:: /1 ~1'3 X /05'~ :::: 4t1,/19m4 ~I (l311 PrJ,.m')(;'9f1K) rn mtJ/e·f::,. ~,~ =- O.09~2. ¥;::. fI,,). Yo 10'm% WA :: (40, rf ~::: [/I, ~~ '2 xI~~~rJ.A0.lfJ) m 5' =7, 23 ;( /0- ttltf/e Is CAr z ~ L J Wd ~.r) +- t ::' ).. Y)'1 2.- A;= :t WI -S' 7,'Z]xlo mj/~/s ~ ml. a) PrlKe _p , /J,r ds %' ~,5')( / [} 1-1 :-:. (), ~$-' d ppre I -;<ftJ-i f1"l if(cp):: (.,.:. cp) ~::::.. (o, 75)~~ oS" l5~ F;Ccf): /- :2.JtJ4cf +::<,p94>~ (j,95'C/5"' =- /-,1".,/01 (O~)..S) r;J" ~r (0,:;.5/ -~. 96'(0,:2.5):5' :... (J,5t)(P OIlKe~ O;B 1[(4) lictp) -:: (I x/O-(()Yl;X)(O.~b~(arrt;J,) -::- :;'.$5")< /0 -IINJ7s 6) V. Iv'It f ac.j' ~ f)/71 ~ .:&:£ - 7A 1i(~e) ~ OJ !lire: IS. C()rJ'J'J~p( f· tlltb::::" OAf; (1,0 - tJ) L.
IF 0"1; T chQl7fes:) n r1 (-&r~er;)Vft,g r:. ::: V.46t,. - ;r '- j... li r; M6r~ ~ /. XIOIc:n':2.(~)(~q!3·.rJ s '29~ fc,/f Pc.:..1J ::::. /).,P/fj On6t. Ti I,e tf,/ % lau,1<B v- ;;'~.17 ftekr 1:-0 eXtZl'Y7;>/e :Z"/~ ~!? -r()fa/ rCE tlClIJtJr C'rIJIS'.)/(:1// ,:ale ~ ~ ~ 1r. 4 'lJ PM". 0118 (r) t. ~ I 1?,~.....-I1 ,qr ,1- Ftl'l --p-- the /iJllaW1i1J t.ltir/d"JC'$ a,".:: t!t!{le rldel? fan T" .3tJ~ f,13 In [ftt') = lIP, Iff,<.1 ~ r_45,15" !'he )'t:1'(:o< ....J;r;li(/4)' htf'e bd 11 rd he/i;' f IS 3rtJ;I')~ !1Je /o/httJ/'{j Exc!;--',L.. 5{JyeadsjJt:!!.t::~6 cCI/c.tI/qleS" Wrr as fA f;,;nctrtlh ,pI: or "/tlh&:/ iC/,fhl L /-PP' /iKed I'Lltl k dftfllJt!':ur ()r 2,Om. !he ..sA.~.Ied ely-ells /~ d/cdle ra ngl!'.1 iPf'lPfll'i'/ l /f;pf de(Jr~dse /te' ,,:"I:I t:I;1ISS./tJl?S' rafl£'ft> 0'-' belP tV fh~ /I')CO< IIJ/dlJr'} t;:i II~uJed. r-~~ eKtllYlf'k:J CL CtJnci&l')sr;:f'I' T a f ~'1:Z A-' Iln,,-I i~ee 6.1p r'~J/ J, e,!41; L..J tJf 3,~ M.) l4e /CE.!' t?tlll$$)tJm: tc?.f.(? IS ,J,:< fr "1,7t'l!-/dp,J" fi, y" ifYi1r::'C'b S' 'J' J r C<-f'-h'r fa e>< C/ J?{j> Ie :J. ~ ,/"
"~" __ 'rJ __ " , ____ ._ , " ' _ , __• ~._. , ...----~.'-.,- PROBLEM 26.17 EXCEL SPREADSHEET MA = 131.4 kg/kgmole R= 0.08206 m 3 atm / kgmole K DAB = 0.088 cm 2 /s To= 308 K p= 1.0 atm D= 2.0 m TCE Emissions Rate (kG TCE/day) L(m) 0.50 1.00 1.50 2.00 2.50 2.75 3.00 T(K) 288 1.479 0.740 0.493 289 1.561 0.780 0.520 290 1.646 0.823 0.549 0.412 291 1.736 0.868 0.579 0.434 0.347 292 1.830 0.915 0.610 0.457 0.366 293 1.928 0.964 0.643 0.482 0.386 0.351 294 2.031 1.015 0.677 0.508 0.406 0.369 0.338 295 2.139 1.069 0;713 0.535 0.428 0.389 0.356 296 2.252 1.126 0.751 0.563 0.450 0.409 0.375 297 2.370 1.185 0.790 0.592 0.474 0.431 0.395 298 2.494 1.247 0.831 0.623 0.499 0.453 0.416 299 2.623 1.312 0.874 0.656 0.525 0.477 0.437 300 2.759 1.379 0.920 0.690 0.552 0.502 0.460 301 2.901 1.450 0.967 0.725 0.580 0.527 0.483 302 3.049 1.524 1.016 0.762 0.610 0.554 0.508 303 3.204 1.602 1.068 0.801 0.641 0.583 0.534 304 . 3.367 1.683 1.122 0.842 0.673 0.612 0.561 305 3.536 1.768 1.179 0.884 0.707 0.643 0.589 306 3.714 1.857 1.238 . 0.929. 0.743 0.675 0.619 307 3.900 1.950 1.300 0.975 0.780 0.709 0.650 ! ; 308 4.094 2.047 1.365 1.024 0.819 0.744 0.6~~.._.1---------~------ _... .. 1.. --_.
;:Lc;r /5' 6'1. == (2H6 0"'13Clts) t ?13 f/(/f of 6" 2 IJS f:; fo Jel /1,18 Mefti / reduc..fiof1 wil16e 11l1/tlenced 6J /lux of~. re(/,c!,dri["I) !teeds 1 I{m/?.) 6) (3) v :3 ~" (I) (jJ...) y 2. t/ 0) ~,,' c D4-d 4[I f- ;tAoIcJ 1+- iflts rf Clvf!q = I m.2. 6-= ,5'"cm ~ d.OS- m ~Ii 0::" O.:L.{) ~fls ~ o. .Ps; = )...3;2. tkm3 Ms1' -= .2f~ Of :J/mok
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;;t" ;1/ (,,~ ~J) , /, Ne> A(/PI1()Je/1e~tI$ red,c'//;n II? S-///Cdl1 r'llbJer- i, S feacl:J-,$IIl~e i'tltJlb5c"'!f.1Y· ell/hJSIIH'I //1 y'--dlY'e:;eI-MIJ any- 3. No 61.//1<. i'OJltrl btllldJ4 -4 ,CtJn5 h:rn f" 019(:3 s: CtJYl~e n Ira fldKJ In v/J,Ct1fj t;,1 f'~ 0 0/ ) . " " q, IJfl r ~ :~:' Ij:i' -dt; _d-(~' lV~f.) ~.~ 0 j ,. A4", IS t~~J$ll:1n f {.1f" f/ C:,,,.. V' 0, i'"~ lJ.13S" ,,~ {>'J£'" .,ll (11"'1) (}l 7~1() ~---""""~-~'--~-'-~ .~ - ~~~'-.~'-' .. -. -"~,~--~--"- @ r'.::: 1<.." ::: <1,55 m}Y/ C'/D c (H S) Cfls -=(}/S) ((), /)5;!) ;: (a,7ff!.bJ. ,(3.ft 'if'fp,d5'tf) maleImf afl?l =- a,1J.3 rr:uhm! c.J _ (;).156-4- OJA3)'t,. (L.) It ~ 0.12.3 t k ~S") 0//5'5' ( '!,S'S' ~ a, r~3 - ~ ~ c:.. )o.1~F (J, 'IS's: o 21 S{;1 oI I C? l, q3.5 S' (),?..O ./,. .I r:;" 0, ?hS·· o...~ -; G'
=t= ~::::: CJ c;;;::.~, S"t1 mo(e mY -, .z..~ Cl.3;Z em· C~~:: 0, /";.3 mole m3 t (1Jtf~) =-0 j ~j? /5 {!oJJs;'an-t- 1VAz-':: .-948 d.5 d'e>" .sL C~} - 0de; dz- - CfJI ::: 0 ~ j- c~ @! c ;:. CJ c;-::: :A, 5't,;f- M;e:=. C;l.- -~ @z- ::.3.'2. )(. lIP I'yt G=-7t~, f? I Gg -= - 7~ 2. f'r; (m) r- .<..s~1- cJ c; ~ _7"-;.,~ de: I Nfl .:::: - 0/18 dCit .=- t:h6 (7'~,?) d,i!r r -1/ 21 I r .>Ci/'rJe tt,e. -=- / )( /() m 7.5 -II :L -9 A#e..-- (7~:;.,,[?X/;(/b ltL):.1,'3x/O m:.JH 5 ~,s 2£,2..3 -L- d [t" /.111 ] =~ fYl V' cJ'r II'" !VA- =- DI1B defT. dr" PA§. Ii [ r dJA..J ,-::.fyl V' d.~" d r r-- dCfl - In r:.t C---~+ I d. r 011.6 ;L @ r::: RJ J deB ::::. 0 dr 0.::: a1. & t C, 0l1g 2 2 C :: - !!!- /(,- I DIf-f3 ?-.. r dCft: ;::: m .t-:z._ m &:J. d. Y' Off$' ~ 0118 2- d Cfj. ;:; 111_ rdr -!1l. R?-d'r' 2~6 ~DFtB 7 Cir == !1L r'"-ttL r<.f~ r t- C.2. 1-7)1113 '). CJtf; @ y=-- R..1...) Cit-=- ~s =- ~ If C~ -= ells r J!L fJ,1...~ ~-!:11 R.f ;L0AS +46 eft ::. CIt.s r..aL Cr~~) - in f(;~C!C..) 4~8 20R8 /(2 ells = fJ, ::: ttJa.fm _/ -'I ~') Yflole If 3- tAd'.-<, - O,71al-"" '!!!-. 1IY13 I W/tJ/e = /, 212.. ~i6~ /IJ1b lekrn3 111-=- 0;2...~mAle.> / 0 -It /. mJ, hY'::: (0, 74 )<./1) ~ emil, S' T' -5' 1. Vll6 .::. ?~, I x Jt) em ~
r 0,)..5' (), '3 0;4- Of S- O, fp 0,15 2'.24 CA(~) -7 r,fP-x./O fj, 87 )( I(F~ /, otiS" 'i- 10_~ I, 0 (Pb ~ 10 1,/"37 >< I~-{, 1,:J.f~ ;<10-' J¥.: J = :2. 11~L N~ =:; 2..11r<L t-f)N3did) )If re r dr r<. froWi "-(,,;;3 Dftt3:: a, IK liscv»Ys Rs ~ o,~!> t YY' 1<.'2.;;: 0, 7~ c.m, L """ 15"em· A::: ~ lufora/Jehlde B.::free om/l1e (! ('-= rc f2ea~ hOj/); Af ).134 Pr~dtl.ct Cit -::.0 o () f, Nit .; ~ ::::..% .Ii-('('2..Nhf)::; 0 I r!l.~ 15 C()i1sf;:,nr df' ) r ci,Ivf-e CtJI?C, d+ A- o"Jsi1w jllk5/d~ J1tJ btilk c.fJ I') f,.././;u ,fl& n Nffr ..:' - tJltta dSt dr" " ~ !~ 10 4f7'r WAr t.r -::: -1rr~ d~ ~ ~ r~ ~c. ~ ftS 11/ [.L - L ] ~ 411/:k.!) C"S /'fA P.. r~· j}(I'r::; -4 jr'[1,8 Cfi s [ ;f{ - 'Ire]
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,~. __~~"_ " . F"~ PROBLEM 27.1 EXCEL SPRFADSHEETPART (A) A- n-octane L- 100.00 an T- 15.0 "C e- 1.00 DAB- 0.OS73 arr/B«- d- 2.00 an e2DAB - 0.0S73 arr/-. w- l00.00.an PA·- 1039 Pa MA- 114.00 kgIkgmoe PT- 101300 Pa PA.I! - 0.703 r/an' cAI - 4.340B-07 grmle{cm' mAl- 14.06 kg Tlme,tCaec:) 3600.0 7200.0 18000.0 36000.0 S4OOO.0 72000.0 Tillie, i (Ir) 1.0 2.0 5.0 10.0 15.0 20.0 NA(gmote,tm2-sec) 1.063&14 3.222E-12 7.735B-ll 1.838B-I0 2.2S2&10 2.402&1Q NAca.mz-h) 4.363B-05 1322&02 3.175B-Ol 7.s45B-OI 9.241B-Ol 9.856B-Ol ; ! Series Term II = 1 .8.158B-Ol -6.656B-Ol .3.614B-Ol ·1306B-0l -4.720&02 ·1.706B-02 2 4.430B-Ol 1.962B-Ol 1.706B-02 2.910&04 4.964B-06 8.467B-08 ! 3 ·1.601B-Ol .2.563&02 .1.OS2B-04 .1.106B-08 ·1.163B-12 ·1.223B-16 4 3.851&02 1.483B-03 8.467B-08 7.169B-15 6.070&22 5.140B-29 , 5 -6.165B-03 ·3.800B-05 .8.904B-12 ·7.928B-23 .7.060B-34 -6.286&45 I 6 6.569B-04 4315B-07 1.223B-16 1.496&32 1.829B-48 2.237£.64 I 7 -4.658B-OS ·2.170B-09 .2.194B-22 -4.813E-44 ·I.1lS6B-65 .2.316&87 8 2.199B-06 4.835B-12 5.140B-29 2.642&51 13S8B-85 6.980B-114 I 9 .6.908E-os -4.772£.15 .1.573£.36 ·2A74B-72 ·3.891B-I08 -6,12OB-144 • 10 1.444B-09 2.086&18 6.286&45 3.951£.89 2.484B-133 1.561B-177 I 11 ·2.010B-ll -4.040B-22 .3.281B-54 ·1.077B-I07 ·3.533B-161 ·1.159B-214 12 1.862&13 3.466&26 2.237£.64 5.004B-128 1.119B-191 2.504B-255 i 13 ·1.148&15 .1311B-3O .1.992£.75 ·3.967B-lSO ·7.903B-22S ·1.574B-299 i 14 4.109B-18 2.218B-35 2.316&81 5366&114 1.243B-260 o.oOOB..oo . I 15 ·1.286&20 ·1.654B-40 ·3.518B-l00 ·1.238B-199 -4.356B.299 o.oOOB-tOO 16 2.338&23 5.464£.46 6.98OB-114 4.812£.227 O.OOOB-tOO O.OOOB-tOO t 11 ·2.828B-26 ·1.991B-52 .1.808B-128 ·3.211B-256 O.OOOB-tOO O.OOOB..oo 18 2.277B-29 5.184B-58 6.12OB-144 3.745B-281 O.OOOB-tOO o.oOOB-tOO 19 ·1220&32 ·1.489£.64 .2.705B-160 O.OOOB-tOO 0.000B-t00 O.OOOB..oo t Series Term II = 20 ~52&36 1.894B-11 1.561B-177 O.OOOB..oo O.OOOB-tOO • 0.000&+00] 90000.0 108000.0 126000.0 144000.0 162000.0 . 180000.0 198000.0 216000.0 ! 25.0 30.0 35.0 40.0 45.0 SO.O 55.0 60.0· 2.456&10 2.415B-I0 2.482&10 2.485B-I0 2.486&10 2.486£.10 2.486&10 2.486&10 1.008B+OO 1.016B..oo 1.019B+OO 1.020B..oo l.020B-tOO 1.020B-tOO I.020B-tOO 1.020B-tOO . -6.165B-03 -2.228B-03 ·8.o52B-04 -2.910E-04 -I.052B-04 -3.800B-OS ·1.373B-OS -4.964B-06 1.444B-09 2.464B-11 4.203B-13 7.169B-15 1.223B-16 2.086&18 3.559B-2O 6.070B-22· .1.286&20 .1352B-24 ·1.422£.28 .1.496&32 .1.573&36 ·1.654B-40 .1.739E-44 -1.s29B-48 ~ 4.352£.36 3.685B-43 3.12OB-SO 2.642&51 2.237£.64 1.894B-11 1.604B-18 1358B4s ; .5.597B-56 -4.984B-67 -4.438B-78 ·3.951B-89 .3.518B-l00 ·3.133B-l11 -2.190&122 -2.484B-I33: 2.736&80 3.346&96 4.092&112 5.004B-128 6.120&144 7.484B-160 9.153B-176 1.119&191 .5.D82&109 .1.115&130 .2.446&152 -5.366&174 .1.177B-195 .2.583B-217 ·5.666&239 -1.243B-260 3.588&142 1.844&170 9.418B-199 4.812&227 2.504B-255 1.287B-283 O.OOOB-tOO o.oOOE+oo .9.626£.180 -1.514B-215 .2.381&251 .3.745B-281 O.OOOB-tOO O'(lOOEtoo O.OOOB-tOO O.oiJoEt.oo 9.815B-222 6.170&266 O.OOOB-tOO O.OOOB..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOB..oo .3.804B-268 O.OOOB-tOO O.OOOB..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO 0.000B..00 O.OOOB..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOE+oo O.OOOE+oo O.OOOEtOO 0.000B-t00 . O.OOOB-tOO O.OOOB..oo O.OOOB-tOO O.OOOB-tOO 0.000B-t00 O.OOOB-tOO 0.000B-t00 O.OOOB-i.oo O.OOOB..oo O.OOOB..oo O.OOOB+OO O.OOOB..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOE+oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOB..oo O.OOOB-tOO O.DOOB-tOO O.OOOE+oo 0.000'£..00 O.OOOB-tOO O.OOOB..oo O.OOOB..oo O.OOOE..oo O.OOOB..oo O.OOOE..oo O.OOOB-tOO 0.000B-t00 . O.OOOE..oo O.OOOE..oo O.OOOE+OO O.OOOE..oo O.OOOB-tOO O.OOOE..oo O.OOOEtoo O.OOOEtoo O.OOOE..oo O.OOOB-tOO O.OOOB+OO O.OOOB-tOO O.OOOE..oo O•.OOOB-tOO O.OOOB-tOO 0.000&+00 O.OOOE..oo O.OOOE..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOE..oo O.OOOB-tOO - O.OOOB-tOO I • O.OOOB-tOO O.OOOE..oo O.OOOE+OO O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO 0.000B-t00 , b·)·/f;~ Cln1 ~wn-:r-·;ln-::;cf.o,e e~~-..Jft'~· m;;:~-IS .1tf'f1!J'/C'd 61117.f<lr~;ftlr f {,I I. oJ '-' lid /Itt>< .;;1 c:::. L (tJl hI r~.$tp.",,,,,t- ,1;: Orne.' <o)t1 Zt;r:l[) f::; (;l.. . -t r0i18L'R t t (-I if #11 ~B 1t:.)7 m/tlt) =: W7A;/i't == fo #tlc.df;:: ~; :IiL L-Y- -f :J. ~5 t. f/::'/ n:l'f(:l.V -~ . J ~?£
, i;t!1t? rejtllred !c;r- fl?/j (f) "':/YJrt; ttJt?5 de fenr?lflc,1 t4$/11Jj //1" f~' Ctw~jJl!litf'r {;pre'odsJec';; (p,,,,,; 13), 5iJt'tl/;.(I'?iI!/J Cl Illne t')e1~Jt"l/',f,)'C'.'tYj One! h117 ttJa$ ca/cu/Clfedr the 1~5;t)lv~r' ftl/}cl/£)tl il ol1fhe C:tJi'Nrft1kr 1- ~---.---.--.---~.-~' - PROBLEM 27.1 BXCEL SPREADSHEET PART B i, A= n-octane L= 100.00 em t,~ 511r5' !;;/tsT= 15.0°C £= 1.00 DAB = 0.0573 em 2 /sec d= 2.00 em £2 DAB = 0.0573 em 2 /sec W= 100.00 em (basis) i ( Calet4 (alk!/~$ 1!111C!t'e'd PA*= 1039 Pa MA= 114.00 kgIkgmole l/t:YH!)' ..5////. 3 n-oc';(1f)6' PT= 101300 Pa PA,Iiq = 0.703 g/crn eAa= 4.340B-07 gmoIe/em 3 rnAf= 14.06 kg It i'j' Id t{j;,f,1/v[ ·//;e. I, .• t= 4~963B+07 sec .l.)(}li:,."J/.1S u ;rock /af/,~/<) t= 574.5 day released rnA = 1.233B+02 gmole (basis) released rnA = 1.406B+Ol kg (basis) L _ n Tenn Summation % Change 1 -1.013B-Ol -1.013B-01 -_._-_.. - --,,- ---_._.-. 2 2.533B-02 -7.599B-02 33.33 19 -2.S07B-04 -S.347B-02 0.34 3 -1.126B-02 -S.725B-02 12.90 20 2.533B-04 -S.321B-02 0.30 4 6.333B-03 -S.092B-02 7.S3 21 -U9SB-04 -S.344B-02 0.28 5 -4.053B-03 -S.497B-02 4.77 22 2.093E-04 -S.323E-02 0.25 6 2.S14B-03 -S.21SE-02 3.43 23 -1.915E-04 -S.342B-02 0.23 7 -2.06SE-03 -S.422B-02 2.46 24 1.759B-04 -S.325B-02 0.21 S 1.5S3E-03 -S.264B-02 1.92 25 -1.62IB-04 -S.341B-02 0.19 9 -1.251B-03 -S.389E-02 1.49 26 1.499B-04 -S.326E-02 O.IS 10 1.013B-03 -S.28SB-02 1.22 27 -1.390B-04 -S.340B-02 0.17 11 -S.374E-04 -S.371E-02 1.00 2S 1.292E-04 -S.327B-02 0.16 12 7.036E-04 -S.30lE-02 0.S5 29 -1.205E-04 -S.339E-02 0.14 13 -S.995B-04 -S.36lE-02 0.72 30 1.126E-04 -S,328E-02 0.14 14 5.169E-04 -S.309E-02 0.62 31 -1.054E-04 -S.33SE-02 0.13 15 4.503E-04 -S.354B-02 0.54 32 9.S9SE-05 -S.329B-02 0.12 16 3.958E-04 -S.31SE-02 0.48 33 -9.304B-05 -S.338E-02 0.11 17 -3.506B-04 -S.350B-02 0.42 . I 34 S.76SE-05 -S.329B-02 0.11 IS 3.127B-04 -S.319E-02 0.3S , ,I 35 -S.27lE-OS -8.337B-02 0.10-----_._ .. ---._-----_. _..
/1 111/ lui l;;;/M / I r'/ ,'I ~ -'1 i. Due Iz> ,sfflCl/; {J;;t' r'U,s/c// 1(/ 1)( If) if ") ClrJd /tJnJ d,.s/Qn~/ /h/6' CL. .5C>ff/I:'- II? hY71 Ie' dl / /JIS fa n ~J1:. :::; n ir.e) t;- !,//f6 ~ dl:2. @ f:.:[) ) c14 :: CAd =() a~:J t~, Cit:; ~s (j) ~::CJ Cf'W ~ CA~ "" /) ~7,3 z.::. 6"cm::- c::? cPSJ11 S.,... t =: 72. h;p" ::: ~,,$"'/ '!< /0 .s o.o5m '2 i(/,/: ~-v",~1J.,5f:'/~fG- s ::: /,0'53 erfUp);. eyf{I,?'5"3) -; OJ '11,)" {Its -Cit ::: ;Z1- Y1 ~ (/.. Cf1t2....· ('lis -L,4 :2.1-tJ C .=- cJ, £ 15' m,j/e,j,yJo ~ ~-==---.: J) ;::bY' fir/I fe 6/)t(l1~dhJ c!dl1rJ;-i/dt)s.; ()nf?-,/;mef7•.<)lollt;? I tlll<;<Pticlr-5 J-~le./ v COr1tt!C')71f"'4 ,1;£)/; rfJrLl/;k hI" /;JeI'7.;f("7F1cf dI5StJ/I/'C"/ III (j}llfr:-r-s't1 ft1tC'lled .5cti//.$ jli/eh bj/ PROBLEM V.3 EXCEL SPREADSHEET A - benzene (m water solvent "B") T- 293.0 K M... • 78.00 kgll<gmole OM- 1.00&09 rrf~ w= c.... _ 24.0 gmoIe,b!' t - 2.592H+05 sec t- 7200 h C... & 0.675 gmole,b!' iI Term Summation %OJange 9.98&02 9.983&02 3 9.85&02 1.983E-Ol 49.67 5 9.59&02 2942&01 32.59 7 9.21&02 3.864E-Ol 23.84 9 8.72E-02 4.736E-Ol 18.42 11 8.15&02 5.551E-Ol 14.68 13 7.50&02 6.300E-Ol 11.90 15 6.79&02 6.979E-Ol 9.73 17 6.05&02 7.585E-01 7.98 19 5.30&02 8.115E-Ol 6.S4 21 4.56&02 8.571E-Ol 5.32 23 3.84&02 8.955E-Ol 4.29 2S 3.15&02 9.VOE-Ol 3.40 V 2.52E-02 9.522&01 265 29 1.95&02 9.717E-01 201 31 1.44&02 9.862&01 1.46 33 1.00&02 9.962&01 1.01 35 6.36E-03 1.0038+00 0.63 37 3.35E-03 1.006B+00 0.33 39 9.686-04 1.0078+00 0.10 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 -8.32&04 -212&03 -2.97E-03 c3.45E-03 -3.63E-03 -3.60E-03 -3.4OE-03 -3.09E-03 -272&03 .2.32&03 -1.93E-03 -1.55E-03 -1.21E-03 -9.186-04 -6.686-04 -4.636-04 -3.02&04 -1.786-04 -8.71E-05 -234E-05 1.86E-05 4.37E-05 5.64E-05 6.04E-OS 5.86E-OS 5.33E-OS 4.62&05 3.86E-05 3.11E-05 243E-OS 1.84E-05 1.006B+00 1.0048+00 1.0018+00 9.975E-01 9.939E-01 9-903E-01 9.869E-01 9.838E-01 9.811E-01 9.788E-Ol 9.768E-01 9.753E-01 9.741E-01 9.731E-01 9.72SE-01 9.72OE-Ol 9.717E-01 9.715E-01 9.714E-Ol 9.714E-01 9.714E-Ol 9.715E-Ol 9.715E-Ol 9.716E-Ol 9.717E-Ol 9.717E-01 9.718E-01 9.718E-Ol 9.718E-Ol 9.719E-Ol 9.719E-Ol 0.08 0.21 0.30 0.35 0.37 0.36 0.34 0.31 0.28 0.24 0.20 . 0.16 0.12 0.09 0.07 0.05 0.03 .0.02 0.01 0.00 0.00 0.00 0.01 0.01 O.ol 0.01 0.00 0.00 0.00 0.00 0.00 1.00m 0.05m 1.00m 0.0 gmo1e,bl'
2. "J, 4- ..0 - n~~OA-8-t4:4 ell-CAS _ 1- ~ .LSinlr11t'~'e /' -trLh LI-/ CRt)- 'its Y/-I tvhere "'X1:::'l::....:::: / m')... A Cit::: /. 00/llm3 fiJ i£':;:- XI Iff 1/,15 (JtJ'l'7l; a/I /he 5"/l/1 /5 c!tJnftlmlnaftJd bect1t1.5("J' tji (,b11116e dl In I i1) 1"I''I/.IIrA., /I /IScJtJer/VY}~ Ilt);1 ttJ.as u~r?J ~f1 aitdc/;edt'prn(JtI/t!Y' sJJt'~(Jd- ..5h~e tj l:.lfI'l~ thi/lle J'pt!'.5'st!d I Iert!7 f; /.Ie1'1 ct n 1-/) C'tl::: j,().h ttl:e::. XI" ./ 1+1 3 A~ benl;tf'ne (,n wa/-t'f"'.J'tJ/ven.f 8) r= ~93 1<' XI:::' ~ ;:: /1~tJft1 MA-" 1 !,~ al?fYI~/e' ~.:::; IdJM Oil"'" /x/~~rm"/$ w:: Id) frl 1,/"3 ,..~ Cill A o:f! C>. tJ gl1'l()Je/rYl c,q~::: ;2f,~ !m~/~/IYI'] "<1 n Tenn Summation % Olange ~1 1.16E+OO 1.160E+OO 3 -1.84E-Ol 9.763E-Ol j18.8 : 5 2.50E-02 1.001E+OO 2.5 7 -1.92E-03 9.994E-Ol 0.2 9 7.67E-05 9.995E-Ol 0.0 11 -1.53E-06 9.995E-Ol 0.0 13 1.50E-08 Q.995E-Ol 0.0 15 -7.19E;.11 9.995E-01 0.0 17 1.67E-13 9.995E-01 0.0 , 19 -1.86E-16 9.995E-01 0.0 21 1.00E-19 9.995E-01 0.0 23 -2.59E-23 9.995E-01 0.0 25 3.21E-27 9.995E-01 0.0-~'-'--- -----.....:..........--.---.-----~-- f(e~u/red t ;:::. 43s:5: da,!f..s ').41 n Tenn Summation % Olange : 1 1.17E-01 1.168E-01 3 6.79E-02 1.847E-01 36.7 5 3.18E-02 2.164E-01 14.7 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 1.65E-02 2.330E-O1 1.00E-02 2.430E-Ol 6.70E-03 2.497E-01 4.80E-03 2.545E-01 3.60E-03 2.581E-01 2.80E-03 2.609E-01 2.25E-03 2.631E-01 1.84E-03 1.53E-03 1.30E-03 1.llE-03 9.64E-04 8.43E-04 7.44E-04 6.62E-04 5.92E~ 5.33E-04 4.82E-04 4.38E~ 4.00E-04 3.67E-04 3.38E-04 3.12E-04 2.650E-01 2.665E-01 2.678E-01 2.689E-01 2.699B-01 2.707E-01 2.715E-01 2.721E-01 2.727E-01 2.733E-01 2.737E-01 2.742E-01 2.746E-Ol 2.749B-01 2.753E-01 2~756E-01 7 Itt t:::. 6.to'I. /0 s -:.. ~/OVe..ar'$) mI'l .::;:..5I~ ,!i.ttlfrJ ,:: 7.1 4.1 2.7 1.9 1.4 : 1.1 0.9 0.7 0.6 0.5 0.4 : 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1
I:/. I g CAl>':= I K /0 tihJl11S/ CWJ CIfG ::: :<. X JO~/ Cl.f~ms/CmJ t: .:. / At" :=. 36c:Jtl 6 -1 Z~ {)...Jr1JeY'c:JI'')$: j.l<ltJ em Dl9-d =5x /tJ- 13 cm% ;2l7 cp == 111.4:11 Vt;'(£l ("-1 Y' f Ih /.7J 17 fJ-L f5f tCS) 3~()tJ tPI13 7fl:L 10,; 7,,64 1~(t1 dJ eY'fctP) 2.551 0,99904 I /.? 0, <Ii91 /1 " 0,91'3 J,4- 0,95),3 I,l 0/1103 I 5' ~ 0~~J /,0 0.1+:<'1 ,0 ;u ~~O 0, 9(,~:<' 0. !:.fp;;., t(hr' / 2- 3 4 5 t, o. 911r = erf ((f )2 q'15i I ,i ::' cP:= ;2,R 7-.tDAfJ1; Z: = 5.''' JSx IO-13~2-#~) :::: 3.9[P0 )(, /~-t;it;) Z: UYI t r lCtnJ Z iJ.Y7f:.f (h1tcrOf1s) 36tJ(J :)./34,7/-;1 ~tJ1~ 7200 -1 3, ~~() xI~ 3;-;6 lC!;i~/) f'//~>t I~: 4;IJ~ 11j11JIJ 4.75)( ItJ 4,7,j I~OtJ(} 5:3/ 'J./o-1- ~11 -1 s,r.2 ")~(p~~ 5:g~ y. J()
6) eNS;:::' ~,O x /O:W a/oms Icm3 Clio':: I. x IC/~ aftll1'ls Iem] C,q.;::' / x 10 IgQhJlJ1slcm~ if: := :z 'I- 1(;-"'clYJ erf(cP)~ O,9?5" J cp:::';(rO " -f 2,():. C .:::. :t."j. ItJ tfY1 .l~D~1; ;z.i~/tf IrC,;-{t S- a ::.70, 71J,) 1:-= 5tJ()/J.s f -4 Omtkln PIn wal'er @ Jx/ocm !!!fl ~ L~ v;i~ Si!- c- ~ If~ =:...1.: 4 Fi~~~--:":i"""k-;xt-65-'""-!J~) >< :2 ~ (0 ~m qr oS - - )(. (Q,)( l()i~(JIIfJJ..s) tJm3 =5.~4:lx. If) '~fplYIslcfl)3 ii!rt =- rflIIIv !!!.!J. -I- m5 ; V V _ S;61~ x10J9af-tJfns(.3tJ.17fJ- CI1)3 irfomJ ---I--=- - ... (~k1:< l( to ;X3t1,'17) +(f),xitlt;ll.07) - /'~4 x 10-3
::27,/() 011'/14,)/113 hm cJl7e .;a~e t ;:::./Ohr = J't Of}{}s , j , /)J/rt>'= o. UJrrs os a0I '1:.(' ~ (.;'hlcKYie~s):r 2. (0.5'mICf'df1) =1n1lcr()y1 =- I ~ ItJ"' 4 CI'J? VAS::::' /,5";< /~-13Cm2~ ... / g , X-::: 'Dl1e! ~ (I,5')f./()crrfI;.XJiP,}o.!S):::0,51 1, (I )(: IO-4cm)~ as t ~/fXl.l Cft -''')0- t',4$ q'1d mA~PlAf fnlrf -:;:::. C,4.$ y7lf(S-:: 0.110 "'3 Cd, ft; I-q! tim"tthl aJ fraf1.5 it:rrc!) Info 3el bead h1 ..: IJ n r;. a, 5" i (n: 4); OIP..1} 'Ita,;):' 0,2.1 Y(VI :r') :::. (}/~:4 W,4s -tUff ::::. 0. 21 .::: /J,()/-tVA WftS-i'Ilfio 0.01 -tJ tJllt -==- '"r;, x. /P- 3 ) 0, 7~ % :J-J,II --CAs'::: tlt / fYJeJ/e/m 3 Cit;::: K4ts;:' /5/;{eJ, I) ~ /bmtJ/ e /m 3 CAD ~O (a~~~~d) fZ :::: 0, 'J.,5'em -/: mA (1;) :::. J NACt)d-l: o 6 Q/) I ( - ~6n~rr7:/{(it) n· 1 2 3 4 5 =:: mAf -.z.l n;. I-e 11' n=-I . ' I: I. .fJ- .1- -Qt/r Z- (/1 -, n;t.J " /_ m~l.£:);:. f. ~ ~ eDItBn27t~k2. rtJlI f 11':t /.., n ~ .,. n:::;1 .YUl'Ylmaflcn ca/ctlkhons are i I vel? in ctJl"rlptltr!3 r spY'eadshee t:. Term Sununation % Change 1.03E·OI 1.031E-Ol 2.80E-05 1.678E+OO .93.9 ' l.44E-lO 1.678E+OO 0.0 9.88E-18 1.781E+OO 5.8 i 8.I8E.;27,oI7B':: -:L)( !{[{,em%- '-.~~-~ 1.?81E+OO ___Q~O1 Cf~ - ~ _ 1!:::..!2;::: £1.20 t~-Cfh?- /5 n::.. () a ' y'}1 :;:: 0 ...:../:j!}_t - (;, ;).,:2. , 1<2 - a 2;), r<..:t l.to< ' )~{ ..... ~__,_. J ::: 0,:2,2, (o•.!t ,;;,(! fI'1 ;;;. b 9(}/Js Q ----;.-(i----T~- ',4e ~. >(to (:»11S - - t -:: 7J.O()s :; d.....Ohr /- m(? (t) == o,{){':5 mflf m;4 ,;:: (), 10:3 t~!l2l -CA :;:::;. is'JS It'il/emil_=--~~7!":;~.~=_~_,!:,:,!":::'=::::--=:,:,".....
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Welty solutions-manual-1

  • 1.
    Solutions Manual To Accompany Fundamentalsof Momentum, Heat, and Mass Transfer, 4e By: James R. Welty Charles E. Wicks Robert E. Wilson Gregory Rorrer
  • 2.
    C.l1APTf:.R , 1.1 n= L/ >( 1020 /i,,;, V::''''; J< ~ R-r = /.32 x 10'" il1/5 A= r(163 ;.,,/- ,:. NA = -'- n OA = 1.04 x IO lg /s 4 P ~p II + dP u1.2 'V = ji X d<j J cv'PCQJb) =f'cv;:[k(cos IsiYlI +2)x + ~('51Yl ICos I)yJ .". 7PCQ)b):::;2,",,-2 [t (~f-2)X +i-(51~ 2 ) 9] 1.3 'VT(.K;j) =To(£.f [-k,Ca5 ~ ccsL, ~) ~ -rt(Sit1 ~ 51nh ~)g J IT(a.).) ::::To £k,[-b.(c.o~1 CO'!>hl)x +t ('5 in ~~h I ) Y] V7(o.) 6)= -r;,e.""~ [l~I~~+ e.-') 5{ -+- (~i." / )G.-l-') 9]2h =Toe-~rC&>-:.1 ( 1+ e.-"2.)'; 2.. L~ -to ~r1 ( I - i:,2.);1~ ::Tc, (O.CJ~:l~; + .1?23 ~) 1.>.1 /(Jt",1j) of 'PROB~~/Yf /-10,,"04t!/l1c.ouS. p~;;J O~ PEo13I..~/IIf 13£ )lO/f!OtS UV't! ocrs/ 12 -:E. ::: [ lof 'S a 'l -=' v z f~ J 1.:5 IS 1.2 WILL IF O~ IF ,)IE: Co/VVcte.S/ON rr'1C70R/ je I IS USe.D, ~ ~ [ csk35 j. I.S ~LOl.J PROP~RT/g s: SrR~S5 / PRE.S5UR.~ ($~ADIE./v~ II~LocrrY. Pi IJID 'PROP£.Rrlz. s : /z./I1?:£RA7U..e£ / D:E,A..)SIT~ PR£S.5 U. REI =':>Pfl:.CII=IC J.IEA0 SPEED of Sou/1/D. I. {, 9 '" ('" I A l" "-e. r:2 ~ r x ex + er ~ e.~ = COS e~.x + sin g e.~ ~ ;:( ~!," e); + I~ IS! e.~ = -sin e ex + GOes. e ~j ..• Q. E. D. A - ~e d e.s e'" e'"__ =-cos <2.;r - ~''( <2.~ de • • • .... :::: - ([.r Q.E. D.
  • 3.
    1.8 {L= ~~ + ~ ~aX" ax or ax ae ~=~a+~.a.- oy ay dt' (39 de r2= )(:1+Lj:1 ) 9= 1:a.n-1-¥ dr - )( II e eax - (x2 +yt)'2 =r' C:S =cos ~ =- y = - ("'51118:- sine a~ )(2 + y~ ("2 '(' dr=sinG .afr= case ~ I ay t' -sineL --r- ae + case L r" ;;8 1.9 'V = ~ a.x + L i. + a- Q.;: ;)x d~!i 02 =(cos8?r - Si~e~) ax +(5ine.L of- CO~e ~ ' e;;, r- c}9) ~ + ~ Qc;)2 =(ex case +- ~~ Sirl e)~ + y!:- (- e.x Si118 + cZ~ case) 2e + er..a..ae "". V= a.,.~ J .... .a... A ;; dr +- f c2.e (}E:1 + er a2 . 1.10 MASS 01=' SOLID =If Vs II /I FLUID == It If x=p~ Vs =>- Vf =/-x r?s f'sVs +,4 V; Vs -X P 2 = fJ/i. 1'><' +~ ( I-X) /.1/ ¢ =3 )(21.J + 1/gJ. a) 7<1 = (6X'g)x r (3x 2 t- 8!fJ; 'V r/; (3) S) =Clo X f {,? g .... " . e ....~s = cos e (2..)( + 5111 CZ!j ••• 1 ¢ • ~s 15 IN THz.. - 60 0 DIRcECTIO/!/. '1¢"~ =(!biY'q)e.A' -r(3X 2 +lj'JeJ •[cos e cZx + sin.e a:~l fiT THE PO/NT (3.1 5).- V ~ " a.s =(90 4 f 6"7 ~ ) • (cas -(,O ~ + sin-60~) = 1-15 - 5'2.02 = -/3.02 1.12 FOR A PERF2CT CSAS/ P:;O KT M FRo/Yl '?ROB. J./~ fY -= I'm ( I - X) I - "om )( A .... --p -::: fJ", (/- X) /- & >( p~ RI"M
  • 4.
    1.13 1p:= A,.sinB (I - -Fi ) a) V'1p:: d 'I' ~ + ~ ~ ~9 ()r r r ae :. -vP =AOSil1e(1 -~) ar~ e WHIC.H REQUIRES -n-tAT *-1V7p/ = ?e Ivlf'/ = 0 ~lvVI =0: - 511'12.e (I-t-~) +C05~(I-~:) = 0 (I) ~ IlIP! =0 : "!>lrleCOSe[C1 +~ f -(1- ~:YJ::o (2) FRo;n (2) 5i"e case . L/a"4 =0 r':4 FoR. a;l 0" r'"0;' sin e cos e=0 . e - 7r•• - 0" _ 2 (3") IAlTO (I) G)=O: 1- a~ :. 0 r2. .. a=f" IhI PasS/SL ~ , :. C/.)AJDIT/ot1JS .4Rs. . e =0; i=a... (3) IS 3 ~ ~ = -jfJv;.'-[~~r] ~ ffE? A- _.J. LJ v: 2.. r2;(l[ Jide fL.2 - 2 r oC L- L 3 if - -~. - ...------------- ,-,15 lAKE R=- i AnA. Wrm s:'&, : 1.01 ?= '3001 (1.01):' 3CCD:; 217 AiM L(o AT Co~~ntNTlEMP,) .?""'/ fOe IO~ ~~$ l,v 9 / A lO'r~EA$E IN PI~ ~o t.l7 DEJJSrry:: 1 m W"'~ m 1'5 MOL&:::u...A12. Wi;(ah'T. ;.tr 2.~Q:;()'-, wt ~ W1~ ~ . ~ (lAwf> n ,:: n ?2SO,,~1 2~,,~ CS).L j>s..l- =2.5'·10" ~(e~ ln 3 ~lc;H AL.TrT'UDc Utrt~ IVf~ G Is CVr~~. n~ L~'(O·~
  • 5.
    CHAPTER 2 2./ V'P=PSj dP.... ,.. d~ e~ =-pc:, e.':j ~t...clP = -p<] C' cl':l ~~ = (JSn @ STANDARD CONOlTIONS f' = 1:>/RT FROM ~.15 f1.IR=O.0"7651 I~~ FROM ~. 15 -Po..~ =211h.2 ~ fr2 h- (21/ 6.2 1J.F/f/.2.)(32.1'1i.f 10.... rt/'5:2/bf) - (0=((,51 Ihn1/A-~';('32.114 fr/s':J.) = 2 T/6~9 A: 2.2 FOR A PER FEeT q AS) '"'P=pRT f3=;;(-¥)T ='p'RT =="P 2.3 ~=-dV d'P P V =7 V L"P '. - A ___ 3000?S1 _ l V - f3 - 30"., oc)o-psi - 100 .: 90 VOLUME CHANGE = '0/0 2.l.f MERCURI{ A • If R='Po. tP"" 5(:2"); -PI ='"P.z "P2. = ~ t-PK 5 ( s") ; "?.s ="'P<{ P'i = 'PA +Pw9 (~~)i 'P,", :: '?s Po. -rPM ~(l~")=~+/tI3(2",)+~9(S:) Bl :'?a, -rpw g~~, '12'/- 2" -: tS'·sj :.'"PA =--Po. T 5. ~ 17:5 == s:~ I?S~ 2.5'" 'VP::: peS-a) I.e.."PR e:sSURE G'RADIENT IS IN THE DI'KEcT/ON OF (9 - a); I :5o'aARs ARE ..l- ~ - a.). TH E BALLOO"-l CST'R IN6 WILL ,.. ASSUME THE (~-OJ g t:>1'REGTlON. .'. 'B,AUoO"-l WILL -0. MOVE Fo~WA'K!) 2.6 EQUATING: -p 13EFO~E ANt) D~N6t ACc.:t= Lt:RI"O~ i -p =P5~ 0 :=. P( <j ;-0.) 'jQ, l:ica. == ~ L1 < ~'3To. -.Jo 0 :. MANOM£TC~ LEVEL 60E5 1:::>c)(.4J N. 2.1 MAt£; A~~ ~3A Of2TI-4!;,~JJ. A Is IN 1n.2; 3J~ ~ 04.7-3?K~ g~h/(# h,. 144 .11.7 I tf4.7A ~~ ./'2.2. -= 2.2 ':: 2'.£c; 1ft.
  • 6.
    2.6 A 8 Hg I q-= ~ -JOlt.~10 I Pc ~~+Yu20a~ 'PD '" /" -Sllff~ I B-~ "J~d(1)-5511;{j-IOgOt"0 Pp= 'iIM I JOII. :O,6JH2-D ~ qf({!5~~~/ ~-~ =: ~(I)- !':>'G24 =%.8fsP 2.9 Air ~.,gt d,j 5'H,.0'"Pa{d4~ +a~~9HJ ~-~::(1-!i1-~)~-(2):02A(2'Z 2- ~- Ps=Z44,7pgf :: 1.70psI 5 ST~JJG troM 16wr Aj ~ ='B..-dl ~j'H2.0 5ru2rtA-q ~ ~ B./ ~ '" 'Pe-~,+dlfd3~~.Jd2Jf~ fuwtr~, ~-?g "'d2iJf~-(d2"d3)Off1p ExPOt;$S"!M4 d IN .r~ .~-~ = SZ.7p'; =0.227 ~J 2JI F -= '? A - '?o..~A ==,oj11 -(fR2 e.G. PH:JO = 1000 I<~/~l) h= 2W1) l<=.3~ F :: S~46 ~~/s~ =- 5"5"'-1 b N - I1c.p. -= vt -t- ~ 1r'R2 ·2.tM C"fr'Rq FOR A Ct~LE J Tlob:= - "'I • v1 - 2M +1rR.~ " "le.. p. - qrr'R2 (~~) = 2.0tl ~
  • 7.
    2./2 ASSlJh1ING, ArlY1()SPHERICAIR. TO 13£HAV'£ I DEALL ~ &- -~Q --lldg - r.) - "RT LET T = a +b~ tJlTH ~/VGN INFORMI1TION, T.: S30 - 2l/ fJ 7; dE. - -g dlj -p - ~5......:30~--2-J.!tl.ly/~ fOP .dE - <3 h (' -2lJd (':J/h) 1; -p - 2i{R 10 5"30- 2~(Y/h) 1n. E =- :ili- /'1 5"'0, ? 2.4R $""30 -p = J O. " "PSI·a. "Po ":: "30.11". H~ .'. h. = q I g 2 ft. 2.13 :r: -. --:'-- --_.-. - 1'lr ='Pa To I'H;1.(J Cj ('-/") +-f'~ 9 (10") PJ: =1':zz: ~ -~ = -L) a (~,'QrL). 'J (10") rH"0 ":J r H9 :: '1.63 psi :. PoIN! A HAS THE HI9HER -P1?~:S5 UR.!. . 6 AIR - ---- -- - D.} ~i=~ = 0 ON TANK Ptrd2 ._ "Pa.tltl. lTd~ _ 2!JO =0 (I) -1l- T @ W'ATER L£VEL INSIDE TANK, "P = P ai", -to PH:1,O ,](h-,:{) (2.) FRoM (t) AND (2)... h- y = 1.27S" Ft. (3) ASSUM£ ISOTHE.R.MAL COM- PRESSION <:)1= AIR IN TH£ TAN- rg~ VrANk =-p[ ~/,qJ P = "3 -p~+no. eo:3 -<j 5 UBST. of ClI) I N (I) G /VcS y= CJ.12f+.- •.. h = I. '3 ~4 q.. b) AIR "':-". -- .-,", .. t i1 !='y = 0 p =P....t- + 2.S'O+-f: 7rd2./J{ @ WATER LEVEL INSIOE TAN}(~ P = 'Pa.fnt .,.. ~H.:20 9 (3-g) F = I q6 (3 -'1) -25"0
  • 8.
    "I>y ANALYSIS SIMILARTO 0..) ~ OBTAI N (3-,)) = 2.? FI. .e o F: Iq6 (:2.1) -250 == 293.6 /bf 2.JS AS THE TANK CONTINU£S TO BE ?U5HED TO qREAT£R DE'P~ THE VOLUME OCcUPIED 'BY THE AIR IJEcR£AS£S AND 77IE 750UYANT FORCE THUS DE- CREASES. 'BOUYANT FORcE =2Solbl DISPLAcED VOLI.JM£ O~ H2 0 = 250 = 1. 01 /f;3 ~o9 !iSSUMINej AIR To -SEHAtI£ IDEALL Sol AND ISOTHERMAL COM?RESS/oN/ ~+m A (3 P. ) In-P(4.01 (j.. f) .::z'C..-fnt f-(-J9 c)(1. 0/) Z:: '15: 'i'l' Ii-. TOP WILL. 8E ('IS":i?~ 4. 01 ff3) 7Tlg;:.) • eo T()P J S ~~ b fI. EELctU J6~ o THE HEI6HT O~ nlE WitTER co- LUMN FROM rHE DIF;::: ElEMENT IS h - Jll-g Q.) FOR A REcTAN6ULAR 6Ar&) d,4== ~'d~ clFw == [ ~ 9(h-4ry) -rPetIfCJ dA d F". -= L6P'S;9'/ilL! + ~ ] alA ~Mo =0 ~ <j(dF"w-d7=A) = 0 (<<{ lj lf9 (h -4t-Cj) - gb~JdA ::0 4 (" CtJ9 hIJ -1)(3 'I'f +;;9!I :L-16¥~JiJ :=0 h = IS: I Y ff: b) FOR A TR.IANc; ULAR GATE.~ dA: (LJrr. -Cj )d'j 2.11 £if(4~_tjl) [G!(h-4+y)-~#Jld~ =0 h = 15: YQ"1 If. STA8LE "posmoN (M =0) Tl??ED 'POsITIO~ eM) M ~ C. '1f''3 Ll){ o.os-d A a - 2 Sa y ,- }(J. ~a dx L,.os = fig L" C.e (0.045"" - /2.) M = -0.0 31 (. :zo~ rad)~J L r 2.11 Q;RESSUR~ 1~ 7 THE 130UYANT FORC£ CAN 13E OBTA'N~D "BY INl"E~RATION OVER ,HE CURVED SURI=AcE.I oR. By THE FOUOWINq "R£ASONIN~: ~F~=O 0LJ =I'IOIJ <3'71R2
  • 9.
    2.1'1 F':J = BOUYANTFORcE ON suB- MERGED LO<:i + Q, WHERE Q= 'w'l:lqHT O~ 420 N SHADED 'REGioN. '1IR~) Q = C"R:1. - T IfJ5 F~ = fJJ7r1?~ of" ('R2. - ~)1'9 =,.og~ (J +-4FJ . ~ ,0 [7!'+ I-if] =,f~ 7r (SI/'JCE F~ ='vJ) p~ =~ +J- = J. 06'1 ~ JI 17'1/:2,0 a.) FORCE 'R£'Q'D TO l/F=T BLOC.K FREE O~ BoTTOM; Z F~ = 0 = F -Flo -F.... = F - (ow 3 22. ?S'+-Pa..+...'P'~s'J - (3',. 3'x.S)A: J F= (31c 3')( 1'",,9 22.;s:.' +R+.o. + .5";.g)gc, 10 = 32/1971bf b) FORcE 'REQ'D TO MAINTAIN FREE Pes/noN: 2 F~ = 0 = ~ -(3'x 3' )(,S'),4 9 -r -(3Ix~')[o4 +'Po.nj , h::.S' F:: (3'x3'X-,S"')(A ~••,,) K3'1C 3'JR.+.... :: (ll.';)(-Pyy:;. 6 I~/R:S) +f9R"){2.J'&:.. 2 /~ F =J9'{LfO 16; 2.21 Tb' J- h == <i./5ft. AS'SllMmows : CD~~~ ~rtr"~ &u.- ®HzO Us&!- A~ ~LLT(!)p y 12:= # j liP dF". llpdA e 1- 01. ~ dA:%z:~ eSWledf} llf-.:5'1(h-kbso<+~~) dFlf ~dFa:>5e
  • 10.
    h fim"~ ~(h-~+~)sm~ Z7reSd C( = - (~-~t~ t 2(+aJDC) '2 ~ 'rJH~ Fa=0 ~~ e~0(+2Q Q-fQJz1) '3 SWI,"l.()( ~~~ '5(t" D( '" 'PIcL Q:)~"/'- rJfct 2 n-: 11-rJid" /-+ (1- V%t.)3~- + ----=--:.~ d 2 3DYct ~ E.>c.?At-JDHS<i IN S'tslZrfS5 1_ 2. (/[) .Ii ~ S£ -+ fc ItI;.)rL J 3 D~ L~ (t llf-nZI ~ d:34~ h ~ 0.28/0 rn. 2.22 .J"D 6% ~ =L)9 =tfge Tde. r 0 (A'P_d(A~) =(!,.q~cI~ z: )0 e~'w,e l,:9-,8 -A~ e ~ ::: /-,49 n ~~ tj~ = -,13 in (1- ~ if"): 300}oook{i-.O'fq :. J'P = ILl190 P$; DENSITY RATIO ..e= e.~ff= UW11/ ~ fJ=l.tJ~7~ 9 2.23 "BouVANC V FORCE = I'v=;~ =- 'F dF =:E. "PRoVID(:::.D VOLUME' dT T 'REMAINS C.ONSTANT BoUYANT FORCE VARIES INVERS£L-V WITH TEMP£RATVR£ OF THE /t1R. AT CONSTA-NT VOLUME. 2.2.4 5.~. =I. 0:25 @ If£" rn. ~= I.O:25"!2,gh.. = (I. 02~Y /000'3.. V9. 101m V /8£nf) >>is'' sa.J.... '/ ::: t. ~to X/O /, ~ = /760 kPa... '" ~ a. 2.25 "'- ' Fan ~ -,.----------..----- 0.30 m /J.P"J"20 6l1.k = 999 k19.B Wl (?2')""-.m~ $~ 10'1 ::. 2.4G Pa.. ~ 'D'J::~ Is~ ~TfUSRA;~~ AN)DlUe.t1R; VA~ tbwN~.
  • 11.
    Po lsT~~~. ~{sT~~~. )(ls~Dt~~ ~E.~10T~~~TU5 VA:Jr;e .. B,i?H~~:::1?""~l"q~)f~ 'UT2.(1 IZ ~~ ~-~ 2 Ylla3a- ~~6~ == 7O.fo7- 15.~ .. 55.1 pJ 10 T. AI THe. CENTER of THE EARTH} z:.:R Pc :: r;.+n T ffjo ~ NEGLECTINq ~+,." ~ =- P90 R :: ~ 6'1 ·/()10~ .9.107'" 2 ml ~ • 6330./0 3 ", = 352 x/o9 k::, m5~ 2.2'1 :-IT H,.,O 12' p= 2 ~k.!.'3~/1+.3 + MUO 10 ' p= 4 '5(u9~1ftl t "'B t=A -~~ =~'J 12 := 24 j 'Pa -Pa..,"", = 2l/'j -1-40, = 6L(j 'Po" -H..tM. = ,ag ~ PAS -Po..~ =I.l ~ 12 +tE J(f-12) H:z.O lit FoRC.E / UN IT LEI{6rH r: f= f=:: f(p - Pa..n..)a'A ~= C~ 9f df +f~j'2 t(! j(l-l2})dc 12- F'=Pw~( Iq2 kl)-t-~ ~ (s-OJi.'1 F::.2·~ ,/9; +l/'9'S'o = 18,790 Ibf
  • 12.
    =fJw9(~6 f20l{O) +-~j (2.q~3 -20L/O) = 2 'i~ '106 H-'/bf 2 == IS". 3S- ff: 2.30 FREE !BoDY ~~~ (FORM INCLUDED) FORCE=f'~H Am e ~ 2 :3 ~ESSURE FORCE =~<.H(t+~ ZFx- =0 I ,', F:z =~(3e !:L'J. 2 AREA =~(~ Ht~ 4r tJfr,=i( 0.1-1 +-5,'") ZF~:.o Fa =f'9c [2rH t~ - & - .E.c;:J 2 2. ;z.J F. =f'Sc. [2 rH - ~J2 . I , TO FIND L.OCATION at: F =Ptjc.H~ Z ::z I "'EED ,0 KNOW' C.4 PosrnoN AND THEN TAKE MOMENTs. ~7___ f'<3~"!fr~ A 2 ~t-C{5'_3~ Tf'<3.. r.." T, ~'~'I :2 r+9 2- ~ 2! M) ::I'Jc. ~"t S"o..rol. + !] rl A ~h.t T!j " "-~ 1Ir 1+ 7(J. r lJ Ij, -r J NoW ZM" =0, SO MAw -f'~.. ~(2 rt-tl~+f'Sc. (lrH - ~1~ f.2r) -fXJ4!:1-'1. - A J CANCEL to<Jc. :;z. A H'" =z,-l.H + 71:a.r3 - bT(,-3 - 11('3 .::. Z ,:;I. 6 A =f +:. +-Jf:r3 - £7Trl - 1.1...r:! rr "f tf1 "riO. 3 H" 'DISTANCE FROH BoTTOM == t +-A if =~ t- ('[~(-R-) +(~y r~l- ~1T"- 1]J q= *+r[~(R-) - 5,lH(JtY].
  • 13.
    CHAPTER L/ 1././ V=IO~ r7x l, AT (2,2)~ {j- =10 ex rJil~j A UNIT VEcTOR IN -304DIREcnON IS ~I e"'_Y3A I - 2' ex -2 ~~ COMPoNeNT IN e. DIRECTION = e· v- (Y3" 1 A ) !J - 2" eN -2 lZ:s .~/ofZx +I'I~) = 5"13 - 7 = 1. 66 fps. l/.2 {} = 10 ~x + 2 x .~'J 0.) ~ = ~ =:Y.. >( 1")( /0 /0 d'J =2>f 10 'J = }{2 .,. C j (2, I) .'. c =~ >(2 _ /0'] +6 =0 Yl )~2J (1,0) )( Q= IT ,.,,3 ::. ~ CONTROL r - - - I VOWME: i~---+-~-r!'L.. _ _ _ _ J 12 FOR C.v. SHOWN; f)c.s.f'(v.nJdA ... k fVdV =0 o V= 'i (I-fi) fp:... )5('.s/,Cv.MdA = )fA/,(v.r1)dA +~~A1P(V-·~)c:lA =f' [112o.ve.. A;l - )oRq(l- n) :2'rrrd~= 0 ~,.. q1r R:2. (f-.,"- -I) 1J2 o.lI'c.., = ~ .. =I 2 $ fps 11 (1.5"~ l/.'1 V;= .of,.,[J'--'-____;::w He.s. f'(v.n)dA::" ))Ai f' (1J·n )dA + »),40 f' (V-. n)cl A = - f)A' fJvdA + (( pvcos30acJA , JJA. = -~/J"Ah +~1.T~s30"A)o =0 ~. =,q, , it - ,/lie - .., .~ V; =A: ,,;;. = 1/6. /9 fps Ao ("D~"30• . Q =Avo = o. S'S-S' fI?,s
  • 14.
    =Al 'LJ +'TrDv-.!:..2. = V-(-n:~1 +1J' 0 L) 2L 2 • ' V V- = ITrO,,/q 'XV;) == V; "irDa r ~ I + "'D ~ 1 = 1.1-1 ~/s L(~~S-)4-G~tl + .••J 6) Q =12.1" cf~ a.) 1)"= Q = 12.1(, == 5.~~ fps A '7r(fft l{. -; ffe.s.,o(o-.n)dA + ~ 5f{~dV ~ 0 fL:$.,a(v.n~ = mout - w'irt = IQ.2 '2 (1Y-)= 0 ?lfl / ••• .2.M=o ~t M:" 70TAL MASS IN TANK IF-" 5:: SAL7 IN TANK AT ANY TIMe" If ,o(fJ'.n)dA =: /9.2(F) - 2(f. 92) ~s. M ~ffL pdll =!flc.v. 13 :. ~ T let. 2 5 - 3. iLl :: 0 dt M ",( • S -,q.:z.t)•• =~(l-e.J;iI M= Z33 I~ I='O"R t = '00 ""i"" S = 15'0 Ibrt .. 0..) F'OR -t: =:> oJO S =I 6 b. 6 Ib"" .. . b) (t.l (S::z __d;.,..s___ Jl; dt =Js 3. ~q - 19!.3 s, I tI t -t = -1:1 £.,.. 3.Zl/ - ~ 5:, 1 I ,Q.4 M '3.!q - IQ.2 5r;;;- , = -~3.S' k 0.39 :;; 6() mt'". /.S'I :. ~:: /;/) rniH.-4.....----- c) IF THE PLutD VOLUME IS CONSTANT; dV/ - dVIde I - cit 2 AI if. = A~ 'Vi 1.1,. : V; ~ = V; (~ r o.:l =A., ( -¥.r~ 11;.:: 2 ( ..;fr)2. = 127 fps 0.2, = 5'(6l/) =320 fpsl. 1/.9 STEADY I=LOW .r. Jfc.tCv.n)dA:.O oR (r d(p-.rft) =0 .pA=c.onsi. JJc.s ) d (evA) = cJA f EY-r.:!..E:::.'0 ~ V-A A "IF ,0 :. Q. £D.
  • 15.
    •~. d M+Jr d rn =0 ~ E 0di: nees :. '"to • • '1.1/ Vi ~ l~",-; v.=0 ~LIIP. I"' ·1 • "I-;( 'j fls.pCi/".n)dA -1" ;~av ~O o CONTROL VOLUME IS FIXED TO WAVE FRONT 4MOVES WITH VELOCITY v,.., TO THE R If$HT. -,.0. A~ T~ A (v-m -1I;.J =a :. 112 =Ym ( I -~) '/./2 v =f r-vdA = ifmo.x" SR21T'" rt- ,..lY7 dr '11 R~ 0 L' R'J LET ;z = % de = d YR ( ' I v-= 2~Jo ~(I-zf' de LET q = ,-& J d 7. =-d ~ ".= - 2 vmJ.0 ( 1- Yl J7Y? dYl l/.13 =!1.J.v:(,0 ma;x .·0 V =o. ilt'1I"mc.x ~I '4 [ p(v.¥)dA + ~ rrvpdv= 0 Cos, ~c.~ o 'STEAOy F~w K~(-o-.n)dA =-1'11; (6cO +WtHoRlc. lb.,. 13J+ 2. jl ]!;. .ydy=0 o 3d WlHORe = f 1.1,; (6d) -f>1I; (3d) titHOR 12- =-;:rll; (.3d) . ~ == 21'L b == -2"oL v, b =-v- ~t ) d... == 2 W,side = 2 ifnr., d~ THUs -2,aLv + 21'fobv d.!:J=0 Lv = fob -z.r(y) d~ a.) -u{'f) =!-AVERAGE' A CONSTANT L1.r = 14:vE b ••• "VAVE =L v b b) 1T(ej) = c. ':J + Cz <j2 TO DcTE"RHINE C; AND Col ) USE
  • 16.
    80UN DARY CONDITIONS: LJ"(h)= 0) V"~) = V,."o.x 0= C. b + C 2 b~ 11"mo.x = C, b .,. Cz b2. "2 1/ • C :. l/ V",&1L C... =-~ 11'wrCJ.X.. , ) ~ b b2. 11" ~ q V-*~" [t ~ (~t] . b slnce LV =C-Vd~ v~~::: -!:L.::...::v:.--_ _ q Lb[t" -(f)jd~ LET 1 = ~b ) 1).,.,"0.)( = --.:L::...::,1/-,--_ l/ b1'(t-yt'-JcJ~ V"..."'.... =.:2 Lv,,-"' 2 b 4.Ju,
  • 17.
    4.16~~r--- - -....:.--, tJ J ----t>- 2ern I J - I ,Scm , 2- I I L_~ - - 4crfl....J MAss~ ~:: MAaSnPw 0," tQ, 2JAzl12 ~?AiUJ "). 1~'16~ 1TQ6)2.1~~O-'~ ~ Uj = B.l5" w.~ ~ _____ J ~AsS~ lA ~ MmJtor,.,<lJr 2 ~ ~ ~;(I'Yo~f~-l~3"!j25 ~ V,3=5.15 ~ CV.-; --1 t r ----; t " .~ . f-.: t ::- - - - J O.8mrn. Zern USlN~ llwSEBVRlON (): ~ As W2t1T9Ilu~CM 4.10 ~ U".5 ~ +rsclm. ,,0 dt: c~ IT d';" .. tDJ .j. 5'Qu:.tlc: ~Cs. ~ =-j'A.V=-ywV Vs CDf +QL( -:. ('ltV ® QL : 0 V=G>'tI : 1.91 CM&- i; QL ~ 0." V: ~.'fw.:1.1 ~ A.ZZ ~MowQre Is ~ lr~~sltr ~.12 "''i.=jrd2..o{~(eo-<)dl- o V.e :: ~:,"" Q= '-'4Ii... I> (0 kr ~oh I l;1J,.=fV, =IZC~
  • 18.
    4.24 v 17 I @BaTVsc:nt (1f(G,~ ~~j'21l'L bV~t-r 4: Vec,er ~ v l-~ b ~~Is~ lTtJar=4lT~(~-Ctr; ~f~~4.'2!2 ~ n1.lA7r " f Ilfe2'1fLd"( o :: 5'!'iTL blf~ ~ 0°0 lf~: ~b. 4 b
  • 19.
    CHJPrE'R S' 5'.1 ffc.s.p(O.n)dA=0 5:pv,dx :: 2 [p~lfdHJ.:C~dX] #v, =3~ .: ~ ::' ; V, =26."1 fps 5:2 1?l( =fls.VXp(v.n)dA =f>A~2. -~A V;2 =I'A(1.0IV;)"vz -flAv,:1 Tx == -~ =",A V; (I.OZv;.-V,) =-~030S" ~XIO.UJ-A300~X6i8 ft) '32. H l./ IbM ~ lb~ Sa =50IOlbf 5'3 Xl=x = Sfc.s. ~p(v.n)dA ASSlJME VN IT L£ NG-rn f:(p, -~)dy - DRA~ =,Pf1(v;xfc:/x+2fv,·'dx'-f!r.'~ =f'~.~..t + 2V;2. -1/ V;=>J :. ~ "'l1..".:l ( ~,~ 2i I I SJ~CS FROM 5:t~ ~ =3 vI) o -=-(1",)(.,! .,~,)(8·OO ~) =179. gVal P,-'P-;a. =t"(J79.e #- ~f'@.o)~ = 189 p~f=J.31p£; =9.MJ<A:,. J8 ~~ ill r" ~ I.. 25"j'p$ F~ ®~ Q =Al~ = Az. V2 = 3ff% Va =~ = ZS fp.s I=~ = Kc.s:.V~ p(v.n)dA I=x =(pvA),V; cos (-.300) -(0vA),(-l/) =I'Q~ C~)+pQV;.= I·g'''f~ F"'j =(DvAkv;. Sin(-30 e ) =:-SI'Q.15 F~ =271 Ib( ~ i='j =-72.71bf IF BLADE MOVES TO 12~ AT rSf?:; RELATIVE' TO THE BLADE: V; = -40fps ) 1.& = 40 fps AT THE LEAVIN6 S£:CTJON: ... ...lJ = v;. r~l. t-4 blo.cle +V bo..cl~ =(34.~x -~)+40ex -, ... A = -(~.~ eX - ZOe~ (0 I = 77.'6' fps " .r - - - -'"1 ".5"~ I Cov. f - ~---0-J 5.5" Lx ~.,. fdm =0
  • 20.
    ~= /S7.t ~/s caltlTROLVOUJME MOVES AT V= 4.S- ~ e.x. MEASURE nUID VELOCmES RELATIVE: TO TANK ~9 = FoRCE' O~ FLUID BVTANK ~I='x = 2.. ((( v~M +(( VKdm dI: J))c.v. J)c.~. Bx ==-if(vx M)+(-m)(2. S"7J %) FLUID IN TANk #-lAS 0 VEL/JC.ITlI R~LATIVE TO <::OOROI NATES Bx= (O)dM -m:l.STI=(157.. }~) a:f :s X-{:2.57/~) =-404N -Bx .:: 1<>4N Z~~=~ ((( ~M +a- Vy drn ~~v. -';) - JJc.s. o 11"'1 OF r=WID l~ TAWf< = 0 B'j =-(rn )( -~OT)=(/57.1~r07~ = II(/N ~=-I/Il ~ ""':'CO r-----,-- i EM 3 :<DL ____ J@ Q= Atr= ,,£2 ,A,=O.2SOQ.:a.~ A~ :: 0. IS";po ~~JC =fb:,.yf'(i-·")J~~dV o &= Jo. A,v,:r. +-f':l~ ~~ =,oQ (Vi-V,J=I'Q (~ - ~) =,oQ1. (-k. -:k,) 19 =1-66> Ibf .: THE TENSION IN TIlE ROPE = ~ = 215 lbj: COs30- ~ zt=J(:: ffc.~. vx!'(v.n)dA 5.: P,A, - fi A2 + I='x ==-1A.2 ~~-;: A,1I,.l =;:; Q(Vi-1f.) ~(p. D12 -liD;)+K =1'~2(*~-k) Fx =--1f(P'D,2-P"~~)+~f'Q:a.(k-~ SINCE ATM05PHE'RfC PRessURE CANCELS..... ~ =p.~ -;: 50 posiC) P2 = P;2.~ = 5" p-s1S F - -171(so.lq~XI)-(5'·IL/I{)--L-l x - 7lC .:z3.O#fJ +;f(O.i)(J.94X 9 )(;23.0~-I) :: -5"630 + 392 :. F"x ~ - G238 U,f b FX ~ .[l::J <D ® Fa ::' 60 PSf''l :: ?~.'i psi~ D. =3" :: .:lS"' Q =i()(J ~oJ/mit1 =. iCJ2 R-~s P2, =1'1.7 psi~ O2 ::- t.sll ~ Fx =KG'S. VxpCvon)dA
  • 21.
    Jr ("'P.D.:z _n 0::1.)_r:" _ LJ LJ(i1.{L _J..~ LI 'r S ~ rx -iff' ~ OJ., Fx =f (?I.;r. 9-/11.7 ·2.25")lb f -,;p(1.9L{'Q ~l{ .qr) 'bt FA' =5'02 - 9f.1 =L,J()¥Ibf 5:9 • ~,--;-~~V; ZFx =JL.s.~f>(1/·nkIA +~~ o == P.AI - 'FiA~ ['.5~f'(-v.nJd4=f'~~lr'~SVltAjYi~ p.-~ =;O[V;l- ¥:l-~i1f;?] BY CONSERVATION OF MASS, (( fJ (v.,j)dA :::0 Jlc.s. 1'~'Vi -~(As~ flliVj) =0 ~ :: ~s lIS +~ 15-:: :!'1(iO/ps)t:~'{~ a) ~ =li+ps h) B.-P, =£If(Jtl - :7{1oa)..'.0;(<10)1 ~.I"W ~ -p. =lilT psf == ~76~, lOO ~ -"---::;~ ~ --"',---'~} ';'i:2"'~~JsA :3~ q F= k5.vccs6dm=(-z-oX-i.Jz -::-FaRcE ou F'LUfO)ALso ow PUl~ 20 5.12 (f) c.v. @ ;;---~ F[:o: ::eJl #////77///7/7177////////77//1/ FOR COORDINATES F"IXE"D TO THE CON· TROL VOLUME; ZFJ(&' fl'S~,«v.n)dA+~dV o ZF;c= Fx (( VA',£'(v.n)M =PK1f-}.f) Ga~e]2A)}c.,s. - P [ v--v;,]2. A Fx =fJA(v:Vc )~(C05"e-I) TI4'S IS THE FORCE ON THE C.v. AT THE' WHEELS. FoRCE ON VA NE DUE TO wATER J:LOV,- RK=pA (1T-1JC):t(j-~os~) POWER TRANSFeRRED TO VAllE j P; RxV"e ::.pA1JC (v-lJ"J' ( 1-c.cs~) LET m= 1rc/v- p= "A11'ttt (lJ"-1J"nt)~ ( I-GOS~) FCR "Pmo..,c.J 1:= 0 I-~Ht +3ttt· =0 :. m= I aR ~
  • 22.
    ttl::: I asMIN1MUM .~ FOR "P='P~J v-* =~ ~a.) THE VANE I~ AlTACHeO To A VH£El of RADI(IS ... ; NoTE TWA1 ALL MAss HITS CA'RT M«j == I'Av-r[1Tc.. (I-'-DSe)vc::ose-~ ::I'Av-r(/-caseX"t1C-u-) m= VC/v- .) ?= ~A v-3 ( ,- ccse)(m:l.-m) @-o' IAA_ ~ dMot - ) nl - '"'- .: FOR -P-P,..,ClX I clc:N -11 Q.E. D. =< b) 5:13 CONSERVATION ~ MASS ~M +5d~ =0 M =IfX T/,'~ Jd~ ::: -~~ (UNIT CROS~ ~EGT10N) flz i +//"i-/iV; =0 X=Vw, ~=-~ ~(1T"",-~) =fl';-~ (I) . MCt'1ENTUM ~ FJ( =: ~ rif-cJM +rifd.-H "Pa-Pa :::?t(~x&)- V;tf~ =~ ~ l.C ~1f4 =~A (vw -zr) FROM (I») ';;,.02 (~-~s) =A'It,1..[ .:1i-P, -A~1& 2.1 COAISERVA-not( OF MAss! V,A. =~A2 MaM~NTUM : 2F=f-oolm P.A, + ?(A:l-A.)-~~-~AASf> ~~ =/rv;.2A;. -;01{lA, REA'RRAWGINq (P.-~)A, - ~ (A;l-A.) t- p (~-t) -f'9A<1 y =- /Y A, v,-(,;;:-tr,) P.-~ t- (rs - P:2. )(~ -I)r'S~yl. -= jJ1r, (~-v,) ~ = H r4"P ) -v;. =V,i'A1f) A2 = At +.AA _ -AP ....(p-~)AA -~4Yf -;>v,£IJ .A, I As AV-o-+dYJ AP-dP~ A ~ A• .1 (p-aJAA ~o So -dP _pgclY -=..ov-cIv :. dp of-;nrdv- t-~ dY :: 0 CD A1=' 0 TO? ",,:l v; == 12 tvJ/s R== 12i KPa.~ A2.,= .113<1m':&. LIi= ?'I{V tHis 11=1l.{5" J<P~
  • 23.
    Q= Av; -=o.3l/"I'4 Ht"l/s m /,Q= 841.1.1 k'~/.s g FJ( =If"V;c a.-H Fr +P.A, -P~A.; CD'5I)-~(v;.cose-y;) Fx =R" -=/,Q("5~e-v;).,.p~cose -BA, R" =(ZCff.1X-S".S'22) +1l/2~o - 9~9. 6 ::: S"OS:S-JJ F'3 - ~A2 s;,,8 =;:JQ. (1{ sine -0) F~ ~"R~ -':jJQv;..s,'r18 ....B.A..1 sine = 31?$ +r:a2 'R~ =H, 3GJS' N· tiAj SEC.TION ® ~ +'P.1 A2 - P3 A3 ::. ~ (Jj-1,.1;.) Fx = ttl (lJi -1Ii)-rf3A:J - P~A.:z. o-A +"R1"m (A3 -A~) - F)(=O o-A =Fx.-RiMtAs + Pc-mtA:z. o-A:: m(Vj-v;,).,.(p~-Rn.,)A3 ~-'P~)A.2 o-fJrof.)=E!' (33ao) t U:~~(:l~t 3!U ~ - SHi. ~ ~(12)· 0--= I Z2/ psi (COMPRESS/Otl) A.UID o;-A, N02lLE~ -SECTlON CD 2Z F)( +P.A,-~~ = 1M (u;. -11,) F'x= mClI:z.-t()-p'A, +P~A:a. o;A. +~A:a""~ +Po..t-.(A.-Aa)-=o 0; A, =-Ii- -O',iA2 -l'o.~ (t,-A.1.) 0; A, = P.A, - BzA.l -m(V2 -11,) - o.iA;l - ?G..~ A. +~ilt'A:z. 0-= L/922 ps; (IE~SION) -~---=-.::..-----, Z F' =rc.~.vdm R= r vdm - ( vd~= Fao~f·E. OUT )n~ FLUID =2 fa3Jf'~2(~)~j t-f'ifo.l3ol .... --;l,V;;2 bd (MOMEN1UM OUTSIDE' R::'2,o~2d..,. 3p~~- 6/,v;,2d :: -r>Vold FoRcE o~ CVLlNDER.: -R=l't{/J S'Jt ~ -~-- tJ;=10fps ~ 0.) AIR: lfw = 1130 fps 1'= O.0023? slc..c.gs./Pf3 A'P= ~ -P. =Pal.{."~ :(.OO:131XIl30)(,q - =:26.KQpsf = O. 116 'i!ps; b) VATER: VW = 11100 fps p:" /.<t3'l "5/W3S./ f+3
  • 24.
    ~rp= (l,q37X 41100)(10) = q,} oi'o psf : ~'33 ps; S.!1 3 ~­ VALVE OPEN FoR AN OBSERVER. M() V/~ AT 3M/s} THE SITUATION LOOkS UK£' ~O ~lfw-3 4-V"~-3 ny~ W/HcH IS :nJs.r LIkE! PRaa. 5".13. SINCE Vw ~ 11133 mIs, Vw -3 = IQ30 w.J.s ~ P == r'V",./A'V= (looafl 'l30}(3) = 4287 KPc. 5:20 FOR STEAJ)Y F~W EMz=ffcfxOz)c1ti "THE RADIAL VELOC.TV AT 12 RELATIVE To TH E: IMPe:LLE"R = <51 ~:' &CO~. ( ~)(.~6S"q fP "- K11f ) bas - cy.1 I = 10. ;J.1:l tp!> THE ABSOLUTE" VcLoc.ITV (TAN6EuTJ = Qr;- ~ =82.38-/0.~1;) =-1'J.17fps. t~= 10.21'2. 'I-.-- • 8.2."38' VR~IO.""''l. TORGU E: = r~ 'tflS5. f' VR A T~ .l . ?2./? •.!d- . Io.:u~ {2frsY-'J 12 32.1?II 14{C/ = 2()1/. 7' i+-Ib f 1=bWS< :: WI = 45: J" np 23 to..l1o( =3E:§' =.?03" oc == 3So ;l<l.11 a) e. = 125"0 AXIAL. L04l) ~ F c }c:s.vdm ~:= J. 71 cfs v= <S2.M V': (i·?fX I'lei) = 2 't?(. fps ~('&-I) vb) LOAD = (t.?lX6'IX2 I. 1') : TT J~ '3:1. J74{ , I------··-=r [ t ~--Lo=- r 1.2in I ---I .'---'"L..- _ _ I c.v. - - - - y ~ M~ =M~ TCR'<UE ON ~PRJNI<LE~ I3Y SHAFT: {{ I ; x~1 ~ p(v.y,JJA=2(pAv't-r;lJ)~."5. M, = -2l'Av2 rfj = -2.('2.~1)'Tf( ~f(C(OO)!s. <jc. =-1. ~ U:)f-ff 5:13 T=J(rxv)d.t:. =-"'R(lt'si~ 1= Mf -w~)'p2Al.fr Mf =2AfJ lIr R (vr 'Sit1ol. - wR)
  • 25.
    s~ ~ )L ~ ~ t II I x i-- 3' •+' /" ----1 XM2 = ff~s('-xV~ -~o)l'(v.A)dA :: sq r(-I La(v)-t dr 3 =-~v:l.t [rP5]~=7'V~t(36) V ~ /') g L. t = 4-;~= .::l.. I.:t = c~/ -. bt' .: M~ =595"8 ft -lbf , I + t f I I IVsr _______ ~-v. I I L 2F =1k<iyp(vo n)dA +;t}[2pdV FaR caQR'DI NATE F=1X'G'£) TO cAR I,." )(- DIRECTlotJ Z Fx = l; r( V;r ,LXO.n)dA=pAj 11 (-'1>C'5 .. . . -f'Ac V~ (-ve.) &~)fc.v. V)C pdV=:. ('(Ae Vs :-Aj~')(O) :.FK::f'[Ac.V;Vc -Aj1f2.] I)J y- DIREC.T/ON l:F~ -= F'j f~c.s.V'j p(-(J·;')dA :: 6oA~ vsX-~) ;- CfJAi Vi X0) ~ fcr v. IJdV=O dl: )J)c.v. Cj r :. F!j =,0Ac. vs:z. . FORCE OF FLUID ON CAR" R=-~ 24- . -mitt =~out plfh =pv-(o. +b) :. b-o-. =hcosO(.J b+o.. =h b = h( 1+ cascX) 2. . 0. -= h (I - cos ex.) :2 ZF"~ ::- fV'j dm F:pv2. h sin ~ b) XMr :: )(0 X O)z dWi F"~l =~ 1!f'Va -~ V";,vb .:: pv2 hsiYloc.R= ~,Pv.Ji:lf'V.:l. ,,_ I , (o.':l-b~) .{ - 2 h ~l"""'- =J:lI(.Y-2coso(-f ~ ?f-2cOSc(~ 1I 2 h sino(. f= 11 cotcX 2
  • 26.
    H2 = h~+2 v-:1 n/9 H -= Yh~+(2V~hY9 b) USING CONTRoL VOLUME-lI) ~Fx= f(t:.J(xl'(O-.J1)dA f~V=i' o ZFx= P.A, -~Az. -""R=YnAV}( 1=1h - P:lL -1< ~ phYa(~-V.) R= Pah -~L-,ohv.2('X-I) F'ROM HYDRO"STAT/C:~ p=:~ ~i"c:X 1. ) «='f) 1.=f' 1,. =~ -P. -=1'<j11 :z L5 R= ? (h2 -L:a)-f'h~(1J[ -I) 529 Q,~j)()ny V.h( =Vz h-z- M.o~UJ-.1 ~h.I~n.Z= ~Al)~ ?"'Sohjz ,~ =5'0h,h Wt,AlilC :z Jv, hi(V2 -V,) ~ ~.-i~~" ~V.hJ (V2-V,) ~GNnw(rr V2. 2~h/h~ dn~ (ft>~:) =V;~h, (~,-h~ 2 ~1... ~I-Ya. h.:th, h~- 2v,~=0 ~~h2 ~l = ~ (~-"("'-~f -02 gh, ~ ~U1i).)vrrY Vz=1~'~~ {1~~V;~k,)
  • 27.
    5."3D r -- -, USD..r:;T~ l~ ,; I ~L~j. ; f:~~1I t : I M=s>Ah Vz - n: m, '"gAV: -~AIi L_k' Y ~ + *dt<A, :.0 c.v. . . ~ gA n--sAtt:rD ~(JJtff1 ls SAr{~USD tv1~ LUrr14 tA$ + Lf(f " ~ -t ~lJ~dM ~~~5 _Asas ~lQAL -~~~+sA%ih~)fh2 ~u:r Is 'kz -~ 5.3l USWG-rut;. c~v. Af!CM5 Wrrf4 II To TH-g ~(~Ha>w) LM~ :: Ccrxu)t>e dM j J ' l: m01n~ V~ ~ := ZL19 +t.;~ ,A: y~ +l:L =O.442 W~"L TAk:l1J<l ~ ~ 6 W~Tb>TW6~ -3'P2 A4T:3VSAV - 3'4~l ~T = B.S T :: 40.3 R-~bF 5,~ r - - - - - --, 2 v,----+- _+ L- e.v-)J - - - - -- - -t Hg roo.TH& C.V. AfDIE L~: ~~d~ ~+~A,-~At%~(V2-VI) fj~ V2 ~ ~Sf;{2~ Of ~J~~~JD ~.~~~ '9,-fz :Tf4Js~ k ~ o:=>&T~~~* ~ Is (Ll~ ~ As g~~) Pc+Jwa(L4-t)=~tS'-t+~tz- ~-~ :z ~~(J~fJw) =71.~~ ZPa.-
  • 28.
    ~ 'J' Q -:::.A,V,'Z 'IT (.08)5 =0.02.51 mi4- rh: gQ :z 2'5_15 tzrs V2 :r V, ~~J'" (2.8 M,i ~ 2 m(V2-~)+~-~)A, ~ 2 19<O ~ 3«) "2 55coN 5.??J SUSCE ~S~ 15 Cbv~ WLW = ~CUT=S<4Xt)LO st~ tno..q =eo] s/~ mOOT ::I :25'0)fJ-dY o =2J152fa-cps~'(}:IY () ~2glJ2[Z-~] ~: lf2 = ~ 1!- :z 55.0 ~~ 4'[-8 2..7
  • 29.
    CHAPTER b I--~ CD II I.Z..,.= 22 -2 ---, IT ' P,=:/S-'"~L -t-_J ~:: 175"KR.. 0, =.25Itt D:z=alS'2 ~ WORK ,.- ~S(et!)d.;,+ ~ rrC..:;{dV o J~S. ~~- :. -1r= (et~J ~ -(erl), m =~[, ~~-u.2. R ';"I :l lU,,-U, +2"- + ~'i +~(~-i')J S/ijCE 12 =- T. U2 .: U, ,/ • m =f'Q =1025·.'2(= 21S.2Sk1ls V, =Q =4.278 M/!) AI V'- =Q = 1/.S7~ m;~ A'l P, ~ IOl/3Jdt-· IS",HjAf- '3~'!?I;) oJ ~ :M.92 il1 ~ J ='i/~ 32 b Po. SU&STITUTION YIELDs ~$W '2C cH =~J1916 AI.., = 35.9 KLJ 5 MIUUS SI~}J I NDICATES WORK INTO FLUID. FlUID APPEA'Rs TO BE H 0 A ;z. ,I SSllME' NO 'PHAsE CHAf-IGE; THEN 11 - LJ V-l) '2.-r,) .1.- I n- de.( T U ~ :z homl~1 u =CvT <H: dot n W d <- = (no - u) WI IN ~t C", II =(Cp To -Cv ~Es.)0Av ),N dt flV ~= (§; To -1R)CAv)'N V V To :::. ~N 1" V,./ 2Cp ::: S30 ti'I()J~{J. 35ST:1') 'B.p.. (:)X. 21(){ 32.Jr'() f.l.lhf/'os"l{t(xl()~j =- >31.01 ~R ~ = (1.1{ ·5'31.0{ -5"30)71(~tOlo) ~t ~ 10 ::: 2"'.io/ = 61!J "E'5 6.1
  • 30.
    6.'I sa _J'fAl.:: ((ore. +~)(0 ·il)dA de cit )lC.~_ r~ ((f 4dV ~t»>f.v.-'o JL.ie~ +-'%)I'(v.n)dA =0 . tri. +t(I+~ =f+~t~~ r} U:z. - (..(. = P. -~ == Cv .1T to AT :: ?,-J=i fJCv c --I ~ v Ib,.,eF =IO·lq" = 0.029'7°F '2.'1(IX??l) 6s - ~~s = ~c~+-~)f'(O'n)dA [£Js =gQ. 6"5"0 =qo~000 ff.~tf tit .K2 o ~ (e.T~)o(v.n)dA =/Avf>1- _~l. ~~. 2 +.! ('Po-~) +- ~ (l:~ -'jA) +C~lf' 0 j Ps =-aws/dt- t'ii tell' -,-LJa (!.jA-~ ) AV 2 Tf- J B 6.6 =(-2010 t 3 g5"0 +-3CJ 25" -I- q~7) == G702 psf"" =~6. S"psi"" CD D-IO" ,7 ®li=LiO~ 1?= -6ps'I~ 29 - [lJs = M~f'Pl. -~q~ + 111:I._l{t+- ~~l de [- (->9 .2 'j IJ =(lXr.:J.l/).trnO+b)/I{I(.r, t 53.7-:2'.0 +51 ~L-62.1./ 9'" t;(32.J~'I) j - dW.s =2?iS-I Ff -If". dol: 5 =: 5"D.6 hp 6.1 ~_ _ _ __ CD • ® (fW-u----==---- Ah:: 2.5'em. P. -B =25"",. 10/, 3:2S i=h./a;fns 102 10. 33 mH;.ola.+m == 2l(5'.;; I=b. v/' = .3.& = :2 ·2'15':2 = ~02 ~ P h22 s~ V.:. 20. 0 I+t/s Q = Av= 7TG3)2fl-O) =I.t/I? mJs-q- == 5'0.0 ft3/S
  • 31.
    -~w= I.:U~ I.'1l1m3202 ",~ de M~' 5* ·2 SS = 346 "" oR .3Yb KW =0.465 hp 6.i ENERGY EQUATION - STE.ADV ,..:" hOI + 1IM31103 = Wt:z ho:{ A'S p=c/ v,AI(CvT. + ~~ t~) t V3 113 (C",73 + ~3~ t ~3) = ~ A; (CvTz +V.l 2 r ~ ) 2 ,.0 AS T, =- 7;) p, ="P3 e=vT, l' ~rv,A, f V:.A.3) t A, v,3 t"A!.vf ,u 2 : 2 =V:zA2 (Cv7i t ;'2 +-;) FRoM CONTINUITY; V, A, + tI, A3 = v2,.A:z J 112 =V. -r 1r,~ ~A2 ~V (T;1 -T.) +P=;P,]= ~,~ lft~ +A3tJjV;~ _ ~ Vl.1&2. 2 :2 CAN ELIMINATE Z6. Cv (72 -T,) = P,-'f;i + V. .!:1,.2 +AJV]V3~ ,.0 1f:2 A;:~.:l _ V.14 T So Cv(-r; -T,) = P. -P:a. + I 1I,; r' I t A3~ 2 A,V, + A-!lI3 V:::)" l M( It 11:):1._~-_~ --v. 1+ 3 3 A3 ~ tA,v..4 ;;. I A,'if 6.9 MOMENTUM: f>. -~ )A. = p~2A, -1'1f,'lA, P,-~ = p -,0 t!i'4 A3 ccs.G + ~2[43~ ~-2 • VI - 2 b, c.osB I ... Ihv3 A. A,V, « p(et~)(v.n)dA=O Yc.'S. ,- lL ~ V ':1 ve, -:4 +U13 - £.lit t "Ps -~ :::a 0 2 ;z> VA ::= Q = 3f1o/s =3.B2 fI'/s AA 701(19-):1 Us = Q =~ tI~ ='-IlI.4 =15.28 fl;ts Ag /fg ~ -~ = Vs:l. -'{12. + c.{~ -U A I' Z PA -~ - 10','" + .liSP. 109 -:2 (3J. J =?'I)
  • 32.
    ~-""B3 = 2./S'Q. of flt.id fCj ~ = Z f1- + 2.IS A of flt.ic:I = 4.15 w- at flu.lcl. ...-I:t!.{ 6.JO ----=-t VA: 2.1{'5'"Y ~:l:: lI.JI V4 2 "Us =3.gj V 1:!§..'-= 1.:3 V2 2 FaR TI-I~ COlJTRoL VOLUME SHCWN; ~ -~ -{if::f{(er~>,(V.n)cM o 0 t. 0 t +~~C.S.pdV ~t o 'C.v. ~ -'PH + VA :l.- Vl.'2.. t ~ (l1A - ':i1. ) ::. 0 fJ .L (IO./l/L/ Ibf/f+2 ) +y2(1.11-"7.3) 6:2.'1 lh""/f+3 ~G + "32. r;L/ (-;"1 -:! 0 y2= 1'/2.3 y =13.5" ~ 6./1 ~LUIO WEltiHT 31 Z~r = rvi! dtH ;:r ( p(O. Vi) V~dAc.s. -F -Lv' +PA(A =-111 VzlA +~(o) USE GAGE PRESSURE ~ R~5Um FROM 6.10 r: := -t.J of- PA/A + mVz fA w:: p Q VOLUME -= 6:l.l./nr~~.s +'lI) =1/1. / /hi ( ~S-7" j.'1 !/rIA = IIlAz :S'1.51(2.7r'12 '-b-) t4 t-1T. 1~ -; lIi IA :: 3Z.6Q fps F:: -111./ r 10 '!!.1.+ 62.'{[,3S'X3r.., I.{ 52.lrl( F=1399 16[ ON FLUID FoRCE oAt LID IS /39'K Ihr 1 b) THF FORCE ON THE LID IS THE INTF6RAL 01= THE' PRFS- SURE OVe;K THE' AREA O~THE LID. WHILE "'BE-RNOULLIS EQ UAT7 0 N Gtves lis P=PCVEL.) viE Do NOT KNOw THE VELO- ern' VARIATION ALON6 THE' LID. CD ® 6.12 Q=6~ AIR ~'S :lCLCOHOL fJ=· ~J.I:tQ "P.-~ =0.1 WI <l.lcohol :: n L/•'l~Pc. A.="'U'(6)2 =.2'83..,.,~ L/ VI = ~/A, = 6",,'!./~/'j.'83 ",.,:1 =21.22 "]If; f + ¥l.+tj rl =, -t lj2+ ~ ~2.
  • 33.
    - -')A;:l· p'-g =7gJ.f.86 N/rn2 = 6LfO.2~ P 1.226 ~/m3 6'10. 2 = ~~r-J (2;2)~r-~ ~t=3."ZLfI Az= .510A, =a./II'1ml. ~ =. tl29 n1 6.13 -- V. ::L_ VJ. 'j"') l. 1+ i2.-p,= 0 2 P V, = 5:1 fps I U;1 = U.S" ~ 11-p. = -2.0'15' Fl- of H2 o,.oj = -2.a45 " H;20 ( I' fig0 ' 13.b "H;1a) = -0. /5"05' ' H-S -: -/.1r' Hj MANOMET~R 'READING' 'S GREATER AT (J) 6.JlI h ~4---~.. '~---------- d .. ." CD :.': .....~~- AIR USE: SfRNOVLLI £QUATION BfJ1JE'EN A) SUR~AC£ (5)*0 BEFORE AIR IS INTRODtJc.e:D (ST'A. fa) Ps .,. YJ.~ +S~5 = 'P.s ~ V'B~+ '3 i!,.B P 2 P 2 ~2. =<j d - '118 -"Pa.+It1 Z f'"~.o a) B£11J£EN STATION lA (AFTER AIR IS INTRODUCED) E @I 'R ,,2 :l ~ +.!2 -t <j l,2 == ?A + V,A t SZ,.A PM 2 PM2 ~ = 'Pa.+m ~ V,2:: II,A I Z~ -2'A =htd .1. '"RA - Po..i," CONSERVATION OF MASS .. . . .mA,R +WI H~o == ~~I)( ~AIR +fH~o A11113 = PM1r A16. tMH:z.o » ...nAIR (O£J.Js,T'{ 'RATOa:.' IO!) .: ~= 2 V2 (Q.fIXI.K)('-P;r]J ~ - 5'. 9~ IHls 6J~ -h- 6' ·1 1(- ~"-!jf/=f{c5.(e t ~)f'(v.n)JA 31
  • 34.
    IAJllfRE K, =2 A P J K,. = :2~ P t: -~ ~~K' +K~(Yo-2)'fs-(KI+K1YO~ ~AT = Gbf = 40.2~ '5~ K2A-r ~ ft .,fP=(5"-3)09:- 46. '6 ~ t}l. 't(,=(2Xlf~.~)(r~.'Xq)(3:;.JflI) 30 zfP' . (. KS") (.1S-)(12)(~2.") = J. S4 ~"'J<:l.('1o-:2B~=~CJ.i+2c~p~12.21£ [I<, fK,. ~y=[3D2.Z +.2~(S~=2l/.99 ~ .: r= -~o.;J.S(~.J? -:2¢,9'1) :::: 109. S- S :: 1.125"',..,;,.. b) "'P. =B -FrS" = 136./3 ~ 'F?z ~1'o -~~ =(1.21 ){24)1.=3'1'l.<fift,.. .2 ~?=B -? ='3Ql,1I1- /36./3 = :J/~. 3S- Po.. AH = A"P = :2IJ."35P.. o.16~oj (O.1~jJOOO~/m3'Xq·f1~ I 6ft APPLY CoNSERVATION Or: MASS ~ + d~ =0TO TANK: ~M f"t c.s. M =Tlo2.hp 4 ~M ='1l"O:1.f' dh (c1m= 'i/d:2..pvc ;it ~ at' )c.'i. LI '7IDf dh +-r-r#dlp ~ =0 i.J at 7( 4h d 4 ...I t-Uc-O~t- 0" - APPLY' 'BERNOULLJ ('QVATION = AJ BITtJ£EN SURFACE i 8I ~ - 'i1t'AC = - lie. 4_'3 H ,a :2 "'S.) "BETtJEEN '5VR~AcE' ~ C Pc ='Ps =~T~} Vc.2 =2 <j L .: 'Ps -i?s = -(L +11) :: -It! Ff f'9 Vc :: ,I;2.qL = 25: 3~ f'ps
  • 35.
    Q =Av =trd:2.Vc.= O.I3i! '(:t3/ 5 ~ ~ +..£ Vc: :0 0 dt: 0'" Vc -: y2'jL - (ho -h) ho=I1@t=o LET 11-h, =z 4h = d~ I dt dl: dZ! d'l...,r dl .,. D~ V2'j L (I +z) =0 -3 - ( dr :: -d':1.Vl~L (' dt )oYlf2A. D:l Jo ~~. @ t=o h". 1,. ,/B t =T ho-S, =3' 2L '/,- 24. . = -::1..~'{JaL T; -3 o 0:1. J T- JL D~ ( ) - d.1 Y;2c.3l I - ..;I - 3//.. = 105"1/ s == '30.9 /H;". 6J185~=/21;..7f.ps~ T:l/o-p PAr... =p~j"~J(1O.?.3 I~ "=2051.11!1l. ~} fl.2 fJ=:E ::. :205"1./";') =.OO~ 39;< slu, RT (,115" ~()O it! PAlM + ~2t7}2._:E t 020P f> ;( -,0 .2 AP =(- 00~3'P'l!5912- #l1/()o) = 1.3(,6psf =O.tXBSpsI3 P= :J.05"I.lr.r/.3" =2052:5 ?sf :: 14.2Cpsi 6.19 Vox- =~. Cbs 30- ; VD<J = VJ' 'S,' 11 30 .". ~. :5.'25'"15 Q = VJ' A. ::. 4.42.10""" m?s HEAl> = 'j + ~."J. .19 =.6+1.6' A Br;:T1JEEJ.J CD f ® : =2.2.1 1ft c ~~, + v;i r ]( = '3 <12 +- V;z'" t- 'PI oP.2 .~ :z;p Vi = Y;2'3 (tj,-~hJ = 35". q fps Q= A;z V:z. =0.733 .f13/s a.) VA :: Va=Vc. =Vt:> =A.l U - ~ A ~ -4' ="/.9rS -Fps b) BETWeEN CD *A : ?A =-"B+TAt 1-,.0<3 (~I -<:1.1) -,0 Yd.2- , ::z = 2'1.12 pSI '5LMILA~Lc,lJ ~ =11> = '2;:;.12 p'S~ 'Pc: = 1£#, IS- P~'t 6.21
  • 36.
    A =".193 fI'J.~ v= ~ -= 6.5S fps ,+g: +':11 <j -= "P.1 t lfl"+~2 (),p- P () 11.= -f:1.Q - V?_ -b(3.l.1'~(/) - (US)). I' J 2"- --r =-t.1,.'L ~: p.::-(62.'1 1~)(f.".2. AJ~) =: -2.i,7ps;~ ~lf ,,~'" / STATION : AT SURFACE O~ 1-1-,0 P. ::'P~", ) ), -= 0 ~ '1,:: 0 STATION : AT PUMP IN LET ':h = q' I ~ ='P.... ~rAl +0 +0 = '('+ Et t 1I~:t -1-4' ~ ~ 2", v:z.":Z.. _ BT.t -B- - "8:JLI,/U'/.7-.2'O.) ~ - p~ 62.'1 -~ = :2S:~ V:l.= ~().¥tpS ~ A='iT:Ja: :2'7.1 ~"2 l./ Q= All ="7.Fo ct5 c..I Q:: (7.loX(0)( J;;r)= ~sol ;;W~ 6.23 I=RoM DATA OP PRoBLEM S::ZOj VElCXny LEAVJN6 IMPEUER J 'lIr =I".~:z. fps I Vt; = 10.22 fp$ J w r: : 1,.:2. fps .,.-- t10.2:2 .fps L.._ _ _ _ _ _ _ '7:2 -rps 35 HEAD:. v~ -= S:21"O = Z2.S-f}- .2~ 6'1.Q ~'P= 11'112 =5'279psf =3'.~i ~I{ THRUST - Q V I V - AnJs hp -- Q Ah • Til RUST -.. Q. {i;i; _ ~ .• hp Q AIt yAh .: HIGH VOLUME', LoW PREcs.S()~E' PUMP. b.'2~ 1>= S'Ops,'3 D: Il I" CD A=CZT'/., ~2. V, =3.6'l,f,,!o Q::. 1.9 cfs S.<i. - 0.'0 hL = 'B-~ + v, :2, _ Va.J. P:J :lj =(1'141)(45") ,'I -"1211/ +(61.'IJ.O. "S) 6 't. 4 = 130 - II :2 ':: J g ft. 6.2' FROM 6.~ ~ V 8 = ~cl- -P,~ - ~,.", :z. f' tt~0 PIA - P,mM = tj(h+cl) ,oM So "PIa -1?1A =P+I:a,o <3 d - f.~B:z.f'~0 -~ <j (h+d)
  • 37.
    ACROSS SECTION ONEJTHE VEL- OCITY CHANq£S BY A FACTOR OF ABOUT 2. UNLESS THE: MOM£NTUft1 OF THE AIR IS SUF- FICIeNTLV LARGE -ro ACC[LERATE THE FLO~ THERE WILL 'BE· A PRESSURE: DROP, A CHECK OF AIR VELOCITV "REQUIRED YIELDS SUPERSONIC AIR SPEEQ, THUS WE MAv N£~L£CT THE AIR MOMENTUM. t AmP. AIR : v,Jj~~ l. BEFORE AIR ~4a-t-~-l rl~ ZFl: = )Vz drM fiB -11...)A =m(v2 -V,B) =~A~ (V2 - ~ '4),a~o "Prs-"PlA =-~2.(I_g ) . fJu,p TOGE.THER WITH BERNOULLI EQVA. ~ vt(J -~o)= CJd~oU-tJI i-~)] I Ll 2. v.l.- - 1M J.. 2~ ~,. = c;;!d PH~O r,-~(t ~dn p,... II - A4 ) 2~o .,..---:--~-----:- '6 ~ 9.iIXI.8~X'-1!) :s 3.113 IM/s I-~ A q2 % REOlXTION. /'.2'1 tM ='pAh ::f' 7:;r'l.(hfho) ~ =p'TIJt dh d-t .~ dt ~t :: ~fi1 vC(At =/l![t.:J.";29h ~ :: -d 20 .bur = -d~ i ~Cjh t)2- D~ Ch~dh =(~-d~ ~dt 2~ Jo D~ ~ :n~I;,:: -~ vSS t -= :2(J-m~-b.S&3 t: -(-G.st>3X/5)2. - /''-.L7- ~T sec i~X-s'J.r~i{) ( ;Y;:2.t . = /l0.~ Ift;K I~ ~~ A p'~-_....J , 1FIlJf!EN A ~ E } -r V.A 2 of- ~ 2!A = ~ f Ve;.2. + «j rE 2. 2 Pz. 2 -PE :"Pc: -I;' ~ L2 I ~ =V ~ = <:JL2 t "Pc _ Fa ~ L~ -rJ!." _ UA:l. Ii Ii If 2"2
  • 38.
    50 ~--Pc =-Va~, Ii :2 "PA --Pc. = ~ L2, (1- P.) t Jl..2. ~ 7J 2 ASSUM INq Va ~ 0 =~ ~ THEN Pa =-Pc =P" ~ =~ L:z. (~ -0 6.2<1 FROM 6.2g' ~ -Pc; :: -(! Va:4 , ':r ""p. - p =,.g U:l +9L2 (~-f.') -~ ~~A C:2 :. I :l 2 CONT/N VITC/: p. 43 ::l) ~ :: ~ VI 12 _ .'.e. AHEATER AsrAo< Vg':l,. : a:l)lJll. ~ LI. l. =JL: - R:1. ;4 ~~ I ~-Pc. :: -A(~rz~l :1( f?j 'R.1. 'R "PA-"Pc ~ ~ }Ll. t~ L-'J.(~-f.) -IiVl 2 ~ ACROss f.fFATER (PRESSURE ORaP) ~ F« s rVx drn Vs-f--i-UA -P1 1---0. ?s ~--' <j (P-s-"PA)K=I'fi'Va (VA -Us)I .. 'P~-?A =t!' JL(V -U ~)c: ~'lf_A) 2 'R R 1< It -;<:1. l Po COMBINING WITH 'BER tJOULL, EQUA. Ii "L~(I_ ~L) = -p,r8.)2~l. _ ..121~ 1(.1. ~ 2"lp' 1<1 '2 '3 L:z. C~ -~ )f t1 V1 2"R2. v:L(1. - ~~ of-.!. t; ~-t" ti -A ) "R 'R"'Pa 1'Ra. If 2 :zRl. = <jL:a (p. ;l! ) v 2 ~ 2tj L :z. (P./,p:z. -I) ~.3{) 1+ I-~~ "'R~ USINe; C. V. AtdOUJ-ll> ~ u,..s. e+Py::: ~. At-~ "8tV !::: 9D(J J l)~::: LfoUr So ~~~ d~IY'::; Uot.:rr t-~~ .: AU "" coAl"" dA~ CU--=C'f=4~DD S/~'IS AT:79.<a(~ l~'" ~ ~ s: 4~r AT~O.~5P~
  • 39.
    6>.'31 tJ~ur;a-£U~ TW*~C»A f -OFT~ 'JJC1DM~AICZ-,1 ~AP T~~ ~TC46 V~~L. ~~ '<'lA5t-DS A~= M~ ~ A'P:z 1?~ 9An. . T~ ~CJJLL' ~~ We~ ~t5N J~ Iw> TS(!; ~AP '(~ L:?, n 'L, ~~=. ~+l)~ s> Y 2- TUO$ o:L ~:z AP ~ (y. .z7(,]w>Z - : i t Ie $ Y J> ~ /~ ~27~2. T~ J7lL)W ~ l~ M=~Q) Il-=- u: ·~2~ .~«r' ~rr Q:: 76.7·Z4·"2. 1 49.4 ~'%' [00 M., ~ <st.76 b~1s 9ol»~ -~. '" 1i+~~)~(e~~)J 38 ".. "2- h :: lJi-u;. + h-h£. - l 2. 23 lr:~JJ(XJU...( ~. is VAL-fP hL.=D. Urgscg w~ Mu~ S~<n nL/6,Twcs <:;'(/E!;~ ~ ~y Be; l.del1FG~ h2 ;, ~(Jt~B-l) 13:: 8~2.. ; - ;Jh, ~B~S IF'h~211,.~~ ~{s ~ ~ ZUi (1.f./J-fB) F SOB<M(nm).J~ 1#T<2 © ~'" 2 +~_L -(~ t'll -4 (0 26 2B o~ ~LA>S ht.. :zoD JOe ~ A~ h1.>D FOe 5>8-
  • 40.
    0.33 GJerr(].,f~ NbPrF16.D &fo.O.JLL{ ~ ~$CC c. £!-tY2,."1.~ls;- =R: + ~~4hL ?J 2(1 J78 2(j k)Zl.c) ~ ~?::~~ J ~zO 25-2:c :::Z H LJ:'1.. '4 ~ +hL=H= 367 ~ 2(5 t (] W~ ~ 2 '0/ (JeZ 9.32f;-f~ q 2 Al& ::: f;.CE6·ro L cfs ~.'34- LSvg:; fu (;.() ~ FOe AC. v. &J:I03Wc:fr~ ~p -?JA= ~ ?-?~% Ail? at g ~ =~ fp'lM:~tR Q-z fr:) Z 3 Yrm:l.~ ~ Q4-%a) $·re Qf/?;;: (1).44·1.25~ ~ ~'FV }/0cur;I2 % ~ :z' fBI U~fJfl .. ~ s fO'~ E".Y~:r~::.4.1{,·10 !!!c..F.".... 59 USl~~t~ ~~Aw9~A ~ J..(~I/l-=. a.+w-tS ~ 20 ~ 20 ~:~=: ~"~%2WV ~~=-2:5VW=L~VW e ~ (%~vw 1')P~ b.% Lcr V-=A~Br:V(r) V(Io) =0 2 A+f>G :0 A:;z -~ro I V=B(r-ra) V(~-)2 wdh ::z -etr{ -~) ., ~ V(r)zu.rl r- G 2- (.-_~ ( 10
  • 41.
    2 &T~JJ~ AJJ.t> ZI ~ ,.t.5....t$ '% nL-~ ~ +o;'l.-,of ~z. S(3 20 ~ ~ ~ 2 1< u: zl) r. --"t -z Ua --I;> I S 2- 0: 2 ~ 2+hL%~ J kl-~D}lo~l£, t52% @.::: (4,0 Mt M::yAUC :. Ill§) ~ ~@ h~'%()J ~ L1:2~ A~A~ } 1.6 ~ z L(O~ ~ I'!L"3~ }.b ~ ~V~tfz 0"2.'" ~ '" .g,291'V1i; 10/),:6,(£ ~ '~ hL~~J~t:'6 I-I~V: LY2}%i~"lJ~ h 1. 1- t...2.~% 3th <J Z%, ~% cfI/~f~) U2..:Z l3~ ~ M, z Lce6lz~ ~.3B II ~~L'-r ~-----.-<-- It- (sT/.(lS~ z;>, ~ As I~l'iiG I ~ ~ ~ '-~ ~~d)) ~,~ l7·S9 ~ &.. ~@ / -!2.%2~J :0 ~zJ2~(!)z~t86~
  • 42.
    C1-lAPTEQ 7 7. I~'lS{~ ~? Aa; ~lN6D ~ ~£x. I . T OF? ~e I A~ Z6, ) ~ & .0177G::O 80 ICO .{){)70L .cor28 .r.m I .Dloi .W'S i eo z~ Foe WAn3f2 C(IV '} Q.~::: 11.32. 2D-1DJ ~ /~ ::.' 1 ;::. :> 7 '-'32 PI+O O.~ ·10'" . ~~~:Z70% 4l 7.W t6e. An2- Q'" 0 QI40 :::}d32. _ LIS:> .10-5 Q32 /4M - (,34::).IC-5 QIM) ~O.~2 41'32 ~b~z-(3~~! 7.4 z =N c = No. OJ=' MOLECULES 4 CROSSING A PLANE W=MOLECULE'S / UN IT VOL£)M~ I t<s mole CONTAINS 6.0;25" • /02J, MOLECULES .? HAs A VOLUME O~ 22.4 ml 6.025". IOU. MOLECULES 2;;.~ W3 =2.6Z·/0 2S mol = 7.6"3'1023 mol m 3 fP - -/Zc - 7r RT =15'0'& fps ~ =? ''8' . /0;).3 • IS-O'S 21 = :2. 1'7 'IO~' mol tP,~ 7.5 7' =.,i/(d~. dr )R V; =1Tm~)(D -(~)J =2VAVEE-(~)J d1,fx =-1./ "lJAvE Y' dr ~ r; ::. -~."lA 1.TAVE = - 1920~ tf = -.~~3 i/:"/R'a @ tCo·p
  • 43.
    1.'7 "IV:::: 2,,"1/".2 ~E¥' + ,.37 J<Z Raj 1,.('iv)= 2-;2v-2-..... f'+3(fj] 4. ('T'v1_- 0 J .r - I d... J ~ - Y"3 APPLY ~/RST LA,! of THERMO tfQ _ 6"LJ= (( (e.t~+~«r ~V dt dt - Jk.?I'"'-U ;eJ~ ~AU VISCOUS lJORK ~ = £lJe- d-c dt [!de :: (Tvl dA dt J ~~~ IlTJ. b - ~ r'-'Irll1V cu"olo.~ - , ..... r v1OUtct'" bouJ'do¥"~ :: 0 T =","!bl = p. rw (LINEAR PROAL.£) d':i t:. GAP . ~O'~TANce :. i~ ='rvA =0'~4'XrwX27rrh) ~ = s:S"?52 l!.:!- =5.S''lW 1.1 j = <fQ= kw2 dt ~=J<tJ,4 I 42. <6 = k w} "7 =2 CcJ, 2- ~2 = 1/ <1,. ~ INCREk5E :. <t2. - ttl _100 <b, = '300 ~a 19 ~ = 2. ~6 q3 -/06 -IMT ,252"" T:. J"15K tr = 3. 611 A M =21 ..0."" = I.lq 42 NTRO<:iEN £Ah<. =cU.S' ~ =I.ql .~ -O,a = 1.I<1J{2 (UIYEAR INTER?) M =II. S1./75' ./()-6 Pc.·s = 1I.5'5",P f>a·s ?JO ® L-I_ _ _>- 3.1 'o/S CD I >- Lf ~s CHOoSE: Cov. MQVlNq WITH SHIP I ~ F= ~ V d", STEADY r=101J c:.s. -§ Ftk;d =~x -11" 0!.A.t5;2~'" C" _ )oX wrrn RESPECT TO Co'! MOVIN6 AT II!!! ~ Po" ;: 0 F~ = -Pix = -V;; m:z -(-.q H1/s) Ir( lal ~/s) F'fluid =qO ~'" =qO N ~ J=rl • I - -F_L'n~CI - ~IIP1 l='5hlp 1 = qON IN THE' Wt;'GATlVE X DIRECTION
  • 44.
    III ~ iJ) ~ r ~7 L_ /a.) dUX » aU; a'j ax " [J ---:I I I J ....- 2-0IMENSIONAL (;(~y) FLO..! Vi! =0 OZz =0 av 0;)J{z = -.. 12-)(=0 =?;,z av~ __ o __ ~ ;?<j ---- "TZy = 0 = '<1r AXIAL STRAIN RATE =li"",;i lfJ((}(rAK)4t-u;,lX')..dT: =~ ~K+O AX4t ~t 45.r~ a 43 VOLUN£ CI-IANlii E RATE =Ii..,i!- AAKle+"t - A.1)t'~ 4¥+ 0 AAX ..di: At-+O =lit1li-r '1r (>ff6X)AT: - I"r ()()At= dl4 AJ(~o A>f .1t ax 41: ..0 FOR 3-DM: BOrn AXIAL STRAIN RATE AND VOLUME CHAN4E RATE ARE EXPRE SSED AS a~ t d 1.1~ + JV2 (5EE p~oa ct.3) ax ;;9 dZ . . 7.14 r- z plo.ne. Z
  • 45.
    B-2 PLAN~ V"-8 -PLAN~ r ".61: =~~O rVrlGt6B -Vr Ie Ar~O t )"'11$ + r(~1,,+6,. - ~J,.)l ~r J =..!.. C?Vr -r r l..(~) r;Ie dr-~r • -,.J rr IT d~ f- r d (Ve)l.. 're = 1/9,. =ptr ;;e ar r IJ ?J5 H~1T 1 ~ 1 t i •'j/t ~h f LL1 --1 E l-- E=.oIGMt -1 0 t- RESISTINCi FORCE' =f:z F2 =STdA = fcr1l'Ddh=rJrDh 'I=,P dv- = ::y: elY ~ .. F = n v-7tDh =.aV'.jl'ltDh.•• Z --E ,-- E. F;i' = 1000 C.osX3:t ./O-3)/olS-J7f l"lo"" ·.S~2 (3./t) = {C07a, fJ "lib Fr. = W FROM PREVIOUS PROBLEM Fz ::;; v"'}:: 7TDh .I ALSo" Lv' =;79 E :. jJ ,/:u7rD h = I')'t~i e 1.T:: m9 £ =b8tJ·9.1/-;o-r pif7rDh a5"OU1XIO~~.~ ".. = o. 7f:>6 nils dA: ....d¢'dL dL =~ sin 01..
  • 46.
    M= .M~ ,..3d~dr l A1ij,1f hSIf1C1C 0 0 .: M=1T'~ w D.y 32 h '51"'''' lvzO~ (?t-~)~:'Trl)L%(J) 4P;<" 41"'= 21.7 rsf4L D 7.2. , ~% 0·76 ·ID- 144'5 -, jLl2():Z: D.~~..(0 ., Xe~:a-5l%
  • 47.
    CHAPTER g t.1 -£= 32"uv. Q cJx 02 v'1f!i 4:: ~Q dx 7T IfI Q. =KD.' Q2::: K ~i K = (-:&Jr . dxjmp. 02 =20. Q4 ::: 16Q. ~ CHANqE = Q.2. -Q• . 100 Q, =1500 ~ INCREASE. K.20RlG/NAI STARr 4O~Km=-_=EN=O:.- '~Km Nat 22Km I ® ®~-------@- -dP - -.1P dX - T ORIGINAL: ,;, ::: KD" (-:~) -t1lf.3 = LI.) ~ K041 Nat: (£) =rHH -A'f.2= LI'l~ L 1'2 K1)'1 J K[)'I f..I1.P) =. t1N/a..,1 -.dl,?3 = L.2.3 mN t L J·3 KO"* 2K04f SINCE - 11"P..310l0 = -41P..1/Na.J-Alii Lu ma _ L..:a. ';'H + L.:1-3 mN K D'f - K[)'12K ()'I 46 13 CONSlO£R THE CYLINDRICAL SH£ll ELEMENT ~I__-L ar ., THE SAME ANAL VSI5 AS IN SEC. S.I OF THE TEXT LEADS TO; 4..(rTJ = rAP a) dr L LIT R ::: OUTSIDE D KR= INSIDED (K.(,I) ) def'Y) = ) t? rdr r"T;: t&""P r~ + C, 2L ,., = -;« dv = .1'Pr + C, dr 2 L. r Jdv= -.1P (rdr - Sfd,.. :2L.,.u J A r V = -.A!:.,...1. _e,k r +co2 I./)-' L ;U "B.C. v=o @ r ="R J r. KR C. & ~ R~(J-I<~) 4 L .t.... VK ~ = 4"PR:l _ 4 PR2.(I_~) k'R ~L. ~L AYK :. V:: ~-Pl?:l.[i- rl._ (I-KaJ.tr1.] 'IAL R~ t.. '1K r g.Lf i(rlrx) _rdP = 0 dr dx
  • 48.
    'Tf.)( =~ dVt:: ~ l: + c. dr dx 2 ... V.{:: -L. 4E r2 t S. .t.-cr + C;z lfA dx oM B.C. Vx • O@ r co.Q. , ~ =V@ r =d :L ;z C, = -A r; -L.. dJ>( 11 k~ LV+ J6,.u dK D~_da~ d . C2.= -2-dP ~_ C, kl2. ~A dX 'I .M :z F :: fA = rC1id .1) .: F::. 17"d,uf}:L (V+ ..L. 2,!:d£..~ l! 16,M «x d (D~-cF») + d &J~dx FOR CONCENTRIC FLOW IN THE. e DIRECTION J Vr =0) Vg = F(r) 50 Ire = A r~(Ve) d... ,..-; Pte Ar41i! X Fe :II 0 I P~ ::. ple.+c16 ••• 7r ~eAZ'lr+t.r -,(,48621,. =0 SO THAT Tr = COt.lSTANT OR )l ri .4..(~) = C J d(lfG) =~ 4r dr r" r A (2- INTEGRATION YIELDS: ~=c, ... -£ 47 lic. Va '1:1 0 @ yo =""'ROc.TT£R 0= e,Ro-S& M Va =(JRu'Nf~ @ r= 'RuIHER :. w'Ri= C,R; -..£ A C =# CiRca c, = wI<: R,-'Rc ~ =G)~ r _ w-"RiRo Ri -"Ro I<' -'"Ro =w"Ri"Ro (r _1::)1(0 -Rl 'Ro = c...J~i ( I - r"fRo ) I-K~~ ALINEAR PROFILE .' OR 8.6 1P.,; 207KR.·I:==::;j========@ - . 0.63501 <D #:: 1/10 X/O-& ~; =. 0165"1<1 ~ms JJ= 5"3.0 Ib"JR' ='l'l'i. <t5lJ ~/,"3 a.) INVISCID.; USE BERNOULLI EQN. P. + V.Y+ ~ = B + ~~+. ~ P elf: '0/ I 7 T / < P,-~ :: £11' ~ =y2pP J m=,aAv==w;o'"f2jJ.AP Q= Av =1J]).'-Jj~P 1./ --r b) VISCOUS" LAMlNARJ -!!P ="32,.u it· -dP = ~p dx 02. J dx L- v: AP D2. T 32...u
  • 49.
    m= pAri =~7rO~41P 02. =1TD;..oilP 'I L 32r' lli Lp =1J.2 GOVERNING EQUATION JS !L (~)( )- JfP -= 0 dy dx FOR N£WTONIAN FLUIDS IN LAMINAR FLO~ -;;x-=fol d ~ dy • V - -'- d? tj~ 1- C, u t C;z •. x -:J"u d}( Z;"J ae. @ INT£R~ACf (@ y=0) I) Vr =V:zz: 2) '~r = ~XIr ~I dVg -=,I-{Jl d Uxrr dy d~ 1.1 g:p = ;11 d:l.~ dX dlf Ix =...L ~ 92.1" c1 Y + ~ 2"a elx M B.c. Vx =0 @ y=O UK =V @ ~=h j~t)7 J 7 J;II c, =A ( v- 2:!: dP) ., .2"u. dx C~=O FOR ~>') =D =0 " d Vx ) =0 ) Y d Y 4=0 c, =0 :. dP _ 2).( V dX' - h~ CONTUJUITY: dP +~ (Plh) =0 dt ax MOMENTUM: dVK +Vt JI!¥ =:1 aP at ax fJ ax 5 til T'ieM 'f' +S5'e", @ 1
  • 50.
    BERNOUlLf f='ROM STO I P5 + ~ + <3 i!s = P. + ~ + Q r p 2 P 2 -J' ~ =9.di!' - !t P 2 l-IAGEN-POlSEUILLE EQN. FROM 1-2 (NEGLE.CTlNG, MOM£NTUM) Fa -~ = 32-" 11." =11 L D2 L 32 .Ltv, :L :: f (9AZ _ Va::1.) 0'1 L ; u Q= 1rD~Li," ~ = </Q q ) 7rD~ 1) = 1iDl/ [~t.r - ~] 121 G. L 11" 2 DA# ?12 tv P941X4!:1A~ APPLY MOMENTUM THEOREM TO THE ILLUSTRATED (LfMENT ~J=x =0 It-J THE UMIT dT ......pg -= 0 d~ 2 ~= -pg dy~ ,Lf. a.) "BOUN DA1W CON DITIONS: @ <1 = 0 , Vx = -V (I) @ I:} = h , 1=0 .: ~:~Ih =0 (2) 49 v)( =~ +CJ. Y -,.0'3 y~ :2p 'B.C. (J) C, = -V B.c. (2) C2 =: ~ A b) v.. =-V-t ~~~'TJ(~J{~J] c) Q= "'evA= -ihfv+ alr~ - ~ h'"<:I"l cl~ 2~ h J Q=Uh-P9h"! +~3 :2.u 6.,u = vh _,.o:rh 3 :3).( 3./3 0 = Ve Cr) ~ ~= ~Ve 4!' ~ +Ve(r)~ dt dr dt FOR FLUID dr=o:. dO': VeCr)d~ at di dt d~ =~ X' ~. w= Ve ~2 dt } r ~ = ~(-~) de r :. d I I --U :2. ,.. - - e fl..,. dt FLUID -;:-
  • 51.
    8.~ ~b"/ ./ --- (NOPRESSURS CHANGE IN e DIRECTION ). g.J!; CONSIDER "PASSAGE AS A STRIP CONSIDER FREE BODY OF 8.£MENT Y n-I -AX·/, Iy-t~ z.~ =0 pi&'-I-I:';LF1A'(.1 (NO MOMENTUM IX - ~- X+~ FLUX) Tty'.AX" )( (PX -1'lX-rAX)AY +- Ci'f:S+.6'1-1ifj)6X =0 . DIVIDE BY AX Ay f TAKE LIMIT E' =d'P = f'B-"B.. _ to? C1<j ~x L - T NoW '1=..udv 50 Ad2v= Ll"P d~ d~:1 L SOLUTION IS V=C, +S'i +A?y:2 2pL 50 BOUNDARY CONDITIONS; @ '1 =0 V=R52 .0. c, ="R~ @ y =h V= 0 :. C2=R2-APh h 2)lL THUS V=1?.l2(I-t)+ ~~"rr~r-*l FLOW RATE Q=i"'vd~= h (I ld~)= l<n.h_ A"Ph 3 o ..b 2 12p.L HENCE AP= J~f L [~h - ~ EFFICJENCY: (il~) '1.= "POWJ:R OUT = I' 62 P) -POWER'N llR(L (-10)) To IS SHEAR STRESS ON FLUID AT THE INNER WALL, -r;; 'S SHEAR STRESS ON THE INIJER WALL. 70 =.",a &1 =~~1l_ API, - dy Ilj=o 11 2L THUSJ 12~(R.o.h _ Q ~= G. 113 2 1 .a~r;u1?.Q. +!1.!!'~ Ql L h Zt~z-1 ~ = 12~ (1?~h _Q) Sl.RjJ [¥+ tr~h -Q)] "(= EE.. ~~h -Q) "R.Q.n [L.JRSlh - 6G.]
  • 52.
    SHOWN BELOW' ARETHE' VELO- CITY PROFILES FOR 3 CASES; ~ =-1 IS MAX. Ei=1=IClENCY 'RSlh 3 ~ = 1 IS MAX. FLoW' @ ZERo "'R.Slh 2 AI=> I· .6 .tt .2 <1 h Q=O ruu, . -:(1 -.'f ~2 0 .2 .1 .6 .Y 1.0 V -RQ 8.10 ~QJTk"6~ ls- (1~ ~== 2J (V--P~PJ6 t::) A}.JA~~ Of!" ~ta.c U 1m=; ~ A~~Y~mt;; ?~~ 51Ax::l5TI-tG IJs:r 5
  • 53.
    B,17 1 V ~~~ -- --~~I- l'A'S S'~ Tul: A1 1-rl' r'rlrt.. " L_ _. 1_ - _ L _I !VET ~lC4L . I I t { j ~'T~ f1..vx.- t ; Ar l I"S~ SO Lf::tD i: W'+- 27f f( fA.t- -1'cr"r'l{ Lxi r.O rt.(r r ~~ II 2. S(j 111( Are 4Fra--rA~w::tlKG LMtTAs Ar~o J<A r --t d (rT):O U dr to ry ~ dU;lcir (. "" /'..-.. :. ~y'G i !1'""'~~o.lJL.Lb ~! AL,J ,j~-,~_ VV'~~~. 'jCJ, t 1.~ £L r%. "2 a~~ U'2, / dr- AT ,-"z Q{ h 40;% ~ / dr v t.4US pra::z ~ ~e~n):'r) 1~004~ ~w Wrr'i q(Q)~ ~v:zr7 Ufo % 2t(c~1h).~+~O-4) 52 8.B k- % QA-VL.-/ ~ z LTIM)Z 1. tr z ,,(e{~ik6+~}1-e(~,~) ~ ~ 21v ~z ~
  • 54.
    '1.1 CHAPTER q e~ c1r r (I) +&~~!.:dV =0 [c~o.n)dA ~ PVr(~iI'"A(:;)lr"~H' -l'vr(~r~e)lr +f'l9(~r~Z)/GtA6 -pVe(JlrAi)le +pV~(r~~r)Jz+4& -p*(r"6BJlf)J z L~ fJdV = E.. p(rAGtirJlZ) de JJ c.v. at 5lJ8STITUTE INTO (I)I D'V'D~ -sy (r A,edf'A Z~ TItEIJ TAKE' LIMIT As Afj 6e~ A~ - 0 !.S-(rV,.) +..!.. ;>Vs + dV2 =0 r (' Y' d9 ac q ,. I" ,.. ~ .2 V =Vx ~;c T ~ ~ t Vz fC.~ t'7_~ fj dn ;}".. y - ~ 1t.)C + ~ "''.1 t aZ eJ (0· V) = Vx!x(il( .e;r)+tI~~(~.~) + Vi!~( ez -€i!} NOTE: ei' e~ :: 0 IF i.;I~ =, IF i. = i :. (fi·V):: Vll'~ t V~~ + Vi! ~ 53 (0· 7) TELLS TH E ~ATE Ol=' CHA~bE "DVC TO MOTION. ~D3 , 2 t CONSIDER 2- DIM. PLOW CHANGE'S IN VOLUME =(1'2'XW) -I - ( i2 )('32) ./ 12 =AX~ 32 =Ay 1'21 = A X t [V)(J<tAXJ y) -Vx(X,'iU& 3'2 1 =4<:!+[V'1(X+U)y-tAY) - ~( X+AX J y)1 At Q2x 3:2.) = AX ~y 0':2') (3~ ;).') =JlXJl~ +[V~ (X +t.~ ~i-A'1)- V~(x+lI.)(J~l~x~t i-[V1(XtAX,y) -Vx (X,!j)J~~~t -1-[ ]At" TIME RATE or: CHANGE OF VOLUME AT A -POINT =lim ~ V t~}+o AX'A~ .1l1t ~t :. t=1.UIO VOL. CHANGE =dV~ +dV", d 'j G;)X ='I-v "BUT v·0=0 FROM CO)ffIt-iUITY.
  • 55.
    42= ~o +d r dO + de ;;0 dt ~ di dr" dt de ~ = ~V~ t 1" aVe p- + v. aedr d r ,- ~ r -e r W -T Ve~ie dr ~ -= ~ ~ +aj~ +Vt"det"+ Ye~ dB ae I'" ae ~ ae ~'-' ,.. ~-:= :;}er ~ = ee~ = 0 dr ~e ar dr (}e,. = - exslY'e t ~ case =es()6 SIM'LA~L'" 9€e, =0, dee =-er, d(' ';)8 HENCEI i' ~ = ;;Vr i(" -t dVe e dr dr ar Q A : = (~ - Ve)~r i-~~ t-V0 ~ FoR Q.? To BE 'D V; ~ = Vr dt bt dt de =w =Ve d+: r .•.-:g2 ::. ~ -rIV('dVr- -t!!dV,. _~~ I.. ~~. dr r ~ rtr ~v. ~VB r V9JVg t vr Ve)~_ 'l r Jr r;;Je r ""'S ct.S USUJ6 THE n",COMPRESS'BLE Fo'RM OJ:: "THE NAVIE'R-CST~ES EQlJS; D v=§- V1=>+ vV2 y Dt" P a.) FOR SlWALL V; ALL TE'RMS OF ~( %f + 0 +vv) ARE SMALL 'RELAnVE' TO THE' orHE~S ?RESENT. l,) F"OR V SMALL. I3UT V LJm6EJ. TH£ "P'Rot>CJG"T at=' SMAll V AUt:> 2~ ORDER OF l-AR~E :; MAI{"BE SI6~IF1C.AklT COM1=>AR~D TO THE REMA/NltJ~ 7eRM5. ~ =~ - 1. V'P + J V:2 0 Dt P ifT Vx~~T ~~ ='3x -;~ () 0 () :2 :;}~v. 'V Vx =~ = 1 2P ~'1~ ,.u 'dX ~=J..~Cj+-Cdlj j.J. ~ I +v'V':Z~ ~ =-L Q)P ':12 +e, <j t C:2 2)-' ~X B.C. @ C:j =:tL ~ Yx ,0 ~=O C2 =-..L ~ L'J. ~"" ~J( :. Vx =..L BP (u';l_L;2) ;:?~ ~ .J
  • 56.
    'V. V= 1.£.(w"R 2 )=W'R:ld(,) - 0 r Oler r- --y:- de r - :. CONTINUITY IS SATISF/E!:>. 'i.j Vp=:¥! +~£t' = - V~ Dt ~ d<j ~~ o = -V;(R, e9j~)= Pc ve-~~ ~ p AT ~= 100)000 tt-) V= 20) 000 fps: I2£ =~~ 000 s+-/s Po e.-1I.91S" DC- 22., 000 ff: a = ~ (O.OI06)~ = a ()o96 Po s 55 +'i]-()J~:)t 'J.~ VVx ) ,.o[;~)( +~ dVt! + V'j dV", + VzdVi?l ~x ay ~i'J =P9x - ~p - d I2 IJ/~ +;~+-~~ ax cfll3'=;lX' dCj 9r')J +.£...(,ud~) of- C1 (.u a~)+~ 1Md~) ax ~)( ay (}X ~l ~ W i-!x(M~)t~(Md~)+;0~) tJOTF: JHElJ 'V-v=0 } A 15 CONSTAt-lT "TERMS ' ~ ~ (; ).{V- v) f '7. (M¥X) AR£ 0 AND TERM ". (~'il Vx ) 'BEcoMES ).).'0'2 V.x. '1./2 GIVEN: f ~(rVr) +~ ~: =0 0.) f~ Ve=OJ ~(('v,..) = 0 .: r"'Vr (e) =Fee) J Vr =F{e) r b) IF Vr =OJ ~Ve.:: 0 -;;8 Ve =fCr)
  • 57.
    9./3 FoR THEINCOMPREsSIBLE LAMINAR CASE) OV ".. rli:) J 2- Dt"=g-7+ V 11 FOR 9 NEtSU6~LE') "D V== -yp ... Jv:2vDt I' VECTOR "'PRoPERTIES DETE'R- f.lUAIm .'BY V EVP wHIC.HI ~ ARE IN"ITRDFPENDENT; i.e. CAUSE i EFFECT., .: MLJST LIE IN SAME -PLAN~ La') IN ABSENC.E O~ V/SCO()S FORCE'S Dv _ -V? -- -I:>t .fJ Dv ~E'7E?M'NE'D 0"1 -JP~ Dt J HAS Pes/TIVE SENSE 6lVEN , "BV -VP OR DIRECTIoN Ot=' DE'CREASIN6 -PRESSURE -b) SIMILARLY" ANY FLUiD.... '5TA11C OR MOVINq.... HAS nils SAME' 'N~WENCS e WILL MOtIF oRI TEN'D To MoVE IN THE DtR~CTION 01= D~CRf'AS/N<S 'PRE'SSVRE • c) 9.1l/ FoR I-DIM STEADY FLOW; Vx = VX' (X") V'1 == Vz = 0 NEGLECTINg 9) pVx ~ =-pof" 4. [1.lp~tf"J.{itx dx (jX <.it [~ 0.)( J oJ( 9J5" COI>JT/NUITV: ~ t :x(p'lx) =0 MOMENTUM: p(~ +V)C ~Va~: :tf l'cu ax) ax 9.1" Usu:4TwG; .c ~(()kJ A~ ~rTtVG 'O:wAl ~ L1?~20 AND ~:: t<r) EC( E -~ y.!WS z direction (a"- .~ v. ~ ai)PWc+ v7ar +~+v,-r; ~ [1a (av,) 1¥or2 , ~2'J=- +pg,+/J- -- r- +, + z r ar ar r 0 9..17 A5$OM,W~ IN ~t&ea ~WJ(bm(}.J()rrY ~ Yt6t.PS rU"C :::.~~ l.J~GLS ~2~=O ~ E-4 TI!5U'S r direction rt' av, v.%t' i ¥Z)' 0 ~~p +v,-+- - +v, t ar r 0 r z iap il 1 il 1 a , 2 • i,=--+P8r+/J-[-(--( ,))+,a7{_~~+ij;,]ar ar r ar r Iii? ryao Pz
  • 58.
    Tw~&~ ~ (P~3lYi)~Jqr or 2-0 ~IB 2 Sf.t1(.oTw @ % -lfe e,., ~ dt r tre :zfCr) ~ trrz~ -z0. U-sUKt ~-6"~/~ T~ TJ.tt5~ .-sTt«5 Lgr W~~(Dg ~Tf4tS E"nli£r-«»JS ~. , direction ( av, av, v. av, v/+v av,)-+v-+---- z p al ' a, , aIJ, az ap [a(1 a ) 1 iv,_2 av.+iv,] = --+pg.+/L - - -(rv,) +,.-=aIJ ? iJIJ a?a, a, , iJ, , 9.{9 ~ £;- 5"'(fS.DS IJ direction (iJv.+.LV'+~~+~+Vz av,;( Pat /fiJ, "iJIJ /, Tz) laP [iJ (1 iJ ) ~ 2~+1z!J= -- -+pg.+/L - - -iJ(ro.) +,. () +? IJ z .1 iJ(} a, , r , ~ ~ &~ ~ %(je~O W~ ~ % peJi e..(n~at or:1 ~ ~)) 9_a? A~<.we: ~y t1..ow" ~~~~J ~[.L d. (r LJ~)l -:.D dr r dr 'J ~ .LQ...(rtJe}=:~ ra-r ~~ 'tJe ~ ~I fur ..... Cz- Ar Q. LYe ~ 2.12.-.1 /tr l4 L1~ I4..a~ lJe".!fe~n,t(Q:Q2Q~OJ~~. r(' )..J?~~,
  • 59.
    CHAPTER 10 10.2 b...;;.~~r t3 ~ tt~t Wi! = ~ (0( +,s) cAt. 2 : lirK ifQ.r1-'1(rv81rtAt"-r~I...) At...O r Ar At: .At .,. to..n-I (V...le+A8 -Vr!e).Ai Jr'Ai9 IN THE' LIMIT,' TAN ~=Z G.;Z =li~ .J{rVgl r+Ar - r~rr) ~}....~ Ar t.z - Vr 18+6.9 - V...19 rAe 5e =1 ~ (rVe) - 1. ~r ;;r r C1e Wz = ~V9+!(h _dVc)." Q.£D. ar r' I) ;]9 JO.3 d '1'= -~dx +vxd~ == -(VQOsirtoc)dx +(~cosoc~ 0/= -Voo(sirlol.)X + ~(coso<)~ +V'o Ja'i V·O=1~(rvr)r..L~V9 =0 r ar (' ;;6 LET r Vr = ~lP ( r'~ 8) ()8 V'.O = J..r~ (tl) + 9Vsl.= 0 r Lar 'as O'6J ~ (9'1' tv.J-0 . I = -.g]J!- - 9 - •• viii ~ ~y- -ar :. Vr =~ ~: } Ve = -!f :. Q. E. D. la~ rb 5 3 5 2- 1 -:: -- X. - xY B.... S~ lJ":z V0/J {bsnJ.J<XTY &l (s v..Gzo DJZ Vf-:'O Ust~ ~ 2'1 + P.l ~O ~' ayJ/ 0)6 - '0X ::30{) lL 2 ~ := Cl!P. :z 5~Z x ~ ar
  • 60.
    /O.b IN CO~Ed"P _ "v~ i.e. w--p'IW " - - -tr-- - ()t Dv:-V:l.C,. Of: r dt' r V= Vmruc i "00 ?l~)-"P(o}: P UM~{"Rrd(' =e.lJttt 2 1(2. Jo 2 I1?ROTATIONAL: (r ~ R) 'P + U2 : 'Poe, p 2 P J '1= Vt'H'"R r PoO - PCR) -= IZ u..,.2- 2 THU5.1 "'Pot::) -1(0J -=,tJ Jw?· So :. U 2 =~fP =- ~ VtM=126f~ ,.0 .002<f a.) MAX. WIN]) YfLOOTV =126 t?S b) OSIN6 ""BERNOULLI 1=>00 -1=> =!!~2: I'~~(~t-=IOpsf pUm2=3~ .... ~ : "$l =J.q 'R2 20 f.:: 13=1.5' SO T/rvtE % (31'.5: 131.5= /.5'6 5 V l? c.) IN CoRE B -=P-r ~J.=r:jP'; fJ V2. = P1'".r: -= :3~ r-t Ra "R~ "Po =(2116-3i ) +-g~~ Po = 211' -3'l (I - t'.t/R~) VARIATION = '3"'8 'Psf 59 10.7 VI' = '/oe CoS e ( - ~~) ALONG STA6NATlON STREAMllfltS e=-~ ~ Vr- = -Jo,o ( l- ~) b) ~lf' = -2 tLo a.a 9Vrl _ -2lbo ~r --;:-3) ar: c:a. - T 10.9 "Pi" pU2 = CONSTANT 2 I~ ~ -=+>00" V2 =Vo02. HENCEJ Voa I -= vel:: 2 b,si)19 sl~e =.5 .". e%!30; ! ISO O 10./0 a) <p =V... L [(::f-s:tJ o=V rp =VX' €)( -r V~ e.~ VlI == ~ -= :3 U ( 2_u2)=a;;)( ---e >f -' ;)u L-~ J V'j -= BaS_ -6 Lbo )(9 -:: - ~cp ~~ - L-:t ~x 'IJ-= g ~ ( ,.,2~ _~) 1- f(X) L2 :3 '"= 3 VoC) X.l. 5 t- '1(~) La
  • 61.
    WHEN '-P=O j'1=0 OR <j =!".J3x ----l-----":~~x 4/::0 b) ¢= u,,¥! Vx =- t} ¢ = u., 'j -= ~ ax T ~g ~= ~ =~X' = -~ afj 1: ax ¥= ~ u 2 +f(:xl ' 'P= -.lx, )(.1 +~(u) 2L :l I) - 21. .J WHEN 'V=O j '1 = :t X ~ '1'=0 ------~+H~----X c) ¢; = Vca L 1M ( )(2 +~~) 2 Vx = VaiL 2x _ d lJl 2"" )(2.+'j2. - Olg VCj = VooL ~ --21 2 X~2. - - ~x 'I'= ~ ~o.."-f(.!i)+f(x) 2. x x IV =- ~L ~~ to..,-'(~) T <3(<j) :. 'IJ= Vd)L[tcl~tl(t)-io.n-I(~~ W~£N ~=O .) x 10.11 Cf= 2r35ln~ J ~ e:J~ '# 0 ~:D(Se~fc 3 Vf(:)TUQ) LQ 'f~~ (6r9A~04~ +~~) ~ ~ ,2:r~ 1~ ASQ-ULtS 2s~~ 8/~ r ;'PLar '(' lO.t2- t-0 -= lftD r$ln9 + QS 2i 6'(OeFlAJlTr61J r~OJ ~ If'! ~>o f:ao Is-W& lwe. 8=6 .e:Tltl; ~v,;; ( Ax,$'. ~ li_~O (f"~ ~ G:;irrTo L~) I OIJl; GB"~ Yzee ~ 2~ Q. St,0 '( Zilttl r~2IilMit(.a e-+o ~w.e)
  • 62.
    10./3 ~VRCE ATORI61N !.p= Wte p2Tr m== SOURC.£ STREN6TH FREE sTR EAM tp =Vc:o y TOGETHfR tV= Va) g t- ~e 211"1' Vr =! ~tp =VcO C05e +..ttL ,.. ae :.27Y'r ~~ r'sine Or' =0 @ $=11 AT a=71 r= ~ _ Q. zrrPl.4x,- 2'ii~ lall.{ As ~iP = pDv Dt =pBftV(~2)-o. (V'xv~ /WD FLOW 15 STEADY AND lR'RoTA- TJONAL I Vp = -Pl (~) OR v?= -p vVv BUT AT STAGNATION PolNT v=o HENCE vP=o 10./5' LIFT FoRCE : F~ d,cj = d 1= ~iV1e = CR '..1 -~ t ." mosiYede1~lae . t'ov ~10'.e) '"' (ir F~= Jo (1=>~-BYR'5IYed8 FROM BERNOULLI EQUATION 61 -p +tpv::t = CONS.TANT 'Poe t' f p uc%)~ = -p i- f pV2 O~ TUE HUT v= 2 (/a:I 'SI'rtlt :. P="Poo t-! PVoD~[t-l{'5;",~e] F~= ro£t'lleo2E-l/~;n~~+45;~ 'R~'rle de F~= 2 f' 14'Rr'LSin~e-~iYl~Iv~ (;) de F~= 2.Rp~ [j- - 2'5," 2eoJ ~~ =0 WHE'N 10.16 ~~TIDkJ 1blJ:r'S tLc~ S~ Bv QacLe.5.
  • 63.
    tf= - Ie(~ r ) ue =~ l.J~6,lJ Z'ti 21Tr Ol2(qw 15 Itr krtk:. .~ ~ f(1,o) ~ K ~ K. Z'ir(2a) 4~a. ~ Lfe(-.:tJ0)'"-I(, e~ 4tT<l A~ If(a,O): -1 e47f(l. tf s;'~ 'f -= +~1r VO#!J'Q(. ~ -t:t. 2.'iT G2. f h. -.1~___~--L I ~5~ )6 Sr.tq.u..trl~'G/Xj <1- lfa>rsut6 + ~ 2'rr 0. _g..~AnClJ -g,AJT O=-~D ¥1~s (Jr: ~2D lJ: =..Lo~ _l.(~ + I.[r~ r r W r 2IT ~ Y 0: ~ - LJtp := - If. ~v.tb e:> or c:IO ~10 e~1T) ra:sn =k=- Q. n~ S, Ar ~~JJA17o.~ VDlAF )("Z -~ -= - l.~ :::- D.02~j.t-... '(:() Z'i1 tTll) Z'il9 b. &py lJ~(Gl~ Sr~N.crm ~1...Ll& l.5 ~-:! I5QDrStnTI + Q1I -z ~ 2it Z . ~vs ~ ~ ~ rSUA<9 +-~ 211 WH~ e:1t~ rSUA8=y:z.. i?.J~ -~)~ $.0.007"1
  • 64.
    C. A.7 Lt~s?~6.~ ALLTf«; h.olV b~AT (,)0" W~ Q=~(2h) h:z ~ = I.q z D.Cf>33W 2o-lt) 2-S d~ tv1Axl),AJ.,W) ~ ~ '0,22. .EIlMM~ '" V Ple) ZE,=O d ,.GlT, p. ' GT 11 O-I:tr- ~1'P5Ilt8d9 =0 o 1/:~TM +~J(~:-U1-~ LJ:-2'tsm,.g « Iff"'~D ~M~~')p.jlf2Ijfs2eJ9 I~T ~ (~. -~A1t''D+.2. O{y"z.. V .,J' ,j (, J ,LV ~Oza 1.257~N T ~ 10. IzN
  • 65.
    CHAPTER" fI.r 1) (1..)cv ( 'Ii;) 11.2 p (MIL') Q (L~/tJ H ( L) n 9 (L/t2) "P (MLYt3) i =rt- r =- Z- 3 =S" CORE ($ROUP (p I "OJ w) 1l;=t1 (8Y INSPECT/ON) 11; =fQ, DbCJc H . V D P (LIt) (L) (MIL') t= 5"-'3: 2 ~=~ CORE GROtJP (D, V, p) n; =Dc4. Vb fC,)J.; 71i=Ai _ 1- r;rvjJ - 1Rc 7T;.=DQ, VbpC: e ; rrr; =L I> 11.'3 ~'P (M/Li-a) D (L) P (M IL3) Q (L3/-t) w (I It.) )A (MILt) t: 6-3=3 CO"RE 6 Ra./P (P.I 'OJ w) r;r; = pa.. DbWC.~""p ; 11:= A'P I fJDV 112-= p q Db w G Q j ~=~ 'O'3w 17; =f' a.. Db W c,,.a ; 77;= ~ PDaW I/.¥ T tC4 tjI L ~ BV GEOMETRIC SIMILAR/TV: d =.J2. v= J.3 V .I L 7rcl2J =..L 'Tl'D'2.L 1)~_ 31 _ 3d i/ 3 '4 d2 - L - 13" :. ~:: (3)~ :: J.I./l/2'" a.) BY 'DIME:.N SIONAL ANALYSIs: ~ ='DQ.wb pC 'P I= La. (Vc)b (MIL~t MJ:~ -c3 '-t=-5'" b:. -3 c=-IJ :. 7(, = _:Po.--_ ,ow3 D5" FaR DYNAMIC SIMILA'RITY: '"P ( --P Ip4.)3"C~ model - ,aW3 D6 proh1:'jpt ~=[~ ·?f·jff.r3 I 3-$'~ =(3.3-~/"3j3 = 3-2/q :. l.)p:. O. 'T13........t - - - - - 1:,)
  • 66.
    11.5" MODEl "PRoTOTVPE DD ,,1> V V 20 knots p p p ).t A M F /Olbf F A 1)2 (bD)2 FOR DYNAMIC 51 MILARITY ; ~'" =1~;p ) Dvpl == DVfJ(,u rtf A- ? ~:: Vp(~ .fI;. .¥t)= 6vp , I I .: v~ .= I 20 Krto-t5 a.) ALSO FOR DYNAMIC 5IMlLARm' £u.~ =EtA?· ELA-I - fAIpU2 m - ; V" ? r?:: F,.. (}t.%.ti)= F~ I 3b J.ri. :. Fp = IOlhF /I.' VAR tABLE C~o.x 0( S M L p 9 1< Cmo.x 0( f3 M L fJ 9 1< M O o I 0 I L 2 0 0 0 I -3 , t O O 0 0 0 -2 0 .: ~ = '3 -.....- - - - - - b ) l= n-r' = Z-3=S .: No. OF" DIMENSIONLESS G'Roups ::- 5' -~.------- 'iT; -= 0<, 112 =/3 'IT3 =M0. LJ., ~ c C¥MX I =M~ Lb (LlP')c ML)lt ~ a. =-1 J 10= -/ I C = -/ 1TS = C I'Mtl.X ML~ 1lq = ~Q.Lb~cf ; 71S = twf' Lb~c 'R ~ 11~ =1::1- 175 ="R-c.) L 11.'1 IRe = L V J, = I '2..&, ~L .10-5' ,..,4-1) "llIa.,.... . oJ 70 5 @ 2iOK (~'1.6°F) a.)~ASE'D O~ LEN~TH ~ = (r:s.'1X22.2)(/OS)=9.21_'cP J.'3~76 b) "BASED OW ANTE NNA DIAM. Re. =6.1/ ./0-3(2.2.2 )(102- 1.3¥?6 = I~ ;16" (1.97./0'1) /1.1 JI. =COIJSTANT ~L '/::a. U 4 .."., - p ---'-m Lp
  • 67.
    (~) =~; =0.1 --.1"", =_31 b V-p MODel SPEeD =31. 6 dlo OF S?E'ro O~ FULL SCALE SHIP. 11.9 RJR SIMILARITV ReM =~FULL. SCALE T£MERATUR£ NOT GIVEN,! ASSUME 'H2 o = 10°C JH,.o = I. 3x/o-6 W1~ 'MR =2t;OC JAlR ~ ,.":>(105' ~ =2.'1'l>C10-6 wsl ~ LV I -LvI .u. -,I J LJ - IT .. ,..- vF.s. ~ F.s. ~ h~ .J LVF,s. m Um= 1l,·2.4Cf·/o-6 .q :: 122.3~ /.3 ·10-" 5 F"l. = .0262 hF.S. 11.10 NAV/ER- STOKES EQUATION; Dv = Q_ vP + )) "12 V 'Dt ..J P NONDIME'NSJONALl2JNG; VC)C)2 DO ~ ,.. P' I ;2 r7"~ - - #' = S - VoO v r" L Dt ~L;:"'P~-- 2 + J Voo2 V'.,. 0:/1 La DO~_ 9L v¥p* J v~ o~- - -- +- Dt* U~2 L~ ~ = ..!.. - V~1l'~ ~~ fj>Jf: Dt Fr 1t?e. 11.11 SYM80l.. PIMEWSION MASS TX COEF. K Lie 'DIffUSION CQEF. D Lo/t DISK DIAM. d L ANGULAR VEL a.. /t DENSITV p M/L3 Visc.osrrv » MILt K D d 0.. P M M U 0 0 0 I -:)L 2 I 0 -3 t -I 0 -I 0 -) r:'3.1 V1=b, i.= 6-3=3 77;= d/o..~pnk; ~ = K cia: ~=..D. cl2 a <"i73 = olAa.Vp~. rrr;=~ =_,J f'd~o. my I'" (K.. I J;L )lReJ) =0 .. a.),. da. d 4 o. VAR II 0. AND/oR d Tl-IEij ~oR FIXED VALUES oT: ~ 'RoT I:>Af;1Q. vs. ~a... b)
  • 68.
    IU2 SYMBoL PIMEW510N FLOWRATE" Q. DIAMETER 'P 5HA~SPEE.D N VISCOSITV A 5U<F. TENSION 0- DENSITV P o 0 I 0 o -/ L?/t L I-t MILt: M/t2 MIL:!. r =3, r'l =b J L= b - 3 =3 CORE" GRo()~ -= P N1) G 11, = pa ~10DC Q ----=-ir, ="ft:>:' '112.= p~NbbC,L{ _11'2= pND~ "M 113 =p~NbDcO"" .-113 =pffiD3 11./3 tt L -t M-rn M 0 0 'D- L D 0 I 0 P - m/L3 p , -3 0 9 - l/t2 9 0 -2 (7- fVlt:1 r:r 0 -2 BV INSPECTION 67 Jl.1L( M L t V 0 0 -l L 0 a 1) 0 0 P -3 0 T I -2 11"; =L/D ~ =~"J.pD2, T :. nD'W =t ( LID) O'R V L Yf -= f (LID) II.IS" ~YM. PIM. POWER P M L2/t3 DIAMETEJ< 1> L RPM w It: VOLUME Q L~/t DENSTY P M/L3 I'ISc.oslTY M MILt r=3 Y::.6 L=6-'3=3 " J CORE (fRDt)? : "'P"DP ~ =-P"''D1o pc. W ~=-pa.DIIapc Q ~.1:... II. =pD~4i 'IT = ~ 2 P <;(3 tLl6 FOR DYNAMIC SI MlLA'RIT'I,I) ~ ~ :.lRe. Fa L...L ScALE :. tFlM == UF.S. LF.s. JM .- r Jt=:'5 • VM =60~(~)F.10~ =2LfO r)'ph 2. 10-5
  • 69.
    /I. 11 AS5UMIN:S/NVISCID EQUATiONS) ~ DO = -tiP +PS Dt MAKIN6 EQUATION DIMENSION- LEss: V := +(~ )t ~ I ~) t£o L L ~2. OR JL = f(>< t~) 'f;L L"J L ~)5IZE" = 2 "" =.005~6 ~ "360 VELOClTV 1r _ J~ ~-~ Vm: ~~IA60 =. 422 ~/5 b) TIME- t: Uoc = canst. a'R 1:- 1:. L '1.0 t*- _ Lwt ~ - Lw.j.Le. -.l- f; - L P Vry. - r; LW' - J1. <i tltt:: ..!1:. 1,,. = 3~ Hti..,. If.t:t II.JZ IRe. mode.l -==~ 'Pl'oto~f:e. I'M =ArM. vp L? A PP VIM L.W ? OR '"Pw -M =1)401 )1"", vp Lp ~ Tp ,up v-,.., Lm 11./9 I=R =~~) r = &. mode.! ~(( SCAle V :2.sr""/s L O.lfl n !2. '15" ~ N 45'0 rpwt v"" =~ lM =O.qc;q V 671~'V L I J::S. =.~ ''5 F.S. F.e;. b) TH-~05T: EM =E~.s. ~~a ) Fr:s. =F)I p v~ F'.~ Af'S pv:Lto PrM FF.S. :: 2'lS (,. ql./)(-..-L )2(:2.ct5'12N j.q'l .'10<} ~- .~I j FF.s. =SZJ '300 N ToRQUE: Q --= FL :. QF:s. = QM(F"•.v LF.~ FMA LM QF.S. % 20 (5'~30D) (-:2.({~) :ailS . £/1 ) ~ 25',5"/1 Nm
  • 70.
    1.20 IN he$r~NT(,~/~ IsW~ g W=-7f+)AV?ll~ -I) f.!1t$(~ l£~ o-~ ~ u-/~;t~ v;,-l/L Ou;~AtJC r "- - ilt: QY.E.. ~~z~~+31~~-l) J L/I/ n.+-" «.~(5c::Z)W' C 7D o!.-Il·.. l~ T~ GrO D="THE ~ vrry ~}./To mt. hpzn~ -rt~t ls I.Z I E 0'tcfr2-J I (L) S (M/k1 ) t (T) TIJ~ Is ~ 9IMENSt:)N~"5S q~u? L.. t=.t -~rS We.~ 1,. f'S.,. lz.EtIs @ ~ug 4r ~ Z. tzEt cit S "8r4 12_ ~ /:4.i"2 5 It ~ ~H.&) L. z ('?/~ m~ d:4:~t~ A- Yr~/z,~~---~-",-~~-~ 69 1.2'2. a (/vA:) )1- (J.vLT) J lM/L~) V (Lfr) d(L) V(L) __ ._ /_ f. r7 •.,r;:?.y< ~ I ~ ~~ ~ ~L.-~Lb..JI'" v.uy ~~~ ,let::5~, ~tVt~ l~(O~) I tv5 ~~AJ dJ Oy'1) YD ) .J-i~~ / X> 3~ ~~ il-g W~$ D) ~) Vf() ~7 {JD~V 7, 1ilu:; J JIrD = ,~/ :lEi. )Gli'l 'I /«- 'j'V") 1_'25 5StEW VA2L~.. A?(r!Lz.) ?(~-t!LZ.) Q( L'L/t ; L (L) Q(L) r2(L), "' net-I) T~lJST~ ~LD £Sf; 4~~ VIA {~(D(;; WE UA~o 0/. 2i ~ ') /0 . _ A . .-7 L e6JLt ~r j J;.. ~N h:X7C~ ~ Q6.111;, , i.MrGrow ~TAl.V~Q - ~Qh
  • 71.
    CHAPTER 12 122 "DRAG= ~ pv2AR C]:) SO Df =.!.pV2~C-r 2 ~L>-t =~(.0023"Y1!rfa)(293.33/"(itof 21100 (.011)(.75') Ibf =202b~)(~O~p~} Ibf a) WHEN p=. 000 'T3? ~IUlj5/r;p. V= 500 ""P'1 Of ::' 3Q21./ I~t ( 5232 hp) b) WHE~ P=A, (SEA L.EVEL) V= 200 mpk Df = 202b llof (IO~ hp) /2.3 SPHERE IS SIz.E OFAGOLFBALL 1ReC.RT1CAl. == 2·lOS" AlR @ 20°C J= }.1/9·/0-5' mys ~D= 2./o'ii" V= :;'105..;2,l/ / D If=:J.·/o'!i . f.'19·/0-~ = 70. 9S Wf/S l/2·/0-3 12.l/ GOLFBALL SIZE SpHERE 1)= ~ pV2 PI ~=.l(.OO23?~JJr([;g"'AJ 2. 4 12 =J.?bb . 10-S'"Cn V2 Ibof v= 1ReJ __1R.e.(.ISq)cIO-?) 15 l.bS /1'- = 1.'5"61R~ 103 Vfp~ 1<e CD Dlbf So ?5' 100 12S 1,0 115' 200 225" 2S() 2"15 3CO 325 350 lfOO J.{3~ ?l5"0 .1.11 .021 611, ?'19 .If? . Xb,505 .lft .0'03 108, J3J .11"1 .130 J 29,759 .lIb . ,'Z3 1'T30/0()I) •liS' . '311 21"/262- .'10 .li~2 25'9, ")15 ;"3 . lin ,-ZI/I'I2 .2 ·373 302" ':;{/4 . I .21& 31f6, 02.1 .08 .220 100 200 300 '100 .J -h:>s 12S" ~ TRANSITION c::: 2:/05' ~x =~ J X = JJRe.TRAf.ls V V X =1.l.Iq -/0-;; .2.·/os =0.099 vYt '30 12.6 F/UD V~ @ [[)5E OF B.L.
  • 72.
    v~ =~ (Jxl.OO)~('It'-of)'1.=5 OR~ =2~ (IO-8.2?92)= 0.1" ~ v;Re;c @T= loo"F JAiR =O.ll·163 HIs lRe.)C = x,VtlO:: X"'. gg =~O/S76 x" v 2· .Il) '10.3 x" .s J 2 :3 'IRE-x 2/)J2~ 'IO,S":; '61,031 121,5'11 X" 2 v~ -Ff/s 0.5"32 0.376 O.U6 0.211 12.7 NO, "BERNOULLI's EQUATION IS NOT VALJD IN A'"REGlON OF SEPARATED FL"OlJ. 12.9 Vx = C, +~ f:j + <:3 y~ +C"f ~3 Va- "BOUNDARY CONDlnoNS: (I) V)( f)} =0 C, =0 (2) V't( (F) =VxF (3) av~ (d) =0 ;/':1 (q) VA' ~~ T ~ dVx == -JP +..M~ dX" ~ c::tx 9lj:l @ '1=0 .. v)( =V~=O :. ;)2Vx/ =..L 4P = - I PVooa'4 ~ ':S.2 'j=O ~ d x ;a cJ.x ... - ,FROM 13ERNOULLI EQVAnONV :. ~ 2 VXI = -/00 cJ. Va1 d~.2 ~ =0 ~ d.X. ~$ = C2 (i) t C3 (iY-t C~{Jt FROM (2) FROM (3 ) }=RoM (~) 1= C2.+ C !>+C,{ 0= Cz +2C3 +3C'i -F2 dvao = 2C3 J ~X _-. Vx =- ~..1 _1 (~)3 V1(S 2 $ ;a E' +£2~(~ _2(Y)!f!!~) 4J dx lJ 0 It}/ /2.10 Ix = a. sin bg Vx=o @'jzO 1J Vx = Ve:%) @ ~= 6" v~= a.S;r1bE ~VX =0 @ f1=d ~~ o =Co-sbd:. bF='% :. a = '.100
  • 73.
    .: 8"-= ttxo.lS....----------0.) ~ 12.1/ VJ.= 2 V~ ~ Vx =VE Sir11T!i = 2VQlX SlYlltl;& :2E it u p=~o - 2pt&,2 SIr12B =~-2"oVC: ~ ~ = -L/PVaJ 2 x dX 0..'2. - d"d'P =To + ~.(dpV/'0.'1 dx· ux Jo -Veri)~ pvxd~ ~ = II d vx == 7r)J. Voa>: o r ~ ~::o a. d ~ (" EPv)(~&~ == ~p v"'~t (dX '2. ax )0 0.2 dx)o ,_ eos'Ti::5Lr dg - 2- =21' Voo:2 d (JX'J.) 0.2 c& Vs ct)~pV" d~ = 41' Voo 2 X cI rax"SiYl7i~ d~ 0..2 dx Jo :::zE ::: ~p Vco-:J. >< i.. (d"x) '110..2 dx COLLecrrt-lq 'iE'RMSj 4p"&1{~x) =qreU ~ ')( + 2I'Voa2d(&~ Q.:1 a. t 0. :z olJC - zpv«!..?)( d- (bx) 7rc..'" &x "fret$)( =11A VQ:l'X T ~,I)Val"Xo a.E ?~ - YJllof-$X + d clr~p vco~)C,...!PV~ ~ '1ic..::1 -ax[ a.~ ~o..:i.J IN LIMIT AS )(-+0; dS~ 0 a)(
  • 74.
    12.12 11771/11111/11//777/7/7 ;( X'+dX XF~(( VXpCO·n1tAt~i(<<~~dV Jlc.s.oti).4C.v.""" g~=PJ"I)( -RtI)(t"AX -tP}X+.4X +r1x (J1X -J/x)-1;AX -----:2-- tAX f1.s.vxpev.~)dA -= L[pVx:ld'1xtAX -LipV/d~x - VOJ(~:fVx ~~IXtAX - tdpvxd'j}x -V'joAX) , REARRANGING f D1VIDINq "BY AX: -'PX+AX -'P'~ JIXtAX 1" (Pi XtAX ~X 2 -1' pI -XI1)(tAX -~IX)-T~+ I)(. AX 0 2 == j:pv/dYXtAX - S:pV/dljx ~x -veo i!pVx d~I)(TAX - fa!'~d,:!~ +Voo~o IN THE LIMIT AS dX-O -a ~= To +I(,,~. +ale ~~pV:c!~ _ /, 4.(c3 P~~ CD ~)o REPlAC1NQ J'f =1x(JVCXI~ 12.13 FOR THIS "REGIME) 1<&<:103 1I?e.= Dv @ 60G F J:zlL{t·IO-S"~2. J - J S "Re. =oba Y; ~ =I J '1'::0.001/6 ~5 ~=as '1'== .1"3 Wo/sI .: 0.0016 ~5 ~ V < . "3 ~/s AIR. @ ~o·1= V=1.5"9 ·10-41 er%; R~ = (O.'2/12)(OZ) = Q220 1.S''l·/o-4/ FROM 'F16. 12.2 I CD ~ 1.:2 -Ft>: /'3 '0. .2 )(1.2)(O.O?6lfXIT):J.. l~ 2· 32.11Lf =.SOII"'f- .: Ft> = .S'Ollhr ~ ~ J; ....~..-------- ~ b) VX:' aSlvt 6j "B.c. V.,.(lJ =-Vx[ ~ =51r1rtr;:i ~:x (S} =0 VXd 2~ .:J
  • 75.
    b) FOR ACIRCULARCYLINDER " 'LWHERE Vx$ = 2 VQ') 51 ( 0. } VxJe2._ 0.'11j)( 5" ~ T - V)(~ 0 V,,$ s:Sir15(~)d~) =¢=fSY~~ d~ _ - Si1'I ~ cas~ _! co.; ~(Z+Slrt2~) 5 ,s =.! - J. cos. ~ {2. +S;r'l~~)-SiY1cos~ 15 ,~ 5 =~ ~ - G?s ~(gtq5in2~ t3sin~~] ~Gl2= o.'1f[1-cas~('irl5in:li T3~in'l~li ,) (2XI5) sin' x s;Y~ a: 0.. et.=: o.47)~-casl (~tL('Sil! +3~j,,«*~ ~ VOl> Sil"l6~ a. c) VxJ;2 2 Va, sin ~ As x-o dR. x«a. j 74 = 2'19 /s 6)IRe = IQ.l ::: VD J U = (IQ:1X ISq'IO-~) = .IS fps I/l/~ THIS INDICATES THAT THE EXPRESSiON t5 VALID OVER A WIDE 'RANGE O~ VElOCITIES (AT v= .ISfpsJ IT IS Nor VALID) 12.1'E D -= CoA ,oVco2. 2. 2 =.S-(2. '29XI. 22G)(30) :2 = 631.1'0 N
  • 76.
    POWER = 30m(631.10)= 1095"o.QV s =25". '1l1p FoR b 'hI/s HEADWIND 1D = .S-(2.2~)(1.22b)C36)2. 2- ='109. 6'1 N PoWER :. 30 !t1 (qoq. 6'i ") s =2721''1 W = 36.b hp FOR 6 Y)1/s TAILLJ1ND lD= .5'(2.2'1)(,.2.2')(24)2- 2. ;;: "I(j/. 2. 'HJ 'PoWER -= 30 ~ (L104.2Q ~) :::: 1212<1 W =16.3hp 12./9 L= CL ~ pv2 A ;;: a4(1.22'}(~4.7)2('2.2'i) ~ ::: 1122 N = 2~.2 bf 12.:20 D'RA6 =~ P V2 Co A~ FOR EQLJAL DRA~ AT TIlE SAME S"PE ED <;A6R= Ct,AI~ATE Ct)A~ = .5"(2.2<1 ,..2) -= 1.''lS"M~ CD APlATE = .01 .'iTt> 2. ["iRe. >0'4] '1 .: I> -= l.20J ~ 12.2.1 JI)::: Co A t pV4 = =1.I1(irlb)i (.oo23nXI7(,)2 12.22 3 W=VV= t~VCoAJ2 fo" ::O.CXJ2(9i9 5(~/fP' ?ttO~ =6.ll'2207 a -, ~ ~ W=~ .2b'R·ttJ (lOZ."1).?i(25.i3J £!2:) : 19.~ Yp b W= gEE ~:: 15.70 tr 5>0 IZ.Z3 T ~ F 6 -? "l <.:Ay =UJ 'v -p"? O.{{i8·fO ~ CL. ~:: '{Q:: 139.3 '2.~IiL 7 D,I~-{6-3 ~ =2f)2, auI ~%0.4 b_1kt~~=~ SN'LC't> A12- <'Mi='0 - ??~u..~~(··_/~.) - . __C)...... ~if JD:: o-lZ8I.16(1~.33}i"-ID7 2. i44 ID :? 0 .42 l~f C. LAMiJJAe ~LA$J2. (As D'5d..~ krYtr; END 'at: ~ 12.2).
  • 77.
    It.2.4 :} J}~ 0.16.1·/0 ~~ .S'T4rlTtN~ AT ~ -r7.5·'cfI Va 92J~ frs 2- 1Dz~~V ~~~== V 2 0/$,@ ~.J64 V CD 7.5 10 15 2.{) Z5 .2 gz.lB ~ 12'Z.9( A6 'B4.% .47 2'45.82 .44 307.l7 .10 ilk / ;' Slt1(X)Thl / (~12.4) 1/ I f / I 11> .072- .1014 .(~ .128 .16k,7 lb 1b 1~.2S '2.. lFT:Z~fV ct~ .. C~~! I V~44.7~ L=: 5('2~(44,7)1.Q) (2.29) -z f. 8CIE tJ (W~ (~a::of-!)J If.2~ W:S~ Ot; = o. 52~'b L= W~ ~gV'2,A~CL Ae2 ~.B{ 1~1. / C,-:% O. 224 ~l)5 gQ ~ Ll42 V .Qz{5LO~:: 240 @at/s ~Too kApID.lIJ.t ~TQE.. Is O.372s.}J~ lY Qw~~ Is 88.5. 122'7 S~ U-Y(k',D)iG ..Tm; NAVl6Q- -~~ ~ At- T~ lJtu 1- JL ~ :d?-tJ(Uf~/ 8y1 .r~d)( iJ( Y20
  • 78.
    ~A~3 I~..' ls- lYm %M5W WIND~ ~~·~W~5PmD 12e2kjJ.a:me~y 12e=~ 2 128 % (~+Vt~~+tft.lf:' z ~ ~(lfa>-t-~~tr:(trm~V) -1."-- - 4- ~ ~ l5~L +- lSi,t. T~(p ~~t~tJ...V)+ l(~~J".. ~') Tug Clt~ ~ TD V (S t.~,.~(V~2'(JtDV) lW~dN fu ~mLt; DJZ ~vt;_~~T~ KWl5Tl~ ~tt &-r~ T~~R.u~ ~Nor-~. '~:2. NOTb.T~-rUi; Buz. ~ Nor 'Stow ~1Z.L~ )J ~ 155 77 I= ~fJ~~~jh/(Ja> TI-lOS ZI?e :%.lJ~.lY~~~'~'L """ O:(1~3r) I.,O.I (Iae~2:91t0e i~~ 15.3 2CJl3A:z 044~ ·{o'2. cPs -1. V~d.>* ~ ~-k2 =- 14524 ftko.44It3!t~ ~ v.~ os O~C:1~ _(O.-t; !t~ V45 ~ '~57 _O-s .ft~ a.~" ~7ft(z)(r4S2)~14('87 t!>.~i .0-t; I ak.1?O ~ 4}ffi) b~ £ z 17_ (§;:S 7m~ rlD I.S7/ )
  • 79.
    x 1Re.x dLJ~~~ G4't1 0 0 0 0 . I 2·1()5 .111 0.321 .5" .2«19 I. Jt' I .352 2.0'3 2 .'1Ql 3.SQ' 'I TRAHsmON Pol NT ~=2'ltfi f.JAR I 2. X, me~ 13.S' ~L = Lv =(Y2)(LlO} = -:l~ ZOO J} .Isq .,0-3 0.) TlJRBULENT FLOW Cfx -= O.OS?6 (';f2(x)0.7. efL =J. (LCL ax=O.o!;".f' (L -0.2 L..Jo TX L(Tr2)0)( c;{x = 0.07-2 == 0.006"07 JO.l/51 D'RA6" =2(bJPv2A Cfl: FOR 2 SIDES =(O.~2373XI600XI.5)CfL = s.;r4L =0.0392 lb. b) LAMINAR FLOW eft.= (~~Y2 = 0.00375 DRAG = 5. ?CfL. :::=.0.0214 lb. I = J+n FOR TURBULENT FLOJ~ d' _ O.3'g1 X - (""Rc).2 ~---x IF Y);: 1./ 13"'7 v= Q == .~b =0. 3'1 Hot/s .7 A l((.u;)4. T CALCULATE ~t f Vt ~ -2 r: J J~1';;'= a022 5'f V;< ma.x --~-- VXmAX ~~ FOR THE Y7~ POWER LALJ v= o:Z{? Vmo.x ("PRoB. '-1.12) :. VW~ :- O. £f 16 t1/s ~h1o..x == t:J. 07!JWI J ':::110- b Hil)S ~ H~o L J )-V _ I 'vxmc..x ~tl1Q.X' - I3.2ct :..jJ;. = O.'{It, ~.022!;= o.ori'll!! p 13.2' s a) LAMlNAR SUBLA YE"R ~+= ~ijJ ~ ::: 5 J ~ = tj+)1 = 0.292 n1m ~,",(p
  • 80.
    b) 'BUF"J:"ffi LAVI:R 30> y+ >S' .: ~~)C =I.?SI./ Mtti AY =1.~'2. ~tH c) CORE 1'5"-I.?£" = 73.25'"......... 13.&' MOMENTUM ,- pV2 ENERGY ,,-.JPv3 @1i?e -= IO~ .&-=~·S-Jk)CO.2, 6L l-s i~~~S-J =2. '3'1 v= V«)f(~) MoMENTUM =pVoo 2 f2.(-rJ MOMENTUM nuX' = f 2(iJP ~2 ENER§V ~LUX = f3~) Y2f1~3 LAMINAR; M = sin2.(i 1J)p Veo2 L E =SiY13j~1r)~pV~3 -CL 2 ~ ~It{~ rrt) ..M- ~L &1- Z pVoo2. 0 0 0 .1 .J5'b .021./1/ .3 · 'I5S' .~ol .5 · ?O1' • SOO .1 · Zq .195 .q .qq .t/f E ~pV~ 0 .OO3E .Oqq .355" .?aK .'i7 1.0 l. 00 J.00 /.00 79 ~ M ~ q PV~'2. ~f'V~3 0 0 0 .~:z • CJ()l/ .2S1 .ofq .1./92 .3f1S- .126 .5S3 .4112 ./68 .601 • ~6b .2.10 .6QO • 5/2 .:25:2 .61~ .5SQ ON 6RAPH: ) MoM-LAM 3) MoM-TURB 2) ENER6.Y-LAM q) ENER6'1-TlJRB J.o .X .6 .q .2 OL-~~~--~~---­ () .2 .'1 .6 .8" /.0 M £-LpV•.2 ,~pVco3. r3.Q "'ORA6 =CfL ~pv2A -2SIDE5 A = T·l/O·2= SbOfP- D= ~(.OO20qqX205)2(S60)CfL = 2~" JEq .eft. Ibf- "IRe. = vL - 205·? - 'Z IL/O 000 1) - 3~6'1'IO-7 - J .I • D02.0~ 0.) LAMINJ¥R CfL =1.32X' = 0. OOL/65' ~ D= 11.26 Ibl b) TURBULE'NT O.OS'1& cfj( = (vx/lJf2
  • 81.
    4L:: 0.072 ::O.Oo2QQ ~.2 L 13.10 ~)< =0" COM"PA'RE' C" ~ CfX a) LAMlNAR ~:: S"x fi& TURBULENT s:" _ •3?6 ~ '1" - 1Re.X •2 C;-_ .3=1€,'ii"".).3 LJ ':UJ ~ - ~ If"e :: -"T7 b) LAMINAR Cfx= ~tt TURBULENT CfJ( =.OS''7~ 'iRe)( .2 Cfr _ .05'76 ~.3= S:'17 ef£. - .66'1 1"3.11 Tl1R13ULENT: o _ o. 3~ C _ o.on. X - "Re".2 tt. - ~L..4. 1Re - V.L L-7 T= 2oDC, J=IO-b ~}§ 'IRe 2D. = Lj./OT D= fPV2 Cf A =~ ·IOOO·JIC)O''1·200 =1I./0'7Cf N efL = .00137 D:::r 5"l./, 'l2S" N 6'=.31(;, ·20 =O-W3)')f -IL/.3cm ~.2 Bo eft = 0.0000664 D= 265"6 N $:. 5".2,0 =. S'/O-2~ ::" . 5"em fl/·/oJ 13.12 0.) J"~=1,(1- ~.&)cl'j = ~s:(1- ~) d(~) LET ~ = t{ J~ (. ~1 I ~ = )0 ~ -(1J d~ = 1- lti;- I +YI = $ V1 (rt+lX(lt2) . c) 2 +.E! = 2 +(21X"H'2) e (~)CV) == 2 + ~ Vl
  • 82.
    13.1£1 J; =V,I cl Vxd"i 2) 2 de P 'X d;"t2te et-Vxcr G& O.022S Vd f. I n )~ V)C~ (mIXr1t2)B = vx~ d lJxJ"(2+3"e +- v~ de ,dx 11 j dx MULTfPL Y eY ekI AND NOTE eX! de = %Je 5N ;L deSfil + e5~(2 +3,,') d v'x~ 5' dx 14 n} clx =0.0225 fr~+I~(Y1tiJ~ (~J~ rS./~ LET eS-lt = U EQUATIoN 15 OF J="oRM ~ + 'PC)() U =QU() ( l) WHERE ~} = ~(2t-3"dIAtVxi Li Yl"} r).y. Q(x): ~O.022S ~. IhQ~ "tl)(m-2)j tvxiJ Ux~ MAy VARY WITH X EQUATIONO) J5 KNOWN AS A L1N~AR FIRST ORDER DIFFERENTIA L EQUATION T-IE SOLUTION 5 u= eSA{ = e- fPr.x)clx5~(x>e ~P(lt}dxc(x < WHeAl vxr.s CONSTANT ?CX) = 0 U =Q x -t C..I c= ul){=o I~J" TM£:A<XS»tE1;> A~ tSb ~Tm:.. VIcM~IM~ S1tn>~ ~~ &t~ ~b-r~~ ~v,lk(~~~ ~DtS~~<1~ hJ 8~£·
  • 83.
    '3.I8VlC'''(~yJ=~O) t ~~./Lx ~Vx'L7'l1!...2 d2.Vx'/.f+ ~ y + X~ 2 + ;;y2. 0 Z "T ~VX'I X~· •• ~J(d~ 0 SiNCE AS V-Q ~/~a .. .~ v/(X, '!J) "../c, ~ T C,.~4 t-C3~ ~ ;;;V' I~ 'j=o etc. ~/ (x,~) :>'j tb,.«:j:l. +~)(~ ;}V'; 1 e.te. ~4j ~eO FRoM CONTINUITY ;)V'/+;;Vtj' =0 ;;x d~ So~ C~<j+ •.. +b, +2b2'1+b,3X",=O COMPARING COEFFICIENTS OF X-/X/ ¢ ~' TERMS.. WE OBTAIN bJ=o} ~=0.l C 3 +2b2 =0 HENCE ~:'(XICj J= ~ y +Sy2 + C3XY t- V~I ()(,<1) = -C3 '{2 ... U ... I / - -c C '{3 - c., c.. y~ )( v'j - 3 I ... 4 TAKINc$ TIME AV£RAQ£ VX ..V~ .. =-Cg C, '1.3 t- HIQ.H E'R OR DE/{ TERMS ~OR MIXlN6 L{;N6TH " THEORy fx'V~/ ~ ~2. ~VX =VM (~)Vn -'-oCj ;t"R ~ AS ~~o ~Vx~(;x, c;1~ As Y=>"R ~ vx ~ v"" ~'1 ttl< BZ.
  • 84.
    CHAPTER ~ ru V=~ = '0 ~'~~o.J ·~s ~ (o~~'f ff)2 =l.fK tps RQ. = )V = V.l2'1/il)(I.Ii) =2 q 5" JJ 8 -Io-S' LAMINAR AP _ ,- - 2 r f L V2 . £. = 6 -- -"L - )~ - ) 't P 1) ~ :: 0.0542 A?:: 2 (.OSq:;J~ (1.II)2(SV 0.0'2 32.2 = 66-=1 tbf a q.b3 ps~ R-'2. l'i.2 ~D~.111 2 AP -= 5"ps', Gl)ESS LAMINAR FLOlJ g = '32.f<2 OR ~;p _ L.. 32Jv AL '[)2 ~f - D-r c V=A'P S .Q.D fj'j2 L ~ =lS".I&ttf ~..J. ~IO~ 13.2~ 5'? 32 ~o 2'Y f""ps ~ =~ = 13.2'1'. lOS:: l'3.fC1 Y 12·1 .: LAMI NA'R J:"LOW~ Q. =AV=1l'D2 y;== aOOO?22 CfS 'i c:J oR Q =2. 60 ff~n1in,= "lettS ~~ (i)~N.'3 _________ Ar 2c?O~ ;::-250-" 'D= .b2~ ~ 2 S3 ~ == ~o...~ J "P2 :. 300 <'?~ Q == O. 56 w.~ S J= 4.~)(IO-b Ml2.J!:> P=2'10 ~ /~3. ~ - ~ =(Pow£R) 1t cH o =~V +ffCe.-rfrM.ito P:: ~ [/2.2 +3.. 't 42 +uz p J 2 2 -Or+~dt,+U.,~ p= ~.;.[~¥,+?j;;+~-i:'lf"J 1L = 2 tf .b.}L2 o ~ ff =ff (1Re) %) 1Rt!. == VI) - Q. 4 ~ 25'S 000 -;) - 'iro"'J " e =.OOOlS fl., E:. ,oooo~'{ %=-3.bl~lo[~ +(3~D)~] =: '(,./3 $i :: .003'Z1.{ V = I.f5 G ~/s r2=O,~!; J ~ h1.:: 2(.003~)(2i'O"O'l)(.~s"I)=1:l17 .62 ~ r>::2, -'P. .= 3'00, 000 -/~ ()OO ~ as.;z~ ,o~ -aIO ,9. 'lo~ ~~ =~p~ ::. if.XV1·¥;lO'.Sb ~ 4441 ?= 4'141 (25',2 -250 r/2/":1) ::: '/,413 I 30b . IJ, "'1/5 = ~~ 13 KW DR.. 6"'Q,! hp
  • 85.
    GIVEN "PIPE J A'P-- .fPV 2 - f iA~ P FoR l=ULL'l' iU~ULE"NT J:'LOW, f -= fUNCTlON O~ e/O ON LY THUS ~?_ ~2- P THE t)EA 'BEHIND WATE~ CAL IB'RATION IS A'P. :: ~,~B ~?2 w.~ P. So t..~2 =A'PIIo.O (~02.J p..... wHa,o ;:;0% .:1'D _ '2 (~~ 6:2.'1 - ,'" ~"nc;' 1°2 .- ~ 2t.3J ?o - 7. T..cr -' 1~.5 I 3.20 KM , ~= 6."1 '/0-6 jlM2/s p.: ZOo I K~ I ""~ v='.1~/5 D=.l"~ e =. 000 ,5 ff- L:: 32q DOO~ 'D e = ~~3 / ~e.:= llbJ Doo ~ = 13,Q"? ~ = .005'12 ~ = l/t~1~ p~ t> ~~ ::: ~(.OO51:2)(32q ~) (l.I):2. : ,-:rl J~Y()7 • :: 5".1 M ~ = M~L:: Z'D11L(.'1/)2(1.1) S"~1.1{ ~ ~ =lq41 KW W.G ~'P.: A"P, +- A~ + 6 'ij I) A? MAltv' n> 'P'~E V 2. ~ "i:) J 2- ~+~=rpt~ :z. ,a T t#o A'P. -= lp:z. p ~ 2) 6."PFRtc.notJ A~ =ZK~~+t(f.f~~~ P 2 t;= ~PlZK or 'It! -'cJ '3) A~NOZ2~ :2 u.. ~ PI" _ VEX,T .:.L-+ r - - 2 T2. AP == V i-xfT _vp:2 == ~~(V£~IT- i"p ~ ~ 2 Vp:1 I) C.ONTINUlTV / Al>Vp -= AlOiZ ~VE)OT :. A~::: .?2.(Ap'2_rp -"2 AN:2 I} ADDIN6 T06ETHER ~:: Vp:l fi'"t"2( : Llf b +Ap -0jJ 2 t: :f 0 Aw?' .'J K:= !/ f! L~ ID 2K =;; -a:; t 3.1 +1.5 == 155 t)/e. == ·'=1¥:J,·5'fOb) = I~ ~y '" 1'1.5;<) USIi v= 1.570 /0-5. Vp2 == 1Cfl1 lSp ~ 9.iripc' 35.CY2 +I0:2'-10fr} r FC)R 'DIe. = 1.2.SZt)lR.c ~ 36 12") ~;J ~- ::: }8.35 I fF= .005~1 U:: 9.81 fps lRe. ::::3~09(/~Vp e4
  • 86.
    :. Q =Av=~~i~l~.Ul=.~cfs - 13.~ 6?M ~.1 AP=hI. : 2 tf 1: )2 P D ~ := (4.'15"'1'4'1) = 3304+2/S~ fJ 62.'4/32.114 hL = 2 i" 2S0fjli/6OJ 2 = 31ls" .£± D &D~ DS §.. := ~ -::: O. lOS"," DS 31:2S lR~ =Dv =- D(ui/bo) V 4 '10-" (1TD)t~) :::: Li 75' ., oS D ASSUME ft = .003... D5" =.02 "gt.{ ~ =3.i".2 x lOS ASS(),tt£ fr = DS= .0'3:1.'1 ~= '3."72 ·/O~ ~p = '1K V~ P9 .2~ D =0. t.f91 Fe ff =.OOl'{ 5" .003'1;- D = o. S"OI-l fI- tf= .OO'S<l1 ASSUME "PZ = PATM = lor kPo. v2 ::. ~2 = 16 Q2. A2 11:2. 1)" CK 85 _pA?=2K 16 (i?2 71"'''' Dc{ Q~ 2 'Ir~ D~~ P 712 135' 32 K; 32 (s)SK OPEN ~ CLOSED '12 CLOSED "3,A a.os ED ."3 Q ,"5 .2 "!I .1 K .JS .KS ~.q 20 Q .2lff .125 .055 .02.s'i Yz ~'1 OPEN MODIFIED 'BERNOULLI ffiUATION BETWEEN I fZ 'P. ~ v.~ ={'= ?2 1" y{+ 22 t- hL p§ -. 29 T i'; fXj 2~ o V. 2. L ~ ~::. ~.,..Z2 +Llff -;;1. f'3 2g 0 ;;z.~ = Zz. +- :1 (1+ 4~ L) 2~ C Q::. Soo tS?~ ::. 1.1l c..fs v= Q : 5.b?~5 'D = 3333 A e. 'i<.e = ~ = So 6:t ',S ·,a~= 1.D3·1()~ II I.'t ' - r.:;oo F l % :.1'5'.136 ff =.00 '(q -1'2, = '3' .f ~:l.(it 'I". O~'1' ~) ~:2~ .S
  • 87.
    -P:a. = "S.SI' ~ '"Pz =-~/q ?sf~ :: -'S~ 'P'$.~~ IL(./O ?>fTWEEN I E2 4f"OIA UNE '2" 1)IA LINE I <j('12 -~,)of-V:22_v.2+ 'P:a.-P,::: 0 2 to -20~ T '1/2. + 1'z -?..rrM -="2 P BETWEEN 2.f3 ~(~~ - t;i2.)-t v·i -V2.. 1'3 -P:a. .J.hL=o 2 P 2. a" V3 - V2 +"PATM -'Pa t- hL =0 2 P ADDING : -20~ + V32. +hL =0 2 V"3 =A:a V2. = t4 ~ Aa nL = ( IS • O.? +-J) V 2 ... 2 t; DL V 2 ~ 2 ELBOWS (ENTRANCE ::r~+ 2f JJi"lv2 Lz f Q/,2J == (2.25' of- 6"QOf;}v1 -6'4~ r(2.15"t 6QO)V2. =0 ASSUME f ::: 0.006 • V2. =6£1l4 = 1,2q.5'7 2.i5 r'i.1'1 V::::. IL'31 fps 1Re..::: 0/.2 (U. 3t) '.22 'IO-S' 1Re. = '3.1'10 5 fj:. = .OO~£ -~y V2.= ~~~+3.J :::/l0.S" /: 10.Lf~1Ps ~= 2."l·/o5 tf -: .o~t; Ok FlOW 'RATE = 1F(t fl.1,0.<f9 == o. q,S c f's "'.11 UESTIMATE: VELOCITY USING &RNOULL'''s EQUATION v 2 =2 q An v~ 25' fps (A11 =10') 1UI5 IS A MAX. WITH NO LOSSES USINq hL = K3L.l == V2 DUE TO A 2 2- SUDOEN OPENIN6 AT ENTRANCE (SEE (;c. Ii -p.79) v2 =SAh V= Fl.i-t'P5 2) GtJE"SS v= 10 fps WITH WATER @ ~OoF ~-=b10c0 I ~ tf =.004'1 :1 f' 2. v1 v:1 a~ =Zh + Y.. ='h L ~ +_ +-J I L Z t5'2. 2 .2 ::11(2 + t4 fr~) .!: :: 2~6 '[) (FULLY DE:VELOPEO) 'i~~ =5".<-11 D v-= 't 32 fps (CLOSE EfJOUtiH) Q =AV =1fL~q)C'1.32) =.0 5J cfs =,q.'H, G'PM PRESSURE AT "PoJNT'B ASSUME Z-R O~PIPE BEFORE B Z. + ~ +1r. = HL -+ Yi+;'+ ~ l 2.; Pj ~ 14 I PS ZPRO ON SlJ1<F'ACE' ~ = -'4 - vi -hL =-1./-Y'"~+4t;.!:.) P3 ~~ .2sl" fc : -'1- J.3S'O(3.n)::- -q_2~ ff P"B = -4 'f>'51'~
  • 88.
    V= Q =~ '~'1 :::: 225fps A ~,~ De = i A~£A = 2 '21 -.:: Z''''=."6t1 l' '32 ~ = q~J 3~O ~ -= •0«'5 ff ~=L'333 ~ :: . 005;Z q I1P = p~ "T k v:z. Dc.2. :l.. =.oO:2.3~· tJ ..005'21. 22 (22.S) W3 2 :' ,~?7? }:)sf =,ocHq II U~O '2II H~O -= 62.Q ;:>s.f Iq.l'S CAST IRON e. = .ooo~5 9: Q= 3·/0' ~Qj/do.~ =4.6417 cfs %T ='PoWER COST +Ulrr/AL COST YR ~V'K5 + _DfI (INITIAL caSi) $ - 'PoW£'R COST + .II (INITIAL YR. - CO'!>T) F'OWfR COST: ~ , it'60hrP KW"'r lj("' ?eWER = P. '::iL[ht.+112]25':l5.KW .g(5S{)} 311/3 ~ =.oOl6QS ~GL t/l'~ KW PoW£R t =1.03q~ (~ Ib;Xhl fl75) == 301. OS OlLt 175") ~,. 10" PIPE: V= Q =~,5JO R-/~ A IRe. =(5'1'X~·S)) = 4,3 ~/OS l.b5 ~ 10-5 87 ~ = '1'gO, •.!- = JLI. O~61 ft =.oOSog , ff hL.=4G b V~ =q·2·5"270·'bG22~ o ~ D:;2Srrr2 1)'1 hL =22" Q62.!i = 2QO.3 OS jl = '30L05" (2QO.'3+ 175') ~r +.JI.(~gO'2'll.lf) =S 153 '321 /<:!t'""/ 12" "PIPE v= ~ = 5.9/0 ~/s A ~= ~.~7f·lo5' .~ =1/16 / 'iff::1'I.2!)3 +~ = .OOQ92. hi. = 22962 off :=. It~. 03' !)S" ~r =~oI.05"(.J.n.o3) -+- .11 4(5"2'80.2'1'1.7) =If, IO~ 787 1<1" "'P I'P~ v= <:) = Ll.31..[2 fps A 1Re. -= 3.07' -/05 'D - l"~" .l- - ItJ 4~ fr=.OO~X'Je: - ;)T oJ " 'f.t;: - 1. I r hL =5"/.10 $/ :: 30J.OS(:226.IO) /~r + .{J-CS2"'!o·2 ·'b.n) = ~ B7,&82 /~r .", Iq" -PJ'P~ HOST ECONOMicAL 6" I (C Lf•24"
  • 89.
    0..) SOO<3~W= ~:: I.ll~ cfs ~(7.1/6) =G2. A:.1rD~ A, = O.JQb3 ff2 l{ A2.,=O.lq 61 Ff2 v= 5'.b~.fpS (IN ALL 'PIPES) b) I~ ~ Io..~t loofl~!::: .00171 n ~ = 5~ J= 1.22 'IO-~e. 'Re =~= O.S(:;.6Z) =2.33 'IO~ J (.22 '/O-~ J1'ff =13.1'3 fr.:: .005'8 A'P = Llff ~ ~~ ~=1-f'V:1=3/.'3~ t = 200 A?= l./{.oot;1)(~ooK31.3) ::: I'iS.2 ,?sf 41P :. 1~5".J. p-;.f ;::: J.0041' psi t-HOOlE 200' e =O.OO;2.~1 1:> J:? - ~I fo 'U'l_ =1.6l! ·/oSe- ~ ..L :: 1:2. SCI t,.= .00 6 :3 " ~f L. :: 21"3 t,.'P ='-I~OOb'3(:'X.2! ~X'3I."3) t> =22Spsf =1.S'Tp~i C) TOTAL ~p= l.ooY +I.S? +-I.ool' = 3. Sg-ps;. 1..-.2 ... CAST I1<ON ;SO~ • lAP: ~ .ob7 COMMERCIAL ST~EL A"P =p Lf t+ J:. ~~=10 3 IS-O· 2 v"-If 1:>2 D .:. ~.'OS' V2.+ f =2-' -lOS D 'IRe = Vb =I06 VD 'T a.)D=.2M "~+f=·l<{ l<e. =2 '10 5 V e = .000 !"S"6' 'D/e. =??:z I ~ = 1~.:213./ ff=.005"73 'iRe =>c:o .: V => '.O~ ·/Ol» Of< Q.= 0.163 m3/s b) V2 t.f-':: .0'16 q 'iRe. = b~OOOV e = .000 IS"H "l1'e =1£165 I~ =13. 53<{ ++=>.00 'S~b ~e- ~ 00 FoR ~= .DOSO V=> 3..23 ""'/5 'IRe. :;> aU~JO()O ~ = .Oo4~5 V= '3. 2;2q ~5 1Ke.= ~S/OOO OK, v~ '3.Cb WlJs Q -= O.O/erg »13/5 J~lb ~=~~ L£ fj !)~ - /1 r L Q,'J. - "1"t"~ D 2g (~"D2)'J. =32 ~.h.. Q~ ~.2. '3 pS 1Re. : VP = qG.. II rrr'D 0 ASSUM PTIONS I)RUB6ER HOSE IS SMODTH "D"RAWN TUBING IS o'*' 2) NO OTI-I£R LOSS ES IN HOSE JbooF =I. 22 'lO-s Ftys ~:e. '11'2 p"5 =ff Q2. P 32. L
  • 90.
    =f;Ql. =1. 36:2><IO-~DS" i<e = ~ = 12.5":2.'°5 Gl 7b~ p a.) "'D :=. Y:2 'I ~Q':I.= 2.301 -/O-b 'iRE! =2."S0'/" 0' Q. fASSUME -= .OOSJ 'iRe. = 5"32.10 fCALL. = .005/1 .: Q. == .02. J:2:2 c::. fs =- I. 2 =t~ c f~ .;. -= I. '32S U:JrK/s b) u= ~c./' ffQ:J = Fl.4"6·10-1:. iRe.. =I."6Q _/06Q fASSUME =. OOt.(4t;; Q =.Ob.26 ~ 1R~ ::: IOq" b I q +CALL = .00 1I~). :. Q== .06:2.<f0 cfrs = '3. 77'iI cfW1 ~ = 3.'1215 tlo""'5 11I.1? A r - _ (I) 89 ~ + V¢+eA =~ +~+Z'g -rhl.. ~ ~ ~ 719' EQUAL Pi! -~ =ZA -L'a -hL (2) ,09 ~ = h3 (3) ,.os ..../ V2. h3 - ~J +f'A -t- ~ = ~ - 2-B - hL 1./:1. L - +- YlL = E, -zB -11.3 ~ 2. =- 60 1M %::. 2.2.,., ~( I t 'I tf ~) =30... 1..3=l!'... ~ .ff~ = q(. ooct)XQ = 3.65"7 .3S v'l. _ 30 - --- v=IJ. .b'8 Kifs ~ <f.bS; Q= 1.2l W1 3/s -......I t - - - - - b) ~ =.2S"0 off ::;:> .OO?I " => t!.~S'1 /MIs 'Re. =:~s ·?bSI =3.03 '/0'" 10" . Q::: O. Z3:2 IN3/S I I'/./f T "~~ 1
  • 91.
    AP ="?.l-~ =ffj(- ~l. +Ac) =fJ~ ft' €vl +Pc)Ai! v= Q = qO *3/5 =4.S'i "'/5 A 7r( S..,p. 2j ,6i=> =10 "'f8~. :>. (</.Si)>'4 T (q:fif?X6h"Z M4j =lO'!.f'"?I:2.'1~ t b5f:7.:?] ~ = V"D = (4. ~Xs) =1.''If"tI T 1.3'( 1< 10-5' (ASSUM~ Tft2.0 -:::IOOC) tve.: Iq 6is -L - -3b I f)·9 tl. I - ~~l f.fi - . OS,aU·'lfl-IO" {J.1·J9~I~J J ::: IX .32./ tf =.OO29Z A-p = 10 3 t6'112l{' . OOl9Z +{,£"r1.~ = ,. 35'8 '/03 K1=b.. 14.9 fi!oM ~UbWlI1·'3/tr,:I.~~ THe; 'Cb 4'rk:W ~1'a.oa;e Ie; 1P=Sl,JV~~~?e-P....?e-Z}hJ U L2~ s>~ '-!t;RE ~ to;;T,,~ fAILS" v~ AJJL)~Pta; kr~ Aa .2. -rt;I2M-6y-~ '1, V.t '. t "" V~" (~JiQ,Y/-A~!) 20 2. ~, L T = -2.03~ lie.-90-::(S-)IOS ~ QS.S ~ )lej glOd -c~-2a 111 - 2fD. 0 W" nj..=hL,~ hL'2- W~~ 1)=(),'ZM/ (): (.<69.)~ ~ "2~QVI ~r'h:O.a:v~ ff ~O. ~ ,~bL,~ ~ 17S.<ff", WIIEQc 0:0.42"" lJ:r 4.CAl "I ~ ='377,~g(I e~-;! 0.00:) 09 f z 0.00371J / tL.l-= 291.95 1P:r[-t.03"Z5.5-Z:D+ 14(J}.~ ::: 4tW(24L7)=55l3 ~W AT 25%'~ Dv5rz.. lUes 0,~2."", VrP5.
  • 92.
    14.~ J Eo:; O.QX)(5 e£.,.o.OCO~ gf5f~ s~ I Qz~t;~ tof , ,-/ 0 1. I ~+~+~t· i"~T~~1 ~- P,tJ:Vl ~ 4 - V~ trl SCi '2(3 tY VIz V1 =~ = G_;4Cot~ Ck1. ~ ZS~8~) L~=ZO.ll TuQ6ULbVr ~ HotJ/ J3~ H~ 4.7. ~6)-t<f) K v,'t.. f) 1- Sd •~ +i!," ~ t ~ -tz?,l-kL ~~ ~ ..R 1- ~i=-lO-~-hL rIG ~.7~ HJLL~ ~~~T~$ ~ .e.~ -:: O. et:>42~ ~~ kL:? O.2{S1 ~-v J 2 ~ = -0.81 ~ -2. %~~ J<:! 91 1«5 V,I.." ~ (J,3.?A-G) 1.f4t, ~ "% (759.3/(( + eo.~.v1) ~ ~-z 4DJ <C42 V't ~ --t. ~ if)OLe VI }~u::: ~) C?~ ~-f - ~G~ -f.v :O.~ ~ ~ 37.~ ~/ ~z (;52% ·f(f t1?::o.ro3e49 SkDw ~ t1"20,<XB8.5J V, :%-3£0.~ J ~:z 4B9( ·(rf t1 :;:0.00385 D~ :D VI? %.GA ~~ Q -:z 7.0T5cfs Q ~ 3(7S ~P)/
  • 93.
    14.22- ~14.~ 4P"y?'f(Arr~h+It]gG' 20 ~A~ V ~ ZI( '" (1.3 ~ (0(.7) ~ ~ (' I- A1... tfO 25711'5; ij.,19.';2 lUU5 -z. ~~ ~::2~[et>.Z7~4.~ 1Q~ :z ~,2 z O.()dr.t;; 92.47 z~~5% 92. }4.f~ WJ2lT~~LLl(~) ~~~~~J)Ulr (~~Pe ~ ?~~) ~'--= ~~-~e)- ut~ t30r AI" l~ hI- "''rtf ~ LYV~ ~ t i. ~ t,.:c-l),~~ of 4L' 1,.: {plf, 23 kJow Q=ALJi, ~ :: O.73~/~ T~<& (U ~(073){ T. -= .'3- 2Q:L:= 0 BT/5" f 4 S§; (,(013) , .18 ~ ~T~14.2. Wrnl ~L~~~ft ~ -tt.J tf ~ (O/~ (~ LA~ VAllJfSS. 1"-1 T4flf-J5 14.Z ~ ~ 2LY~) ~ug tne. f; ,:::(J~~?7g) ~ ~ I~ ~ 2~ ~~ ~.2C ~<: ~7.39 f:eTf4t1S~ LetD~( _S~ l1> ~ ~g z3()S J Wb ~y ~~c~ Fbz-ntts ~G Clu & ~.
  • 94.
    14.25 T~ H.a.u '"~ 1t:4~~) ~ ~ =240 1 No ~AeE;CI FIDM fiG; ~4~ 7. 93
  • 95.
    ~t _~ '7G- 'bD F 7 ~~ h f2~ 1-~L • v4S6 ~ -r +~+- 0, 'tF2 O.(Ylg G,QS OlO2.. '::::<- .•.-~~.-~,---- O!81~ T IA~ + %2+ 0,14 l.9'6, lbtuIPtt- {"'T.t.. ~(a,) 'PjIq G.) Ze= '):2,,4- .~ ~~ f,()j,m. b) 3rl= ~14 *~IJ{04 H c~ 4eO# ~/1~ ~ :; 1,94, ~ lrl 3 '-. .?Sla~ ~ /,. "' 6.~M ../ '-.. Q,(P'Y; CiI/I I 1 / ' / ' / , · r/ ?40~ f , / ' / / ///~; ~~s t:: ~Y'=-t;1H:J ,( -<_. ",-.' ~... +S CD f1~""1 @® / 1 -+ ~C;;; !A't~~~ (zOJ0)'=~7Xl(l ~{):o '4.{)~o:;: (4~J(.1) ':1 o,')..g.. ~ l -:.. 0;:::; Ol 100 = <Ot07~~ ~t (l.~'X.J) £'7..;:" 0 ~000~S :. C48 X04' 4~·,'7 Z R.. -= co {l '" I ~ ~ ';l,A,()-'l-~S == C)0Go W 0,1<.0 ')000:;: ~~Tl ~~-:r'Z. ; -r~-13 ~ <. 12.7.. .~ T3-?715 {Zo H~~. ·~:~~U~1j3 S f~.M p{({~00S ~.0&~EM e~ --~o+V'l ~. ?·t:v ~Ct;la'~;i- ~ (;, Ct.)l + L/O,o<oC) '" u, ~.' 1"" le1/9 L.
  • 96.
    SA 19"sc. '1-- 7;4.().f)J,S f)•." - ...-(' "/ . I~-~____~__ ~T ~tf- V'I QI01'L '}oY7";'. ~o-· ';J,S1-'-..S_'·_ OIIIl11 + 14,4·" L L-:;- 0 f O~'I(O v0. -,.. _--- --------.---- f ...~-k~t~ c. U,)S W/lMo,?~S v../~/Jeo~JM') l~9 ::: 0-0?17 INIW~ = b.T/R tq'-;;: Jo'LS (t!S)~ 40s ~ TM~ -:= ~~-' 40'0 ~ 445 ~
  • 97.
    SJ fj I ?CO ' IS,IS ~L 01t; ~L-=: 2.f-= l4GY':'Y4)0l0.1'O~1- ~~ 3.{o ~/w ~-6I.-tCil~ ~b{ ~ ~SS­ ~C:l~M, ~~ ~ k~~'5Os: ~ ~l-x';bot. ~fl6~ Rf6b~ b.Tkt~ 1,Qo -.= ~l3A '-/w) ~3 = _ +-__ - I ~l I~,~ 1~A' ?-/~i~ ~~. tI= IJA,s W ~;f.. IJb.l, lftJ/;;1* '. R,~ "" 0r'~~-= O,~YZ3.)% t, :=: ~f"Ir = OroolOS ?Ti~1 ~ 1. -:;; b (:/"1-. ~ 0 dSirG1- ~l ~,'j.
  • 98.
    g,,( letJJGG'~~ y~L~~- -:;: CoI,1. b ~~~ __ ~~,~ U~ If~~P'~S ~ttlt~ r;40~1.. leW" ~~)(r;X~J."IiXil,'-~ ~=1£~)(On~,~- SA-~J -.. sSll~ ~1J/~ ~= '1:1L,,9; ~ %(]).TV "".]& 91 ~ ~ ~ ~ ~/L
  • 99.
    ,S/)D %00 W-=fl'~D~!J(H~_. !s- ~" L. 01(:{;( h.~t~ ~ S)(f1V,£ "c~~.q+GAt~4-r,;'-1 _ 1Jr~s0~4~O.Illf(.)~1-S,<fJ , %( l'~.~M.- ~y ~-, '," r-- c56~ e.. c 1o~ f.
  • 100.
    QO'L.. ::: ~17.-~/911+- -o""(7-2A-"''j.:.-'?9-''-j ::> 4,1A~ ')( vv'" 1. L/~ ~<>J~~ (Aooo~;uv..,,,O~) = lto'J,~ L T~1 -= ~() 4- <C9,~::.: (938 Q., l~ = ~+ I~~("~~ - Jl,4~~IYt 1~1)
  • 101.
    ~lP-Wl h,JS.Jl-A't~ I ~e.- I fuA)~~'L.5 J /J w; t).TtL L l,'j t- fZ-XO ~l) = 0,(0;(0 ~/W t).liL ltJl' -l<S0l:f'1.CN ~ ('01 .- L~.:_I_r~~1ILtS;+ _I F7a~lJ ~iL[ 11,3 l1-Yo 0(1'7 = ..L rC;,LcfiX~ t _I +~V'~It~,l'( 1d-1'L l 2..f~ Ot~ J K= ~UJ= ~w6/4 LKUj:=: 4'h~ ... ~'~~kL ", S'J.'flX0.I~~ot ~':~,1=1).,1.91- ~1 T~M" ~ &~', '('0" 011'""1 M NS()~"T~J ~5: ¥O-~ -= Od11- od1:>l ~ O,()} M -= 4tM 100
  • 102.
    ~~ eo ((P,? leOtiN C:-tL~ ~~~t€Si (c.} ~+~~~o ~+t~~)~ a( &2T =- 0 -£EJ'2- -"'" c~+C1.- Be I 1~~C7-
  • 105.
    <6I '2.. ~. f)N ~)UdN) k=- .0-~r ~~ ~- (~cU'N-t-~?)~) LV T"l- 6J.;., 01('~fL) --~(z.o-a.l) &1 o , ~" ~{~~L)1[~-I,6i+i~1(T.:r~
  • 106.
    ferl.- T~ '6So~~l/&¥.~ - ~~csJ 1-/M -=; _l170)(}ljt) ~ ~~O W/M2. b- '~ - ~b-r) 1(../W ( O?~ W~)::: 'JG t:- -1~ ~ MiD l~ 10K.. .-.= fJ.,SJ) ~ fIr/~~. ~ ¥'iM D"'-(7,o)l'd:iG .:.~) ~ -~ WM H~L'" -(}o,,'(O'~)'" ~()C- 1-,: 'lOt. --c::=:r~ 2s ~~ ~CS N ~ 'S <&-~ ~,-b'~( lU-r- ~ f~)(J, ~~1:'SI fl'2.. los
  • 107.
  • 108.
    ----..- - -- - - - - - - - - 1,-1 ~fC~. SRt ,.. ~tlx 4,~ ~ 10" r~~:'t_t I ~~ OA4~ -r -=- ~9-'Of W<Yt ~ *~ k~ o'~4 1 T~~~~t{)" Mo';"" 'L.!DljOM(~ ~iWbfij'A~.n S ''0 )St ~ ~Xt .~ ~ I A~ ~SS (~tt ._ (L~ ~> jSt:tt ')., Wt~I k) t'i~ 1~ SJ(t l~( VtS ~t~ ') U((;-1f.t~ ~ T~ c;;e)f, (r --- r." ~ rJ:O<lO": I ~ k_'J,c,'" -~ ) lit ~. fJ~ - n '/1: f" (.- ~'V.) -=- 'd.'3!~ IJ, LA,". 'j,= f)..~ I~:"J . (a x'1 -- II. co' t 11x'2l"".(,- .}f~, __ t,V ,.. f ~ oj) l"I>Sr.,v,r<t';,· 'bc;~ 4'15 f hM<J~ ()A~ (~~3CO) '" !). ,.,1, fT =-- '3,~ II,) I I n ' ? ~.~~):; -= "J:; I~ tVvbs" rW~j~tN, lI:~ ~ _.... __.•_._------------ T;o~. 9.1S ~ ~ ,;; 2- tJ/M;~
  • 109.
    l,l ~r, 'd-l1&o-(J _Td~.(o'r0 I{ok~ 1).1(fo-r~ J':'-~~ ~'oo • 1_ (roWLj~1~l i-- 100 'd-- ('fo- r'l ) (fel ~ ...fo/ . ... - ./~'(:~. J y.J..- 1'(',. y... I(J) ~~o;f~-I) ~L {?. :=. ,5 ~o~UjJ:=c· ,; b/o 3 tl =' (J,O" S 11 -.c·?-o0 1 11,"2.. q~ 4wh. f'oi( b.T V ,(o-f'", - to. ~ 41CrJ--fC) ..., 11 (V" 2'H" ,'2.."' ~IY' - ,.~..' 'C) . J ~ 1o~~ 411'fo~'L -?ow(fJ1j'(1) 4T,)fl ~ 1-~G1-~fo) ro/r~ 1- /1 I.. = , I'> 3 %~V-~ ~f~% II ~ G<o,(.Q II ~
  • 110.
    '7NS, C&-J't, ('):-;;.L -;.; OfO~S t:.{.1 "0 1):6 7N Lg':.'! oS)("3 ~~ A'~ ""& ~lo ~ 5)eo W!w?- ) 1(L Ol~ . :::n~,'S NIpl~ 'V- ~QO-~) l~"':S~ L. nl'S ,1ft,- h)(,0t: til :L~(2. if -= hAl' 1D"UI, L «: 122.~'" 0k'N V = '6£0 WIJ:..K. L ~ a10 N J.)1~· ll'$:) ~ 1S CJJ~f', b -.;: .4 (0 ()(.)O W') . (1.q,o ~)Jl·)100Mt.C::.:) IN!v"l" t.) -= 0 ,a9~ M -:: ;J£ Cw' ( lJ -3 (4 ~~ ~ ((),0'c4 I}.) I ~tMv ~ ,~,-l;'"{) M L= 1/J~rv (b; 101
  • 111.
    n,lCo ~~', (p)1~ ~lX,~~ L;E,Q'i-=L llL)~r+ ~,~~o'~XO,~) (j<lOOJ =- lW ,t '~;() ~- EJ'r~ ~ CC') ._-_._----_..__. _ - - - - - S-t ~ Ps~ ';"'1 ~~l.o.w'{',
  • 112.
    1,1C) ~lJ ~ ,~U~ ~o--rt'l 1~~()s =-~ ~ -::> ~K ~=-(06r~~,· ~ ~:,H <..~J l/}.o ~SSj(;1t; --~~ - lJ~-o ~ J@?Stl. l~ -n ~ ~(.=lblOAi >r.--vv---~ 1"11'-. R. fLo 1)..'1<6 ~ 1, 1 1 1/ 12.:;- 15'-..1. - /'(IJ ""- lOS- /0,<;':; ';11.'2.,4- 4l~- 4,:(0I Q01) I 'R - l - I - 0 d40-' 4-Ti'fo'L~ ." 4(eSs')t~~ , (D" tl~ ~~~j () r ~ I -4 I. / IV ~ )'&" 1/d9 =-1/J).,'t X,c') v.fj/5 ~X.OS ---------------
  • 114.
    l~~'(r-~~t't~-T~ ~ .- o/6<~~W .---------..~~-,- '-.-'---~ -~ ..-" - - - - l.'J..l r')2=: b2 ~Q~o')0)(OPl9':(4') z.A lSl.-"{1)(()tO'~)2. =1i~S w'7- {j=o Go ~~i ~ML/~ ~ =: lY~o ~/~ v.1 .:? ~wt~O ~ ~'ilL/I}., ct'f...=0 -G() 4-S :'- ~ --UJJlA f/¥L/I)...- L&lA tL,02. 1 f~ (ftS ~ 13
  • 115.
    lr~c ~'"(- 11~1~y) Tt'It~ OC.C",4L'f:, ~~re ~J..-~:- (J <6, u ..··q,I J Q, - r _ tZ-"1~·L-e. ~.- 0 '~"1 T~·~t ~ ~J);j~?~.', 'k"oI 00 bleG 'M T~':I ~(q.~~ ~.'M!, 1-2 + B-Cro ~::: t/~ ~~ ~ 0~'f.-<4) AT -l+l<) yot~T' ~ :;- O~~ -e-~) = T ~ +ro,Cj"i~-eo ~- ').S -- Offi3C0s)~ 1£<:J,o C
  • 116.
  • 117.
    '('Off..::: .3 - /,,1'0 C'l L ffL-~ tlb 1, ~f:;< ;JJ ~=~)fHJ".:r~) ," ((),~'t:'~O,9b'XlLJ(?lO) ::: 3S '1 £e1Lf~j ~.~ ~;o '3 ('N_~'N-tr Ql'~ ~ 3lW ~ to kW 0.3 QooT";:; ~~-N-=1kW ~OON--r T"1-- ~V 1~= OS(l) =~,~ kW m'---L-'~T L~ ct) L= ~ MM b; t:' b Wfl ~ ~ ~~ ~ T~:= ~c.­ T~= 10C 'h-= toOW/J~K, <s.s~ S,?J Wk,~ ~ Gts~ ~ ~~ 1)0 V1fh~~l ~)lb1 -t_hf1. I;I~ (Lt-.) ~: }...-V~'ll 1'2.. _(e,01.+ (),OO))~/1-_--",,:(p~O- - - 'QS,3~,oOo'0,oo) ~ orS~~ 1f~ 0/60 ~ VV'I C- V,h'O-VW i (N~~~') tr=()&0(""'(ho)0-)(o~~o) ~ f?~ ;J/M ~ ~ )') - T~~~ L';/z. r~ V l~ L.::.£L-J J - 0 01.-"r7.-fus~{O,ro:'X9,o~1~ = O/l').S ~f- ~ 0,6 ,~ V)f~f h{j'o :. ~g'(~'0()rz.]((co':Qtro') -= l<14-i4- N/ W
  • 118.
  • 120.
    I1A4 ~~ ~kI, - ~ 'S- ~I ( -' ~~~E.'J: ') ~ ?8 ~; <DS E= Vb So: 11 -= ~ ~'+~-7,~ -==9k, t = lo-s bl-= 0,01-"'k!/,el(x,fjJ ~ l,lo,:S ~/-tt-~·fJT 1A-:, ~1 fw'f. ~urr ~~-~ rIVt-S M~S ~~t;s ~~. ~.,S~T=- l~ (§i)c:1OX~) -= ~ kw ~ce- ~O M I1A~ 61 rL0'f. ~tjJr S=~ ~ ~ ~= O,Ofp ~'A,(!<>0~1,s~-1 f ~~~1Aro ~'f ~ ~e~ ~u~tt-" s~ ta ! ~~Gtl f3(~ !. 2~t€. 11d ) ~: Q,Q(p (t"XI~" o, ~r~-f1 9 0.~ +-0 t '1T'1...-4- T ~D 1,00 t- 0 +T, -3-"T'2..:=-O o TOtTIl. -413 .::: (J 1c=9,1f Tl." ~3,~ f -f~== 4.7 f t"<6~r~1.l t 0-ct)-~3,~ =- ?os ~/~--fi
  • 121.
    L -..m ~~~~~~__••••• __ _ , . ' ""l.- °0 1- 4 " ~ (0 12- ~0M60.-c..M.., SoW1lLN .JSl~~ -A. '2 7--'2. M£-~ '(leWS ~ B>"'~~~( , ~ ~ l-4w ~~f'Z. f€Lff, t: , ' 1- Af 9L~ f ~T l).J ~ '1./2- MIN . 1,So ~I f'vJ'I- lWf! Y' ::' N kb:l~= ?[ 0?3)000)(~) ~ M /I' -=- lCl~ptJC ~t-L ~T ~.ONj1 S~ 11 :::- 'b,~S ~f()lr~ -0,'):""1 :t -= ~ ,3S CJ~'XLm?) L _ 1'3 1 et>O ('-'oW/flt n,S( ~ fLw ~T; S~~=1~ ~o ~S~~ Cl?~)~7Io)~) ~ -::: 14'7)()~ ~-w/tL 1,51 9M ~-?Io}; -0,11/ ~ ~fn b= ~SLbT ~ (Of07)lt...~Ily:::100'(So) =:<. ~9,() ~/W--- ~~ ~)Qj~~ ~ ~ Vi~ ~ '1.1~O "" 'Lios L~IIlL '6~ =~,n ct~ PbT V~ Co,(o<t; W/M~~)~,I1~O~)~LS~ ~ t13 W
  • 122.
    (~:j jStW"~::( s~I, "Is-T = eo-l).So :::: 0,5 l~-To 0<) -4~ Ye,Y~ =-Ol~ V'lA'= tf f(/=- Vc 0 ~=Ms"'Mc..;:;O 1..,,= 44~t: x. ~= 10;'1 t 'v 'i. c~ Ol'i:,~4t 1.~~ I '&t ~~~~: t~ '6 I~X04t- ~".Oo S
  • 123.
    l%,l ~~. h~~ ~ ~Of.t;J(0;~J.s>I'~S) ~:::> Oc~ [o/..ci...CNS'kl..) of 0 ttplo,~'Y:J.) _ t O,3(O"V;)CtJ]
  • 124.
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  • 125.
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  • 126.
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  • 128.
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  • 129.
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  • 130.
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  • 131.
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  • 132.
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  • 134.
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  • 136.
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  • 141.
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  • 142.
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  • 143.
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  • 144.
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  • 145.
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  • 147.
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  • 148.
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  • 150.
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  • 152.
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  • 154.
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  • 155.
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  • 156.
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  • 157.
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  • 158.
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  • 159.
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  • 162.
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  • 165.
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  • 174.
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  • 175.
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  • 177.
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  • 179.
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  • 180.
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  • 181.
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  • 182.
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  • 184.
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  • 185.
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  • 186.
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  • 188.
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  • 190.
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  • 192.
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  • 193.
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  • 194.
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  • 195.
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  • 196.
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  • 197.
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  • 198.
    v,. .L J-] 1/:1, 'r [~It+-~] .: fJ1-t-..t8 ~ a.~5!) fc I~O .,,)"" _ <f'A r db.- 3,gg r3,.(:.X I - 3. 70 v,,(3 - _'7_c> _ - • (J ~ A- 0;f6~ ::; 14, Z9 f.'i.~;: Fi~ ~ f(m;:rY3;) ~ I(PAIl. I.!S. =: 3E ~:;., 1St • .120 :; /,0-1 f eltlb IID:J..'). ..) ol-t 'i- tJ .:: tJ.00 MS~('-543XrJ,').55) ~ 2.. (I )(/4,;;' 5)(1,04 f) or: 0,1 Of c fY/ :1./.5 fI~5 - S0z. ~ Oi. G.fo/K, H'LS 34.0 3.!8' ? t7."t 502. (,.4.0 4,7..9 Z62.tJ ~ !/.. (Pir-t~~] ~;::.[3~ -I-j;,1 7.- tJ.:l.I1.. 4/3::' ~ +66::: J.fg 1'1:2.'1:::. 4,085' ~ ~ OAe'--;. /{P,(P1 e~t3 [2-" r - K -::. V ft E~ ::. V(if fa, 4)(;1S~) ;;:: Z't I "rGJ< =:.. _350;::. 1.30 ...fL0 ::./, ~73 /tIS 2,(.9,./i ..) '. ' VH,.>_5a')..-::. 0.00 I 'l5'3('54~)(d.2.I:Z) (I) (J&,,(P9X,,;l73) :: tJ, 1:2.1 cm% ~l M,x/tlY"e J1:l.~ 311% 501.. 5"..1% N2. q:t..;'t, ::: o,()s:::. 0,/15/5 0,,91 !f:,..-= ~tJ,- s olli: ;;0, 94-!5 /-/l1I:t.S O. r1 , DII1..$-11)/ ><::;:.. -----:./---- f/102 + ff~'). O/f;z,S -5(j:z.. 0//2.5 -M2J I q,051b r IJ.91KS 0,11..1 {j, "" f =- (),200 cm.:2!s .2:1.1:3 1JCOj.-vrr r'x @ 3.23 K.) lafrYl. I
  • 199.
    CO:z II? O.z.... IV)IV 0-;(; e.-t-/K. CO2 41 3~ 99' J'1~ c?..t. 32. 3/f33 113 ? / 3/';.. r 31 .2. ::: (323) ;:; 5tfJ5 ) ~ J I]~ [ ...- +-L] 2. [~1' - -- 0. 232f{l(tt MIS :::: 11 32.. - , ~13 ::.. 3, '{crt. +- 3.133 -::: 3,'l11 ~ a;;e'- :=: /3, fio G.II-t5 r------:--- K =- V{l90)(113 =: /46,S' IK. ::: ~"' ~, 201 ,...an::: /. 011 £fftB 1&",,5 .J ¥ OCO -0 ::: O..Of?/~f£.f~3{jSt1_~$JJ A 2. (1)(f],rtJ)(/'(}4f) ..:: 0,171 C trJ2/.S !fa -Co == 0, O()) g5 ? (:5'8"() s:l(0. 243) 2., (f)(t1,39){I.05&) ~4t 11 -::: 0t /7S- em0/5 I--~~"'--~- ~--~-""' ......,._. '~---~...~--" / I I !i~ 1-- f-/!!L + ~_ Dca..,-tJ>7 {"]'o.,-(o Dr!'!-t/.... "'-, .,- , ~U~ .1. If c),(JtJ:, +- a,llt f-'!!.dP. 0/171 d,115 ~,I [16 8en~e/}e l'n aJtilc?'· (:~ 2oi~7 _8 f/.. 0.'!:b!!6 -:::~ ,'{"'I K J(J (Je/v(r3) J• r- VA 0,';' T=- r;)Jf3 K 1'J- 113 ~ ;;Z, ~Io (SPr~/v~) :::. b378 1'-16 ~ lEi" .)113 -:: O/q5 "f-lti~ Pet,s.; 6/15C/O ,
  • 200.
    6) '/r/~hloro E'1I:.y1e~e/1') UJoft?r' ;I C:zc/3 ;--- 293 K d(3 :::: 0, ?5 C(f C(As 1,"3 ) ~ .::. fo,37i ~ =- J. (11,~) "t I (3,l) -r.3' (2.I.~) :: ?!( ~cJ,~;::;: 15.~ 7 Dfll3 ::: 7,1 x lei€'(6,3Jg) 'J.. -~ :t. Is; " 7 o,?s- :::: ~J.9:< Iii ~ CJJ-I~-C.--_ _ _ _<~ -;:::. Cf.,:29 x (a-liJ 1'Y).2/s -===~-=--=:-.:=:=.-:::--=::.::::..-:;-.=.:... Dt4t5 ;:= k r - (Pll ~8jj8 /.=: 2.93 K. r= liL- -:).3 k.: /,38 K /6 L{q'j(Olre Us K /#6 ~ 9Cf5>< (;/' ~-S r.:: t3g1</01"!>.r... (:1.9J/<.) --.-:..I<.~--<----«-«<---<-- 6 if (.5. 1'1 x/a'l!JJ..~)C'fc(~;r.i;/4'5) .f5 7 ~ x'. (0 dfJnt;5-M (j !Xl- • /,tll$ y. (~t~ J /~()efY1 1.;"/3;,Of4Jd,Jrzg. CrY/2- X (.171- '2.. 'I. t1 I'YL < IIXJC~VlJ Ii"1'1) ::: 3;'-37f"l1 d = 7.2, 7 r)I'Yl 21-. I~
  • 201.
    2f,/7 WI' Ike -ctttU1(f ~.IJ -F ~ 1/11(J~ /<-'18.- 7,4x 10 (tPf!)Y/(j) T V. 0" A Me:::: 32 Vc/~:: I v'c of- 4 'leI = I"'/. f f' "'1('2/,./) -:::: I ()). ~ '1ftfJ.,." = (101,,-)0. ':0 IS; u~ 1' -9 2. -5" L.l48, ~ /,7 x'4 I!!... =: /, 7 xlo C'mt .s ( -S':)/, I. , -i' 112 1.7~ 10 ,,~ -=. 7,4~ /0 (if;. 43:L) ;LYf' /5: 'I' 6 D;;I3L"; L ,:t.. VA I,Ig As vA == 141.2. 0 ~ ~ = (/()J.2.) 3'= 1,~53 I<= ~,J. '00"LI /- (v:f~J Ve.::: / Vc. +-1 V'H r / V() ::: 11.8 r 1 (5, 7) f 1.1- =- ~1 2. VI!> '" :Z,S'(37) = 9;t,r V/f ;>- ~,st8 - y (3C~z) )~7 k == e:t Y.. /0 [/ TO /(/1.:1.. .J ~ !'t92)( /0- 1 "'7 rl - I,''l~)(/~ 2i't>_/,..1..4.<3 - • ----' . 4, {,,$3 {/, t,:2., == /,(a '1x ItiS;;m~/.s 21,/1 .C /I. ())-/ /nld bel7itBne.z S r::- ;;.gK' 4/5 ~ (),7S4f <PrJ :::'/' /J Me..::::. 7!' Ie 1-1 Plf = 2 Vc. F ~ .Ie+- JVoz. 5 ~ "- (j4,8) t-'(3. tJ r h-1 ~ s<!,).. V"t'" b..: {5'fI,~)o.ft:,:::: //,57 -t'. JDI/fa -8'1: -::; 7,4-;( IrJ (~!3~ ,,2J1' If, 07 {),7.5"
  • 202.
    ~~-Illc ~;: 9, ~ ;::.69,:;.. olife -8e- V;t ;::. 5f, '2.. V6 == 9' -6' OAf/!- 6~:::: /K." X I~ I • 21% (sr.:2) ~ O,7S" :::: III 3{' -" to-SCm'is 24.. IY ~ D,q~ -::. 7,1XIOf(q,f3M8)~.L /.., V. 0, /P ..H~ A 4!.,0': /, I"'J e,o // If 17:... v I 72. ''L. T;:: :z K8' (cPe Me) .::.. (~.~,,, II) rPl$ .::: :?,~&> M/j::: If ;:~,"5f' ~ , O,b VOl- := :J.~ b j ~ I ~ {.2~ (,) .. 7.tJ -/ , Da.2....If~o·=-' 7..4 ></0 C~.3f.))I. ;2.gi' 7.0 1,/4
  • 203.
    24.21 Corhol1 dJ/./tls,n7 /r-;Icc.- fro)") :l :1.. Q = :Z,,?,"It!1!J- K (£!!L )_-o .$ I0rf1rY1 :::::: 2~5 x: /o-:tcm7.S Q =- 111-J.2tJo J Imak -. Q Vi == DD e ~.: -1-4L/.;~oO.~Je -::. (~,s)( 10 )e (g.314{;;'(e)(J(}()OK) -/a -8.2 ==- 7,3/1 x/a cHi.::::. 7,J4 x If) Jt1!t1s _ 5 -13 ~ 15" f( Vlf~ = I xlo cmVs @ 14tJf K. f)flt3'::::- I'l.J~ --/2 cm2i.,. Dt.' =- D() e - Q./f<"- h f)~ -;::. --'n Do"- Qjr< T' -f$ /) 71 _ G (-1..--) @1316 ~ (Ii-If) :J ~ AM £/0 ~ 17/'" --12-. tJ Q..(. f ) @/40f ~ (/ '/-1 () / -::.AI1 D" - r<.. A-;;;8 SaIV1f?J ~::: 4.. 1'015"'1<.101- O~ == 2./g, J// 4 @1.3 73 kl lJ; :: )f) (;2/J,.3 /~ -- 4, fp15~ IrJ J 3'73 D~ .::: 1,33 )( IO-/~mY.5 24-.2.3 D-:;I/-!1- lIe @ fOb K Cil')j /J,3l~ -3 1'" r / ! -. '1'Jv Vr:r6'::: I, fiSt''' It) 7"Y~LiZ~ -r ;VI's) P 0;13'--12 0 - ~~ p.= ;G,3?o.. afm _ -1 IIOI3'1./f;-S"Pa. - /, 11j-;. /0 aim 3/ 3~ T .'1.. ==. (~()O) -=2J..) t:17 M111 (ii k.. '/ 0;: S"i H+ 3:2,1111 ')..()J,t. 4-. OK He f, of) f(). "-'- J, '57~ [ _I -t-..LJ1"t. rL -r 1- JJ/~ 0 MR- M6 :::: ~~/(f 1r~tJ ;:;;:;/),,53 6it1J = 4,6tf~,S'1' =:::. 3~3.:z&> ~ cJAl3j.:::: / /. (j 7h ~.=. J(~O7. ')(;(J::l.~) ;::. 1bf Ob2 /1<_ -::= i ~tJ ;::. 17.:57 Gil!; /If .,..~, d'J... ftIJ .:; tI; 611(:; VI1l3 ;;. (J, tJOlf5Y (2.2./ &J.,~(c, 5-5tJ!. {J... 313;< Ir;-'fX/J, ()1t,)(0.r;~4t,) -;:::: :<.,'-1- 'f. I() 4- em:t( WIll; Sft1~/hJ::::' f ml'v7 I~n <: 1.0 knuj~en t!,!lvSld~ aJ//J lui be 1i?7[/p rJ-anf- kn -=- _~ -;:: /(,~ x,lti"fY1 d{? ! )(. /0-'3;; ::::- (), ().2 / ). ch:t It1 e ;;.tJI'Y) eXQ /nl)e ~,.
  • 204.
    24,24 ~ 51"'41J".f ItJ6AcPo ye s df -= I~-' eIYI PKA. == 4r50 dl? JI -' MA [}/(R -=- 4- £,,0 (.z,;>c IO~f}') ~/37'-i" :l. ' 01.5' ::::. IS.!'I7 C'fY1:J)$ Ofl, .::. J / e.. ~ 1- 1-:::' -.'-,/-"-.--I -::: -48.5'0 (10-') j ~ij'== 0,(J6 ~cd. ~.OI5" os 0A(j' DKA -:/, 1;l4-f"'13. 1'17 DA8 e;;'9t /<) farm:- tJ. 743 a~ DAd 31sK)afM .: 0,71g (¥f~)('~. ::: /('').~ Cb1% 116S/.lm/~ dllufe )(7 ~ J eJ,4 e :::: I / L l' L '-'.J- f-.l- DAB {}J<1f 1,/~"t tJ.~6r; :::.:::. (J,062 cmo/s o b) I()t) A U)/14 cfC 0,1·' n / ::1.. J(,//1 e -:;;- ~ !he;~ (,tJ. 4)(o,{)(P1 -::::. ~ CJ.< x(O-3cm% ) -5' C. df'::: /d eM OK11 :; 0, ,(;.'{) .cm 7s- D - / %II - . .:::: 11.& r) eme I I .• IIft):oS .-L-- f-~ /,/21 (),~~~ DA~;::: .EQ.OAe~ C~/4)2(tJI4!tJ ;:;: (l~ [J0 & $" &;;>7.5- d) 5irtJ /0 hI; :;l 0 O!J{)'I t.~;{)()YC$J .J (I tip;::. 1..)( IO-1crn Dflf!J '% I, 12.'fem'"-( hl~) P2. S P2.. 'I A. = _k_T_____- {£. 11i;,)..p :: /'3gx/o-J~ (111M 'X-r) _ _ _--=-1(_ loT~ 6..1((a:l~'f rim 1m )'~ (I~ ltJ~qnTYl t C,.g.) ==- (J,03/S' P(.f'u) Jp c-= IO-~m kn ~ ~ == dlP Dlte ==
  • 205.
    (), ) /, tJ ,0.0 lOO,0 V;~.tJ 01 ( /.0 Id. O / (j/J.O ~otJ.O /1.9, i 12.'lf /' ')..1~ o/I~9R o.o~19 I o.ot~ t).Ob6~ O.06(P O·04~'!; O. a"_IP ~d)41 b (j. OJ,' (). CO 9{p O,()(,{g o.ODSlt .!..- r J- OK.It D11.8 /0,4- = --'---- .l..-...+-L. /)KI7 o/f7Cf ~ a AOf ~5tr%l...L r....L-] 2- Vo -co :::. "v MR U{,tL :z. ;L U ?o;;: Slo 3f" 3/,2 -r !L ==- (1073) =:; 3S;/1~ 1/ J~/ [ -h- -r 1-J ,,% _ [..1..-.J. ..L~ .2,;,0 0. ~2. fYI, M -- 32.. r 11 .A .8 ?~ /, safm 0;.1/ =- 0; f"tJ8~ 3,1331"1'11'(" ~ 2- :::::. 3, 71+ ~f5:'L::::: I~ '19'7 ¥t ~ [§i~-::=- /(J /3i)~:::: /46,5' -{I< -:::: /013 =:; 7,3:1.1 t./'KS 14-~IS JL rJ.-:' tf, lP.ft:. Oo;...-C02..;;~ (), tJbI f 5<1 (.J~J1t)(P,232) (J,-::rXI3" 79'1){A 7!3~) :::: tJ. r35 crn'ls [)kit.. :::: 18'5"0 "L.1I1'r' V' £.~~o~ ~~ ~n ;:;.1f5t7 {!o¥·6)p-~1[· 44 -:::: 0;. (}231 ern Ys
  • 206.
    D - --,__ liE'- J I - / - - f - I .J. D. n -L..- f- - ~8 I/J(ft 0'''3ff (Jra'2:~r .:=. (), {):2.33 C'1)1 Y.s n l ~ z (,/lle e E:: fk.e:: (tJy~) Co. cJJ.3) .::: ~i3 xltJ- 3 c;n% I(n Ud.5"tN1 ell ,c~$/tJJ? CCln f-n>/..s a)h6?//l ,P /,7 ~#bkcl ~ ..3'afM /' :2.1.2..R /Je =~b (I-(~/'-(I-;J..IMf!(+:?,tJN/ - O,]is W5) ell? (II) De veldfJ raft:: e!uaflt7J7 r-= ~ jJp,5, ks Cfiz et~ C5) /)/;fh ...0,5'1 f{: (), "4 ~ Clnd U. effnJ (tJt ¢= YL ~ ~tl ks;] :z. (~) ILL De, 011/ ~ S. k<: =4 Vf W1<..5_•ITl ::r « ~ p 3-..,; V~ d s 4: e'tn {t:t.) P/i(g' In -~ 5r -0.:;'95 r.:: (),64 V( 0( cptp [ltL] I [~] " ;"4. Db [ 0( cp _ -(j,:<fI5 {I- cp )').{J- ~.1()1;T2,ar~OI?5iJ 0,205" rII: ]-(),S9[ 1:' J-tl, 2.~5 r-= tJ,(p f'X:. c::.L - "At Db ," ~--.---.....-" @ ~ O,1f)5i, ,. ,/) • (1- tpJ cP LO-tpJ[I- ZIP4"f- s-C-::;.9 +J..tJf~(J,/IS'flJ F(>..) tJ}/'e rtf' ep ":: eb (1_';).2. /.e. r,:::: @.f(>..) F() yo ~p rlmuJYI t1tJre ->/?>e/ 10ft:" d£ ~ 0;:. (P dfC<Pf)fi) clCfd)r.. ;, df(C"~(d;)-==- 0 dcp f 1,>9 (J,l/)5'" d (<j.)::.d [(I-f) cP (l- ei t{J dtf ';J S' d.1.~ (2,/ly1 fJ"'~O?r1- fJ.15{;J - r 0,7oS" 2SZ dJ ~,.,o3 -L f (I-f) [J-:J,,/t1fr f (11.; or:r't _0, 't5l{J~ -0,70>;
  • 207.
    {11)$ c/t?t'IVC7liue,) dtyp,)t?!uaU O. d<f ) 5~JVf? hY-'<:p rt 6~ rj:StJlv~t''' fUl1chc;'n Of? If'(ce/ {f~tJjsheet '.. CD.::: 0. I 9b===- Problem 24.28 Excel Spreadsheet tp df(tp)/dtp 0.02 1.90E+00 0.03 1.54E+00 0.04 1.29E+00 0.05 1.10E+00 0.06 9.34E-01 0.07 7.97E-01 O.os 6.7SE-01 0.09 5.72E-01 0.10 4.7SE-01 0.11 3.93E-01 0.12 3.17E-01 0.13 2.47E-01 0.14 1.S4E-01 0.15 1.26E-01 0.16 7.2SE-02 0.17 2.42E-02 0.18 ·2.02E·02 0.19 -6.09E-02 0.20 -9.S2E-02 0.21 -1.32E-01 0.22 -1.63E-01 0.23 -1.91 E-01 0.24 -2.17E-01 0.25 -2.40E-01 2.00 1.50 er "0 1.00 --..!t :c 0.50 , 0.00 '", I ' "..... "----·0.50 .. 0.00 0.10 0.20 0.30 0.40 IP_ 0.50 2+.2, 9 '-f50zgrne (SfeClBS A).- (V}tt ::: /"(;IOtJ fl(y )'YlCJ / e dsA -= 11 I), J1 m 0;,1i 0 ~ /,o4x/a'(I'rl:L1s ~ C!afaICl$e (spec/e5 /3): H8 :::. .;2S'g CltJtJ 9{jmo/e ds) e :. /tJ, 41 nm 1")<::1 -1 ,I vlJ-f/;P = 1,/() ;.t.IO em ;)./5 . -r;dns{Jorf fafle el1 ;l1ft18 trltJ/ecv/t!'s ~r't'l/cf.k cJ>P'r6?S i O'lli !Jf/UldaldieI" I(..S" Cl )1/l;Ije ytJ c.1 d//lw;~~r' JJrtl~e~s, - . 0.60 (jJ1t ~ d.5A :::. 4)~ nm dfO v-e. dpc;yo e rpf3 ~ ~ ::::: /(1, 11 nm d<fore d(to ye 1 1 5()Zc;rnej srfec;I85 A r;(CPfl)::: (I'" Pf~J:;' f;..., (Cf(4) :r.. / - 1.../1l1 ~ -f j. 09 fJ,/dJ 6- - 0.9,5'lit l'f;e effecf/flg o~f/z;6"!(/;f,1G ~e~ D:'HzO r;{%) fjJiftt ) C -' !! i CJ m j>!.rl / n9 tile ':Iirv 0,'-::' ) i/ If • /' / 1;_,.<:' )'4{)r] ;"Il/ 11 Ii ;!;k' ;,:J IJj, ,., . vC/'" ;/ i:~ ,#... -, /11 -ftFrlJ/,( d/' '/d:Jc<nj 1.5'
  • 208.
    the rt:1(7,1- df4;/1tll7~;'edr efth::1INJ~ /5 C,C;iJd/I'Jc"',:/as./~t /If£"::? If .r,,/ver Ij Mileht'J/1 0 ~ liJeros-oil; E)(~e/ ro Ob/all1 df!..[f~ li~~~"1 I ------_ IProblem 24.9 Excel Spreadsheet Solute Lysozyme (A) Catalase (8) dpore = DOA-H20 I DOS-H20 = 21,3D <PB = F1(<pA) = F1{<pA) = D'se= cx= Mol. Solute Molecular Wt. Diameter Diffusion ds Coefficient (nm) (cm2 /s) 14,100 4.12 1.04E-06 250,000 10.44 4.10E-07 14.3 nm 0.394 0.729 0.074 0.080 0.006 15.00 <PA= F1(<pA) = F1(<PA) = D'Ae= 0.288 0.507 0.443 0.225 D -t) -7 ,/ 'AS ~ 3".1t, x /0 emf'S dS A ::::: /:1..,31 nm' () oAe .::: ~-If.2 (/ 17(~) Ii(tf!t) dfdvc> ~ ItJlJ n fJ') 41 ::: dSA """-=- 12,gf{nM:::; t),I'2ilcf IJ cirp{)re Me nfI1 "2.. F,(1h):: (t - ~)~ (1- (), J23?) :::: ~,1617 r;,(~) == / -;z,/04fh f- :Z,P'! ~3'-0, r5'tit~r =/-:;',/04 @, l:J.3t)-f,1.,(1/ (011:85/) 3 -d, '10'(rJ.I-:2.3 &,)S';:;:;. 0.. 1-'/3 ~07 =J, 1" xlofoi7~rl)(a 743) ::= I,Cj7K(O'eiYJ~)
  • 209.
    -7 DAe = 5:()'1-/0 Cln~/.s ~~fI~tJ .:;: /'J?;< /tJ-t.em Y.s dSA =-:1, t ;1ff'J -1 -~ G', ~1- It) .:: ItJ'! x/tJ ?;(tf1,) ;:; (tt) (), 1.2.~)'::: (;- 4Jr+J'2.(]-:<'/~1% + :i1t2flfff:: -P/!s %4"] ~:tJ,lf.! ifJ",. :: 0, f f3 c d.5~_ d ftJrl? dfP...-e ::- I~,]f tJm == £7- £ ;)/11 O,}8"3 ~ £eClChIf)M oC'Cllr.s- pn!:, &11 5PY'/Ju:e' I,e R.., =.0 J J. eras stPt2ce 6e.fNJt!'t!'n .,ta;(7 a/,4/Cr..$ /s sla!"t:I'7;j· m~/e~tI/t2r dlyC~s/~n 3, 7£0$ (jonc. ~ Y'"=tJ .::md r.::/? CIIY'e. CdI?s-le'll1t' 4. F'/~)( df TlfoS 1$ ftpP-cJlf#6?f7IiI.?hO£ Alit?: tJI'J d Aillr S, 1hIci<ne$s t:Jf..r; !t'~ fill'Yl /~ !.Ie!",! If, /11 yel4 hvt? rtf rJlf/etlltPY'J tp,tfJ/ I.~ Sft:?()dy-sf"fe dl/~.:f"ltJr/ -> j 0 /Y'fo 1t IIf, l' jff. -=~fr d)/It~ 4- oNAY':.:; 0 c!'-<-- 01. df" o NA ~ ~ -cD/1"8 4J/f1 f:.~'(rJlt..f'~'2t- NC;e)di!",,(f"tJ'" &." rVlfr ;:: -·c [)It$ dUo -r t/l(N;t~ f Nd.4r·}I~~jJ' - ' ; Z$',~. dl(fr~ +- ~Y"- 0 ,.,~_ aE d'f' - """ - CDh8 d~ - c liAtLd~ "-~ () n z J'ft.. WI&' C!lJl}sftRf)J. C ond 7)1t~ d''-tI£ ~ '2l/ ~ t- q-4.!i ~ tJ .~",,------ 02"2. dr~ dJJo.. ,::: tJ @ c:::' /../:1, d2:" ,/fl -= {) ~ &-.:;:. tJ Clt}j. ,f.-:-:; L ifi -= .1,1) @ y.c R. <J~::; /1,0/ dP r-:: () ;l6, :3 /lie I- ra/e or A e///ed /i-tfm i'V ~x A!Allx+-~,. - /IIf+y.A1I!Ji: /y. tJ!t1 AX 1 b J;j-r,6./I- --- hit:! I1x 6 11:1 tlf1c.A.'I../J.~Jl:r-b..c - fJI-1F,6J<6tj Ig f<afe tTf- ticetll11,///eifuuJ III eft C}!dt. ~,,/luA.l- dt; (I J<ale a/- tJr-aJpc!/tJ# In C V· ,.e,q AX tid /l~ Con.,5erva!/tJP1 a';: Jrlass (Ne f- Y'fltfel J~"Ie~I f-~I-eJ?fj-::.o t e/l'fLl.J< r l #cellmll) (j;r(}JULf N~x AJ41:sf'l:-rA;-_~~J( A~.~~1x AX!:1:16.b + tJ'1A'J.A1:./if"Ai -J.I~ AK/lir- .1.X.titf AI- - - r NA~AXA¥!~r~-~~AXAi~ by., !fAt: f 1: - R.ff =- !J
  • 210.
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  • 211.
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  • 212.
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  • 213.
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  • 214.
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  • 215.
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  • 216.
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  • 217.
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  • 218.
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  • 219.
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  • 220.
    (y- NAr) ~!:'e-;:.. 'OM lAJA - $ rz r<. l' Vh,!. "oJ -IS If r= ~'13'S 7k8::.4,1/fx1tJ m% -/~ ~ (Ii NffV' 'r-:! ~(1:..1.: 1,-1f('f./(J JL2[0,5''I-/() Ii) J., ~ 3 C?3/1-~'~' l(~rJI<) mole ,I<' V-Nfk·/ (&,.f7(J)':: r.;;'I{,;</i/+~~Je r;; m· s bJ C~Y?cen.fygl/t)rJ (DYt)/iie: L (r NlfV');::: .sL(t' dCA) = 0 dY' cdr;rF Y'&;:"CI dr C.1':::: C; ~r t- C2. ~ ri~ 5'mm ~.:: ett,LIt. r<. r Clti == ffr..= 1,5;( /tJ5'Ii -=- to/.59 t'Ilaje. (ogS11 fi'!!;'X~'I3K) rn3 Vfjo/:;'[< ~ '("0 -= !mrn c.. :. /,() 1- lOs-~ 1- In I"~no :::: j. 0f:) -P./.!'E.. (g,311 Pa ,m3 1...2~51<) fY}3 mo)el< (.))/Ii Cfl 111 moll?:.. ClI)d t" It> /4'71';), m3 (p /,:;~ =- c; ~ (5) i- c.~ 4;, oS- ... 0 ~ Ui) ,J- {7.- C!(.-::' -13,[;¥' ~:2-::: /3/1ft' fA (~) ;; 43, /p~ yo{vm1'9 T 13/, Pi' :;.. t;>, '1 .Jv.(r"lMi~) = O. J y2. Nt4r is cahs/anf %r -=- - C l1t.e ~ +Yft (ll,t t I~;d r' 'r t?e, NfI't = - C DA-t3 ~~ 1-'fA dr <:?J 0 ( ::;rrr"Nn~Jdr. = ::71cQ'1 f-A!JIL~ R. r'A 8 I-tift ~ )j14s @ t ~ t:)) Y':::.. S"rnrn':::' 6r ()()5'm fP ftI 0= 311f:L4mm Id)/~ / SeJ , 7' >< ~ x 0 r0.. (p(J vr/m ::. 1J'J.11.8 ?a. ~lts: 't :J.~/I f:fl. .:;;. OrO 117 . /,61.3 '/.)0 5 & ~[-/;-CJ'" 2'frc Ull5 Ge[i;;r5tJ Wit (-kJ:= ;2.jrc 1JfifJ ,t,(I, D1S~) J..t~ -= :1 rYe Dr'l6 Kle'1 Ct(t1'57) H').):>
  • 221.
    ~*'c ~6 Rtr.(1.0<130'" -/J, oss-If7Id1(}1 CDlfe~ {!,{)4J7)d~ .::.-atJ5~r, ~Jr< if' • r. R" cV. ~ (1./)437) fdt: =: '/),6.55tJf(dR.. ~e 4( ~f C D,tB h (;.~4~7) -6.:; (/~OS"~ [~t.?-- R./) 2.. P 5~ C ::- r-= /,PI3x/o a... .:. 4tJ,/~ tV.Pif If (!-3/1 ~. rn1X.3l>3k) m3 m~/e,1< ::. 1-. al.l K /~... ~p/e/cltl O~(3 .= o/),t,() ~~( .X>~~ d '~/~ c~ s :L'1I') -- ,;trt> S -~ (1.112 '1./0 lI1.P.leXO,~h~ C.!ll-Vo,(1)'f) t-Cmo :s A aoS5'~ 1r14)~ ( {(),5('.WJJ~- D) CM 1 ~ t-=- I,S~:2 x I/)~ .:::: 1.;:22.7 t,V',$ ;2t" /0 (J D 'V,NA ~ ~ ::. fof j- {(,:J..NIt.,..}:::. () ,r:J.Nft fseol/sfanl a~ ~ r c filii r := - CO".e 1#r fll [NitI" r;(;] AlII Y' -= - Co DITtO c&e /- fjl't d y.. QIP 411y"~~ fc;k =-1trcQ, f /i)dff'tr ~ r r~ '?f1J /-'1 J,~ ~ Ins t7 fr ,IT ~ [-kJ :: 41r'C ~t!J ,)t1 [-I~) JV,q.::' 411C DI1l! Rk Lf-y;) Naphlha/el1R tN,lttl1oe. " , {[npub) -= {ol4lr;ufj~[lIc!cu~,,-kI7CJI11 o -:4 fr'c:, 415R~ [i;jt&] ~..P~& MA dt ~ lJA8l?~~];: -j!f~/(d~Y" . <I"S v It?,4 cI t 7r;t' Rf C~D ~[t-rw 7;:tr ::: -ft#(r<dR. Q '(/"'$ I:> ~ ~ d4c;~!f-tns1~ .~ f-!.!!i! [1(/"-8/1 J.1A- :l.. ". -4 2- Ii .c.. tJ.tJ/rn 1ft. ~ I;t. /0 rn 'Z. -£ ~ Rf =~, PCJ~$" 'Y: :::: '{.)..5'J< la m l. :2. -5 ~ ~i - ~ == r."!75'x../~ Ir? fig}fl4 /.14 <5 Jiclft s-:::: ~ 71)(/~1(1l"le tv?1/- 12Yf}/l]Id/te cm$ == ~91 x lOS'WId/elm '6 s' c::;. e. cot. /'(15)( /1) ~ ((.1 (f,gJ4 ~3X:3'171<) W]pfeK. -:::: '35./i ;"Jut/mlff . :lfts=£.:: ?t;" ~.... ~ /lJiJA'S-, P /'tJ!!X/CJ 5 Pu... (35;;1 ~x.j. /7)Clip)Aio.fr93~t;::. (/fJ r' f/,?1bX/Ojmo1tt..,['9,315)CIO *71113 ~ t -:: ~,~J '/..1t)S; :: '-;'1 hr.
  • 222.
    :2~, 1/ ( Vrj:: 10",,,., .:::. I eM 1 I Y,., :::: 15i7/fJ') :: I,!j~vn 1~25c~ I () <:> 'l-';I} 1- jj ;;:fo ;b(rNrtY') ::t. 0; r NflV' IS C07AtSfcn-d- C t 02,. -.:;. cOJ... N~.'J.if' :::. - tlc~:;.. or J 0t::- A -/Lhv- WPjv:: - C q,C4 ~$a .. u~OJf t- ~ ) dr (/' to / ... WITr" == - C Vfi6 ~ dr tJ r:t1.. ~·~I 'l~'j 4f :: -1 'ff"L C !)1t/3fdyfr y~ r, 0 PYo., .-On (&) ::. -:J.1rLc l/t,e (o,.tV ,... r, lAfo.::: -:2..;(Lc4+e ((1.:2.J) 1- 1-" (~) Vi C ::. f ::: 2,()2(P"/.. /6 $'flo.., ",,,Ie r (f,~J1 ~~:)(JIt4K)::: 22./5 m3 C mtJle.", -:::::. ~, ~J" x/; ~IJJe(em! ~f5 :: O#J7S~2(~XJlO{)K. fzs .2. ah-n ':)73k..) :;:! (),70! Cm2.= J,tJixl;~Ys s t//h eY) t;; CJ) Ij:= ICrr1 . -.Y' t Jta'2.. :::.-2 't((25'Cfl>,)(2, 215'j(./O 1I16koX,a 708 t;!!#-)'f) _______.____ C~___~ k (id-cm)',0 ~WI .:=" -/~ 9 }<. 10-3 mol/s lis V; dee'l'eases Wilt -f/~ ~ -:::. - ~ ffL C VI9D (0, :1.1' 'r"'2., " . J . 111 ntl'l1 .1m ( !:.t5) J y .vYc" =-;¥to2. 1... to r60n btl/aYlcG {.znj?utJ.:: [tJIAJIJ,(ff rfi;~£tJnJ((/a/-,;,n} C1 .:::: 2 errc ~6(()-:1I) t fl,.. c/JI.. lnCr"~5) /2. dc dV-= ~tr'Y"L 4.C ;r:b de ~c Oae{tJ1 :2.J) t g (vf)(r-)dr::/)" k (r¥) I~ J(: Ir r'l cDJ9(j {tJ.21/lt; :::.. -iiiV'h(,:.q)Jr- o (:J.. 0 r c Otff8(q,:J.I) t;:: - ff/'~ (~Jr ?c/l't- 0 ... r.-:::/ (1;:.::./ == 1 t.y-fh.z 6..r(),~?dr- - J Y"kJ V'Jt" () '0 j,h,s. CORe ((J,)'J)f:' -= (.2, ~ I$'~ JO~~7~J.t,..vJt' Pc /J'-. '2,j)53.1C!!,"$ 111Jm,lf> :::/./6'" )(li~t6 f". h,s, (J (I )() r .e,,(rf- o,5jdr -.iD Y'1m V'dY' = == O. J 15'5"em 'L /Y/ feJrafed by leI- a = y" I-I),$'" . 1"'.:::. U -(},6" d r :::-dlA
  • 223.
    " () '7, IJPt+Jfi:;~; V· JJIt :;. /) Use a. conf"."J va flAlIJe. I~~ ~' ~ -.L4.(~A)~O 1/1'- A dZ:- ~ • N~ A IS a.. COr.J.t"/-d I1f "l-, :.:. 4- 917~t."wJ @r:::./J trJli.s::::' &:; 3,0",)( 10 4 = (},3()3 P I. tH5 ~ J{)'5 ]::.:::. -4 'I. T!JcWl itr,:;:. tJ- c,:. f..,:::; /,{)/Jy..lats"~ ..:: 4~. ~1 wlt)/e reI (!,~/1 ~aX281f() J-nD mole.·K _~ J / 3 == 410 Sf! ;< It) h1lJle 111m Ofit3 ~ a {J'?j qd- (JlJY'$eh fc/jel') :> ~ [#-{/1J-1 J.:: ~[~]::: 0,3t;,{ r--yfts o~t.r1, WI i~ I!...:::. 5LJ L'vr) L £..'1[~fl.1 J:::. 1- in [rw]:;.ft /<" I<.:-2:r J.rr(fit)) . 0, j5 :: {),D/'l/ ~ {(},(l/?I) ~ (4.CJI9r.i{fJJlj )~.6fJ'!d){O.J6tCh13 s
  • 224.
    :2d.l1- ___ ~m--~ ,,--JO,I5'm- -,-, - --(j.()5'fY/ -~ FrofYl :L&-13 01+(3 :::. OJ{)5 CMY.s C.:: j, 77 >< 10-s;"LJL.; Clh.:J [!orr/-Ytij 1./0 leime NAc1Y'r~ 2. J -'" N~c1t'r1::; O. cff.H:: C 'st(r?'''' ) ::--u . rill;.. /s cons}4nf di!:. '~Az .J Ill; o ,) 1! -Nft.;; NAt":; -c D/18ifftl(J,j~l!!~E:) NAt =- -Nl6.c as ~&,13 ~~~ P,J N..2; 71r') ~1:. := - C 46njj~~ ~ 0 c1,d, r=-lr1lf'b ~ I:::. 0 • r:~, 615""111"::" l6tJW/:: b<J @l:: :rt70 J'r:::: SenF:' ~rt(5~/.7.) f 7,5- 171';-'- 5'1:/0-3 , ~ -J I ' r(em).::: -5x/d ~ + "15 =:, - i: f 15()r~ ~(}O :2.. r;2= (It>tJtJ -l-) /I)(/02f )N'fi- (4Xta4)1500 dt ;:. c. Vftfj fifo, /P - /J,;) o (J'5d~ - 2;)2 J tfoo ,) ~ (4 x104) L~.c- a ;::, c ~rC(!>. 5) ~ l4'1.I0 4 )C;tf)) ~ c11trprr{rJIS) jA/ft~ (3,77y: (O~rruktOtto! fJ1fry'~J5)~ en-is S J< IEl2 '" l- a'!) 4><10 ~ = .If,~" )( 10-7mole/5 = = 2~,/5'
  • 225.
    Wtt(h ~J =c ()fJt3 1m C~) JiI;.:. C Of1l3 (Od9!) c:::: f.. .:: /1 ~1'3 X /05'~ :::: 4t1,/19m4 ~I (l311 PrJ,.m')(;'9f1K) rn mtJ/e·f::,. ~,~ =- O.09~2. ¥;::. fI,,). Yo 10'm% WA :: (40, rf ~::: [/I, ~~ '2 xI~~~rJ.A0.lfJ) m 5' =7, 23 ;( /0- ttltf/e Is CAr z ~ L J Wd ~.r) +- t ::' ).. Y)'1 2.- A;= :t WI -S' 7,'Z]xlo mj/~/s ~ ml. a) PrlKe _p , /J,r ds %' ~,5')( / [} 1-1 :-:. (), ~$-' d ppre I -;<ftJ-i f1"l if(cp):: (.,.:. cp) ~::::.. (o, 75)~~ oS" l5~ F;Ccf): /- :2.JtJ4cf +::<,p94>~ (j,95'C/5"' =- /-,1".,/01 (O~)..S) r;J" ~r (0,:;.5/ -~. 96'(0,:2.5):5' :... (J,5t)(P OIlKe~ O;B 1[(4) lictp) -:: (I x/O-(()Yl;X)(O.~b~(arrt;J,) -::- :;'.$5")< /0 -IINJ7s 6) V. Iv'It f ac.j' ~ f)/71 ~ .:&:£ - 7A 1i(~e) ~ OJ !lire: IS. C()rJ'J'J~p( f· tlltb::::" OAf; (1,0 - tJ) L.
  • 226.
    IF 0"1; TchQl7fes:) n r1 (-&r~er;)Vft,g r:. ::: V.46t,. - ;r '- j... li r; M6r~ ~ /. XIOIc:n':2.(~)(~q!3·.rJ s '29~ fc,/f Pc.:..1J ::::. /).,P/fj On6t. Ti I,e tf,/ % lau,1<B v- ;;'~.17 ftekr 1:-0 eXtZl'Y7;>/e :Z"/~ ~!? -r()fa/ rCE tlClIJtJr C'rIJIS'.)/(:1// ,:ale ~ ~ ~ 1r. 4 'lJ PM". 0118 (r) t. ~ I 1?,~.....-I1 ,qr ,1- Ftl'l --p-- the /iJllaW1i1J t.ltir/d"JC'$ a,".:: t!t!{le rldel? fan T" .3tJ~ f,13 In [ftt') = lIP, Iff,<.1 ~ r_45,15" !'he )'t:1'(:o< ....J;r;li(/4)' htf'e bd 11 rd he/i;' f IS 3rtJ;I')~ !1Je /o/httJ/'{j Exc!;--',L.. 5{JyeadsjJt:!!.t::~6 cCI/c.tI/qleS" Wrr as fA f;,;nctrtlh ,pI: or "/tlh&:/ iC/,fhl L /-PP' /iKed I'Lltl k dftfllJt!':ur ()r 2,Om. !he ..sA.~.Ied ely-ells /~ d/cdle ra ngl!'.1 iPf'lPfll'i'/ l /f;pf de(Jr~dse /te' ,,:"I:I t:I;1ISS./tJl?S' rafl£'ft> 0'-' belP tV fh~ /I')CO< IIJ/dlJr'} t;:i II~uJed. r-~~ eKtllYlf'k:J CL CtJnci&l')sr;:f'I' T a f ~'1:Z A-' Iln,,-I i~ee 6.1p r'~J/ J, e,!41; L..J tJf 3,~ M.) l4e /CE.!' t?tlll$$)tJm: tc?.f.(? IS ,J,:< fr "1,7t'l!-/dp,J" fi, y" ifYi1r::'C'b S' 'J' J r C<-f'-h'r fa e>< C/ J?{j> Ie :J. ~ ,/"
  • 227.
    "~" __ 'rJ__ " , ____ ._ , " ' _ , __• ~._. , ...----~.'-.,- PROBLEM 26.17 EXCEL SPREADSHEET MA = 131.4 kg/kgmole R= 0.08206 m 3 atm / kgmole K DAB = 0.088 cm 2 /s To= 308 K p= 1.0 atm D= 2.0 m TCE Emissions Rate (kG TCE/day) L(m) 0.50 1.00 1.50 2.00 2.50 2.75 3.00 T(K) 288 1.479 0.740 0.493 289 1.561 0.780 0.520 290 1.646 0.823 0.549 0.412 291 1.736 0.868 0.579 0.434 0.347 292 1.830 0.915 0.610 0.457 0.366 293 1.928 0.964 0.643 0.482 0.386 0.351 294 2.031 1.015 0.677 0.508 0.406 0.369 0.338 295 2.139 1.069 0;713 0.535 0.428 0.389 0.356 296 2.252 1.126 0.751 0.563 0.450 0.409 0.375 297 2.370 1.185 0.790 0.592 0.474 0.431 0.395 298 2.494 1.247 0.831 0.623 0.499 0.453 0.416 299 2.623 1.312 0.874 0.656 0.525 0.477 0.437 300 2.759 1.379 0.920 0.690 0.552 0.502 0.460 301 2.901 1.450 0.967 0.725 0.580 0.527 0.483 302 3.049 1.524 1.016 0.762 0.610 0.554 0.508 303 3.204 1.602 1.068 0.801 0.641 0.583 0.534 304 . 3.367 1.683 1.122 0.842 0.673 0.612 0.561 305 3.536 1.768 1.179 0.884 0.707 0.643 0.589 306 3.714 1.857 1.238 . 0.929. 0.743 0.675 0.619 307 3.900 1.950 1.300 0.975 0.780 0.709 0.650 ! ; 308 4.094 2.047 1.365 1.024 0.819 0.744 0.6~~.._.1---------~------ _... .. 1.. --_.
  • 228.
    ;:Lc;r /5' 6'1. ==(2H6 0"'13Clts) t ?13 f/(/f of 6" 2 IJS f:; fo Jel /1,18 Mefti / reduc..fiof1 wil16e 11l1/tlenced 6J /lux of~. re(/,c!,dri["I) !teeds 1 I{m/?.) 6) (3) v :3 ~" (I) (jJ...) y 2. t/ 0) ~,,' c D4-d 4[I f- ;tAoIcJ 1+- iflts rf Clvf!q = I m.2. 6-= ,5'"cm ~ d.OS- m ~Ii 0::" O.:L.{) ~fls ~ o. .Ps; = )...3;2. tkm3 Ms1' -= .2f~ Of :J/mok
  • 229.
    0;(3 -:::;. ')..9hf~1'()J:::.3,5:24 2. ~13':<':; 1.1,116 r=ft.f3 ~'~---- 7<=:?" V(53,3X:z0 7,t:, =- 13,/15' .1<'( ::::~, ?tJo ::;:. IO.f). 'J10 -Q7Jt:; e:fli3 t3.145 ) 0 116 =- 0, ~{)/J'$g (').Z!JOtJ)(f),7:L&O) =5:'77x/O~h11S IZ (),57J mrs I (llfs ::: /vlt.l!b (I' C Ai:> NIr~ ~ CDII"- ..~ [ 1+'1,1+0 ] o 1+ Wt4'6. c..t<$ N~," c cflle[t"CJr~o)-£~ (1+t{)] buf h(/+x)= K_~X2+~X3+-,,,, If X-::::N;r 'J )(2 J )(~, ,.tVIII C:; be vera' 5111all f, in (N t1i~) ~ rJA~ C s c7es HA?:. (I -t ~ ):=:= C.!li6 ~ ({+'I(to) o,k.s () . pjfrl:' =: eTASh (I +!Iff,,] I 1- D196 o~s / t- DAB;:. J f S;11;<"lo~cm~k::::. r.t.4 cSk$ @tM)((.:2.5'~) Ii ,,(9r3S5x.lc/~.I XO,571tj!)-tn{J,:;)/'VAt: - . m3 _ _ (0, () s'WI1.9J..4) 5' {Ij. == 2. I I 3 x I(F flh1 Ie!n?..;,,?:::&;::::::; -...- 0.)Nr~ cJ}'2'8,t" (1,:<) '" ~,I hiD"5(1'.</1) Cl -- A I I == /,97 X 10 trJOif?/l172.S
  • 230.
    ;;t" ;1/ (,,~ ~J) , /,Ne> A(/PI1()Je/1e~tI$ red,c'//;n II? S-///Cdl1 r'llbJer- i, S feacl:J-,$IIl~e i'tltJlb5c"'!f.1Y· ell/hJSIIH'I //1 y'--dlY'e:;eI-MIJ any- 3. No 61.//1<. i'OJltrl btllldJ4 -4 ,CtJn5 h:rn f" 019(:3 s: CtJYl~e n Ira fldKJ In v/J,Ct1fj t;,1 f'~ 0 0/ ) . " " q, IJfl r ~ :~:' Ij:i' -dt; _d-(~' lV~f.) ~.~ 0 j ,. A4", IS t~~J$ll:1n f {.1f" f/ C:,,,.. V' 0, i'"~ lJ.13S" ,,~ {>'J£'" .,ll (11"'1) (}l 7~1() ~---""""~-~'--~-'-~ .~ - ~~~'-.~'-' .. -. -"~,~--~--"- @ r'.::: 1<.." ::: <1,55 m}Y/ C'/D c (H S) Cfls -=(}/S) ((), /)5;!) ;: (a,7ff!.bJ. ,(3.ft 'if'fp,d5'tf) maleImf afl?l =- a,1J.3 rr:uhm! c.J _ (;).156-4- OJA3)'t,. (L.) It ~ 0.12.3 t k ~S") 0//5'5' ( '!,S'S' ~ a, r~3 - ~ ~ c:.. )o.1~F (J, 'IS's: o 21 S{;1 oI I C? l, q3.5 S' (),?..O ./,. .I r:;" 0, ?hS·· o...~ -; G'
  • 231.
    =t= ~::::: CJ c;;;::.~,S"t1 mo(e mY -, .z..~ Cl.3;Z em· C~~:: 0, /";.3 mole m3 t (1Jtf~) =-0 j ~j? /5 {!oJJs;'an-t- 1VAz-':: .-948 d.5 d'e>" .sL C~} - 0de; dz- - CfJI ::: 0 ~ j- c~ @! c ;:. CJ c;-::: :A, 5't,;f- M;e:=. C;l.- -~ @z- ::.3.'2. )(. lIP I'yt G=-7t~, f? I Gg -= - 7~ 2. f'r; (m) r- .<..s~1- cJ c; ~ _7"-;.,~ de: I Nfl .:::: - 0/18 dCit .=- t:h6 (7'~,?) d,i!r r -1/ 21 I r .>Ci/'rJe tt,e. -=- / )( /() m 7.5 -II :L -9 A#e..-- (7~:;.,,[?X/;(/b ltL):.1,'3x/O m:.JH 5 ~,s 2£,2..3 -L- d [t" /.111 ] =~ fYl V' cJ'r II'" !VA- =- DI1B defT. dr" PA§. Ii [ r dJA..J ,-::.fyl V' d.~" d r r-- dCfl - In r:.t C---~+ I d. r 011.6 ;L @ r::: RJ J deB ::::. 0 dr 0.::: a1. & t C, 0l1g 2 2 C :: - !!!- /(,- I DIf-f3 ?-.. r dCft: ;::: m .t-:z._ m &:J. d. Y' Off$' ~ 0118 2- d Cfj. ;:; 111_ rdr -!1l. R?-d'r' 2~6 ~DFtB 7 Cir == !1L r'"-ttL r<.f~ r t- C.2. 1-7)1113 '). CJtf; @ y=-- R..1...) Cit-=- ~s =- ~ If C~ -= ells r J!L fJ,1...~ ~-!:11 R.f ;L0AS +46 eft ::. CIt.s r..aL Cr~~) - in f(;~C!C..) 4~8 20R8 /(2 ells = fJ, ::: ttJa.fm _/ -'I ~') Yflole If 3- tAd'.-<, - O,71al-"" '!!!-. 1IY13 I W/tJ/e = /, 212.. ~i6~ /IJ1b lekrn3 111-=- 0;2...~mAle.> / 0 -It /. mJ, hY'::: (0, 74 )<./1) ~ emil, S' T' -5' 1. Vll6 .::. ?~, I x Jt) em ~
  • 232.
    r 0,)..5' (), '3 0;4- Of S- O,fp 0,15 2'.24 CA(~) -7 r,fP-x./O fj, 87 )( I(F~ /, otiS" 'i- 10_~ I, 0 (Pb ~ 10 1,/"37 >< I~-{, 1,:J.f~ ;<10-' J¥.: J = :2. 11~L N~ =:; 2..11r<L t-f)N3did) )If re r dr r<. froWi "-(,,;;3 Dftt3:: a, IK liscv»Ys Rs ~ o,~!> t YY' 1<.'2.;;: 0, 7~ c.m, L """ 15"em· A::: ~ lufora/Jehlde B.::free om/l1e (! ('-= rc f2ea~ hOj/); Af ).134 Pr~dtl.ct Cit -::.0 o () f, Nit .; ~ ::::..% .Ii-('('2..Nhf)::; 0 I r!l.~ 15 C()i1sf;:,nr df' ) r ci,Ivf-e CtJI?C, d+ A- o"Jsi1w jllk5/d~ J1tJ btilk c.fJ I') f,.././;u ,fl& n Nffr ..:' - tJltta dSt dr" " ~ !~ 10 4f7'r WAr t.r -::: -1rr~ d~ ~ ~ r~ ~c. ~ ftS 11/ [.L - L ] ~ 411/:k.!) C"S /'fA P.. r~· j}(I'r::; -4 jr'[1,8 Cfi s [ ;f{ - 'Ire]
  • 233.
    r2e.Cl-<::- !Ibn /'5cO/YJ(//efe aJhen IC. =0. t=- li._L- [K_l<j M~ :lDIf f3 efts ~ 3 -::.fl- Ii --1-- - ~ /iflf!, :ll#B~5 ~ ~ -4 ~::: 3{JO mole.> -.= j;<./() moles M(6 m~ em 3 ($ ><. );~()k.s) ((J, 15cm1J -t :::": I CvJ13 1:<.. (1,1 x lo8c-¥XJxl;S",,!:oj,~) :::.. /, J'llK It) q;s :::::; 332.5'hr SpY'e4dsltee /:- used h eva/l(qle t ;: E(yc.) Pi. ~CCti~-~3) ~ C}J.8 ~ [1- )fIT).JI em :l em /- Vhl -s I~ (c. -0)== I em-Itt<- &,:1..3 )(~~ ~1I5)atl-/pi. 1 -;'CfY? /J,9'P-Ri C : ;:::. ~2S7 £JI-tRJ.- ] ~~ ta96~~ ~f1~ and (JA-i- tJn ett.li/;'br/ctm lIne, So Iv'e b:1ir1cJ I t:I nclerr~'r:
  • 234.
    aSst{me ~,I.. .:::.:25: f fnrrJ JItA.:::: rlR",;. ~.25.f mm = a 0.:3'59, P 7~O mYl1 ., 's- Ca/clI/qf6' C. .:: tJ, 257g" (0, 'U~ ~5"] IJA- I 'I- 0/1(,5'3 F: ~~r. U(- 3 fi(~ ~ur;tg.) 1, Nit T 2'~,#( () jr (r:l.~r)=- 0 J r~r;i> tdf1J-hYJI: WUK (-'--):: 4 rTc DAB/.1'1 [Y-.] , ((.5 ;L /,0 WLJ~'=-" ~1rC ~6 .en (3.0) '£ S' e.::. if :::: /,Prs~ It) ~ f! 311- !6.'h1 3 Ylo~aK mole'f<U _5" ::: t~t I! i'l1(}le == /.:;, Ie '/... /(J I71Jlie /In:? cm3 Wv~ ~ :).tr ((.:21 f x 1:;~eff()'33~.e y [0,:;. ~m) ~1 ($, (j =::. 4.5'9 )( II) -, /ndkls /"," I .~ / + I {/ I ''IAr 1i: 13.=: 37~ K J it13:: aiPS- Ba615': L:::. 1m ~. - I ~ --11/ 1 Cr;-7j) =~t7tl/: ca~73-7;.),. f~)1~tAu: Chec-k fp s.ee 1/nilIIIr4 / Convectldn IfI1O:>tJrtt'll1f: !Veed tt ~ ohi-'41r; t /. f;/t)"J 'I"'/J r fr'()Ou! (' fIe s ryuJ (Inti (In'/J'''J 4SSUfJ1e f.::]:I.J'k 7{;/m =3.2 ~t370-= 71'1 '" L' ~ fi l~,c::: £ J.. f(fv.)rdlff :pJ~/4 3 L L 4:41:<' @35tJK) R:0,(;'I7 i(Pr)=-0,51.9 '9~{~= O.4>r;IS'/.. {O-8'
  • 235.
    ah~ 71;:: 3~!J61':: 570--:f.t?:::.1';. Jt/J.r.:::; O,tJ/5" dn/mfIJrjpnr I~ ) , Itl (1).-7;) ;:: (- ~r )(1;) Au ".Nfl 1- Jjf: f}{''' t (rlJ/'IY') -:=. 0 ) r Nhr IS' C(}Y)6m"r o Nflrr =- - C 1)116 r!.!b- f 'jr:d~r- tJ}l~ dr- Nftr :: -c Dt48 diB (- fA d". R.~8 1't rNftrf ~ -::::. C DlTa (- ~tp R V I-,/t+ Vff~ rN/tr Rm(f{jj) =: ~ 11,1< ~1/~'~5] R r I-yflfo Nhr-I ::: C Dflt3 im[l-jiAsJ R" Rk[~J I-yfi~ af asstlmed 72-= 32-f K J ~ :::.34'lK filii..::: @..c;. ~ ~/!";'!!'-:; tJ./5b p lJ() i11 WI A,.:; 2370 ~ S' C :::. .t:.. :: ItrJ/J )( II) fa., R. T (r,311~' m.!X.34f!X) wltJle' /<. _s ::::; 31JII rYlIJle..:= ~1rtxltJ It¥J.t. m3 errl 0116 @ 2rfK .:: 0, :Z~O c.m~/s ~ ~Vc97XJ;' := 115'. f @0= :<-'13 TK::: ~~J." ::: 1,'~4 i-Afj Jas:r ..fLp ;:' I, 1'1 ~?;. ::;5..!ft? R:; ~ .:::. /J!1K 6!tB 1!5/f Jl.o..::. ~/{)~ :1~ ) ~G :: (),:u, () ".!J).f4 (W) (IrUp7 r", S ;;''13 I. UN) =O,35~ tm% NAt'': eV"B .In.C:-1i4J Rk[~S] :: (3.1'11){ lri~X'o.1.5?J 'I)in (f~)cm.5 {.1I6 (4 em) k [%!-] :::.- - f.()17x li-1- moles/em2. s Checl( /(/ ~ee /r 1i~ 32f:- (~~ ~ )(J:ZJ:rSJ,,310) rn ~5·f< -1 =(r.tJilx Ie; W/i?k.s Xlo1:.m~/!li)(2 31tJ~ Cm2,$ i'H~ AhlJfI (f 1{;,j ~ S'tJ .:= -4tkI?I / " lIe ltc.·.!J2.(" 5"
  • 236.
    d. (NAf:) ::OJ" ~ It, tans/anI- de ~ IVA .:: -c ~e d.!itJ. r ~ (14t2:+- tieC')n~ d~ ~ / Me.),A ::::- - NB;t Ag NAl(so) ~ - Nel; ~3) J Nt3;/::' -O,9tJ9 1v'A-c Nit2-;; - c lJ"e; ci..jp f U(t (~ - 0/1()f/NIt;;c;; d 2:- if~, 0" tJ9/ flfl Niti!::' C 0,,8 f~(T~ (;,091 dt 0, OCf / :flta> J- 0,0'11 #14 ~ Vll8 k [ J-o,bfl i flsJ {J, 09/0 l-oJ),!1jtt<XJ hir sphey-e: J- d (rJ..N ) -;::;~.1 elf yJi. JY- t1r I ~ ~ - T;?,q~ r dY' - [)RI! sL (V'/),JCn) == - Ie eLl r2. d r ;J1 ( n 0.. d-: (y2. ci..1t):=: ~I Crr r d,;' ctr DfJ$ (a.) let- j/c CITt' ' s!. 'i- -:::; Y' c!Cff~ + ~ cd r oV' Stl6sf,.ful/~)1 Jlllt> ta) lIJe'k/s q2.~ (j '/1 -'- ~" 7J :::;~; G, d ,:t 0,.1(3 .', ~-=- C1 C~~A(rr;r;:;;f}d) .___~ ..,. Ct}. '5m h (r ,r:klfDfJj!.) :::: tt't r @ r::: 0 J fI:;: () and (!./ :::. CJ ~ r:: R) Cfl -::;' Ctit) C fla R % C::L S)n~ (R.Jh;iq,e) c -= c~o Rz ,..-.-- 'Sm I, {R ~ I«!DI18 Czj. -:::: ~ E Smh (('~Q)rr (Jr, .- .sIr; h (f( ~70;713 )
  • 237.
    hCJWJ eXQfflcP/e 2~,1 h-If) '1j 41A13 =- ~)< / /J. fJ17S f( .:;:. (/, (JtJd.. m II '3 CfttJ'::- ~,":l. m~ m k,::: /.9'f. /ti:l. /5 R(F:t :;:. o.O~~YrJ /,q ~M-:J.~ . == 11.1'9 01'18 :J..'I.. IO-IOm:2/s :16,,31 ' fir high cOl")cel1 t,.o hb;n,) GA .»> k'r-r RA :;: - t<AY'r1O-X eli ==.- ~ ;;:: - rn Cft mCl.)'. /. let/'() tJrJer fA Yell/fh o" I hIt) fI'lm :<,,!Va }"teSIS /anc'.:£ It, cpnvee.f;ve mass -frans/er" @ 6oundaf'j j,e/-weel'? !lui! t.:lnd b"/tJfi/n ) :>p{riace I,e. if~O) eft':: C'l+o': $;p M.:JJN!rJ):if ~. lit 2'::~) dCIl /d1:::::' O. 4. SfeaJ3 -sfafe d,/fu5/~n In i3-- dJ reeflOtl onl;!" s: Nt) bw /1< l2onfy'/ btJ hbr1 4.fa ;: P1- 1: - J12.- t5 Jt;- "ile OA6 C~::: 121- ~:2. -~ ~ ~ f' LIlt!' :2. 1I~6 ,*,8 ~ l- ~ - 0lte ~ :::. ";'Q,~ I!!1- c--f!J} ] cI 't' P,f6 [J~t3 :::: W1 ( c5' - c-) Nfl};-::: fi,7x/i:moL ~,dtJ.:l-lJm m3~5 .
  • 238.
    /he? UP7.s-/eQa"{f'-s/'q/e cO}-Jcen-rY'ahon rfl"tJ//kait:fn,f pas? hdn e /6 f1fVef7 ;,'; ? U'Ct'hon C:z?-:uj .. /he' 4x t5 Clb I'?//Ic>d 6y c!;/hr-~p?h4ho~ of Crf (~tr) aH4 tC".s"j.lh?,c,/1"1~) h/haJ~cI 6{ S-ub~-/,I-~IIQ'1 or E= L r c£J c. H' - f1~1T;:(.4t6't 1 ~ .:: 41sLI- ;? -.2:- i- -A-starr)e -t.;=~"'-":"::""'.J L "lrf1;;'/ ?.rr'1- t Jell; = Cf1;5 [_ L - 8:.:, l L n1'1't'os(r;J[.fi)e-17 :;III!;de:- L. 1:t' I):::. {n I- I- M? d''''()ce.5s II7~trf COo¢h!,tJltJt/.:;;- CiI'lJ ~~~;7r/es ('t/ .Ie?! /crl/?71"l6 are /f"t7v/deJ iJn olf-QC'!,t!"I'I[::5t1tIJCI!-C-Y' ..:5(f't;("'dcl6-6C"t?i: /l./CJffl..; clur'l/Jf ~P fir:>! htJuY' 1/;4/ IV/t.-z: Is (!/o.>e 1C7~eVtf al.z-:::;L CIS rhtf' CpJ')/n'/ /1 I , l L " ! ' ;'/,;./, ~j vV'/ t-Ime !.5' >",;1/h'?# ~t;t' ?t!/",; /!' - ()t7'C1nc t/4'1'1,;)r'.. 12;7
  • 239.
    ,~. __~~"_ ". F"~ PROBLEM 27.1 EXCEL SPRFADSHEETPART (A) A- n-octane L- 100.00 an T- 15.0 "C e- 1.00 DAB- 0.OS73 arr/B«- d- 2.00 an e2DAB - 0.0S73 arr/-. w- l00.00.an PA·- 1039 Pa MA- 114.00 kgIkgmoe PT- 101300 Pa PA.I! - 0.703 r/an' cAI - 4.340B-07 grmle{cm' mAl- 14.06 kg Tlme,tCaec:) 3600.0 7200.0 18000.0 36000.0 S4OOO.0 72000.0 Tillie, i (Ir) 1.0 2.0 5.0 10.0 15.0 20.0 NA(gmote,tm2-sec) 1.063&14 3.222E-12 7.735B-ll 1.838B-I0 2.2S2&10 2.402&1Q NAca.mz-h) 4.363B-05 1322&02 3.175B-Ol 7.s45B-OI 9.241B-Ol 9.856B-Ol ; ! Series Term II = 1 .8.158B-Ol -6.656B-Ol .3.614B-Ol ·1306B-0l -4.720&02 ·1.706B-02 2 4.430B-Ol 1.962B-Ol 1.706B-02 2.910&04 4.964B-06 8.467B-08 ! 3 ·1.601B-Ol .2.563&02 .1.OS2B-04 .1.106B-08 ·1.163B-12 ·1.223B-16 4 3.851&02 1.483B-03 8.467B-08 7.169B-15 6.070&22 5.140B-29 , 5 -6.165B-03 ·3.800B-05 .8.904B-12 ·7.928B-23 .7.060B-34 -6.286&45 I 6 6.569B-04 4315B-07 1.223B-16 1.496&32 1.829B-48 2.237£.64 I 7 -4.658B-OS ·2.170B-09 .2.194B-22 -4.813E-44 ·I.1lS6B-65 .2.316&87 8 2.199B-06 4.835B-12 5.140B-29 2.642&51 13S8B-85 6.980B-114 I 9 .6.908E-os -4.772£.15 .1.573£.36 ·2A74B-72 ·3.891B-I08 -6,12OB-144 • 10 1.444B-09 2.086&18 6.286&45 3.951£.89 2.484B-133 1.561B-177 I 11 ·2.010B-ll -4.040B-22 .3.281B-54 ·1.077B-I07 ·3.533B-161 ·1.159B-214 12 1.862&13 3.466&26 2.237£.64 5.004B-128 1.119B-191 2.504B-255 i 13 ·1.148&15 .1311B-3O .1.992£.75 ·3.967B-lSO ·7.903B-22S ·1.574B-299 i 14 4.109B-18 2.218B-35 2.316&81 5366&114 1.243B-260 o.oOOB..oo . I 15 ·1.286&20 ·1.654B-40 ·3.518B-l00 ·1.238B-199 -4.356B.299 o.oOOB-tOO 16 2.338&23 5.464£.46 6.98OB-114 4.812£.227 O.OOOB-tOO O.OOOB-tOO t 11 ·2.828B-26 ·1.991B-52 .1.808B-128 ·3.211B-256 O.OOOB-tOO O.OOOB..oo 18 2.277B-29 5.184B-58 6.12OB-144 3.745B-281 O.OOOB-tOO o.oOOB-tOO 19 ·1220&32 ·1.489£.64 .2.705B-160 O.OOOB-tOO 0.000B-t00 O.OOOB..oo t Series Term II = 20 ~52&36 1.894B-11 1.561B-177 O.OOOB..oo O.OOOB-tOO • 0.000&+00] 90000.0 108000.0 126000.0 144000.0 162000.0 . 180000.0 198000.0 216000.0 ! 25.0 30.0 35.0 40.0 45.0 SO.O 55.0 60.0· 2.456&10 2.415B-I0 2.482&10 2.485B-I0 2.486&10 2.486£.10 2.486&10 2.486&10 1.008B+OO 1.016B..oo 1.019B+OO 1.020B..oo l.020B-tOO 1.020B-tOO I.020B-tOO 1.020B-tOO . -6.165B-03 -2.228B-03 ·8.o52B-04 -2.910E-04 -I.052B-04 -3.800B-OS ·1.373B-OS -4.964B-06 1.444B-09 2.464B-11 4.203B-13 7.169B-15 1.223B-16 2.086&18 3.559B-2O 6.070B-22· .1.286&20 .1352B-24 ·1.422£.28 .1.496&32 .1.573&36 ·1.654B-40 .1.739E-44 -1.s29B-48 ~ 4.352£.36 3.685B-43 3.12OB-SO 2.642&51 2.237£.64 1.894B-11 1.604B-18 1358B4s ; .5.597B-56 -4.984B-67 -4.438B-78 ·3.951B-89 .3.518B-l00 ·3.133B-l11 -2.190&122 -2.484B-I33: 2.736&80 3.346&96 4.092&112 5.004B-128 6.120&144 7.484B-160 9.153B-176 1.119&191 .5.D82&109 .1.115&130 .2.446&152 -5.366&174 .1.177B-195 .2.583B-217 ·5.666&239 -1.243B-260 3.588&142 1.844&170 9.418B-199 4.812&227 2.504B-255 1.287B-283 O.OOOB-tOO o.oOOE+oo .9.626£.180 -1.514B-215 .2.381&251 .3.745B-281 O.OOOB-tOO O'(lOOEtoo O.OOOB-tOO O.oiJoEt.oo 9.815B-222 6.170&266 O.OOOB-tOO O.OOOB..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOB..oo .3.804B-268 O.OOOB-tOO O.OOOB..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO 0.000B..00 O.OOOB..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOE+oo O.OOOE+oo O.OOOEtOO 0.000B-t00 . O.OOOB-tOO O.OOOB..oo O.OOOB-tOO O.OOOB-tOO 0.000B-t00 O.OOOB-tOO 0.000B-t00 O.OOOB-i.oo O.OOOB..oo O.OOOB..oo O.OOOB+OO O.OOOB..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOE+oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOB..oo O.OOOB-tOO O.DOOB-tOO O.OOOE+oo 0.000'£..00 O.OOOB-tOO O.OOOB..oo O.OOOB..oo O.OOOE..oo O.OOOB..oo O.OOOE..oo O.OOOB-tOO 0.000B-t00 . O.OOOE..oo O.OOOE..oo O.OOOE+OO O.OOOE..oo O.OOOB-tOO O.OOOE..oo O.OOOEtoo O.OOOEtoo O.OOOE..oo O.OOOB-tOO O.OOOB+OO O.OOOB-tOO O.OOOE..oo O•.OOOB-tOO O.OOOB-tOO 0.000&+00 O.OOOE..oo O.OOOE..oo O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOE..oo O.OOOB-tOO - O.OOOB-tOO I • O.OOOB-tOO O.OOOE..oo O.OOOE+OO O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO O.OOOB-tOO 0.000B-t00 , b·)·/f;~ Cln1 ~wn-:r-·;ln-::;cf.o,e e~~-..Jft'~· m;;:~-IS .1tf'f1!J'/C'd 61117.f<lr~;ftlr f {,I I. oJ '-' lid /Itt>< .;;1 c:::. L (tJl hI r~.$tp.",,,,,t- ,1;: Orne.' <o)t1 Zt;r:l[) f::; (;l.. . -t r0i18L'R t t (-I if #11 ~B 1t:.)7 m/tlt) =: W7A;/i't == fo #tlc.df;:: ~; :IiL L-Y- -f :J. ~5 t. f/::'/ n:l'f(:l.V -~ . J ~?£
  • 240.
    , i;t!1t? rejtllred!c;r- fl?/j (f) "':/YJrt; ttJt?5 de fenr?lflc,1 t4$/11Jj //1" f~' Ctw~jJl!litf'r {;pre'odsJec';; (p,,,,,; 13), 5iJt'tl/;.(I'?iI!/J Cl Illne t')e1~Jt"l/',f,)'C'.'tYj One! h117 ttJa$ ca/cu/Clfedr the 1~5;t)lv~r' ftl/}cl/£)tl il ol1fhe C:tJi'Nrft1kr 1- ~---.---.--.---~.-~' - PROBLEM 27.1 BXCEL SPREADSHEET PART B i, A= n-octane L= 100.00 em t,~ 511r5' !;;/tsT= 15.0°C £= 1.00 DAB = 0.0573 em 2 /sec d= 2.00 em £2 DAB = 0.0573 em 2 /sec W= 100.00 em (basis) i ( Calet4 (alk!/~$ 1!111C!t'e'd PA*= 1039 Pa MA= 114.00 kgIkgmole l/t:YH!)' ..5////. 3 n-oc';(1f)6' PT= 101300 Pa PA,Iiq = 0.703 g/crn eAa= 4.340B-07 gmoIe/em 3 rnAf= 14.06 kg It i'j' Id t{j;,f,1/v[ ·//;e. I, .• t= 4~963B+07 sec .l.)(}li:,."J/.1S u ;rock /af/,~/<) t= 574.5 day released rnA = 1.233B+02 gmole (basis) released rnA = 1.406B+Ol kg (basis) L _ n Tenn Summation % Change 1 -1.013B-Ol -1.013B-01 -_._-_.. - --,,- ---_._.-. 2 2.533B-02 -7.599B-02 33.33 19 -2.S07B-04 -S.347B-02 0.34 3 -1.126B-02 -S.725B-02 12.90 20 2.533B-04 -S.321B-02 0.30 4 6.333B-03 -S.092B-02 7.S3 21 -U9SB-04 -S.344B-02 0.28 5 -4.053B-03 -S.497B-02 4.77 22 2.093E-04 -S.323E-02 0.25 6 2.S14B-03 -S.21SE-02 3.43 23 -1.915E-04 -S.342B-02 0.23 7 -2.06SE-03 -S.422B-02 2.46 24 1.759B-04 -S.325B-02 0.21 S 1.5S3E-03 -S.264B-02 1.92 25 -1.62IB-04 -S.341B-02 0.19 9 -1.251B-03 -S.389E-02 1.49 26 1.499B-04 -S.326E-02 O.IS 10 1.013B-03 -S.28SB-02 1.22 27 -1.390B-04 -S.340B-02 0.17 11 -S.374E-04 -S.371E-02 1.00 2S 1.292E-04 -S.327B-02 0.16 12 7.036E-04 -S.30lE-02 0.S5 29 -1.205E-04 -S.339E-02 0.14 13 -S.995B-04 -S.36lE-02 0.72 30 1.126E-04 -S,328E-02 0.14 14 5.169E-04 -S.309E-02 0.62 31 -1.054E-04 -S.33SE-02 0.13 15 4.503E-04 -S.354B-02 0.54 32 9.S9SE-05 -S.329B-02 0.12 16 3.958E-04 -S.31SE-02 0.48 33 -9.304B-05 -S.338E-02 0.11 17 -3.506B-04 -S.350B-02 0.42 . I 34 S.76SE-05 -S.329B-02 0.11 IS 3.127B-04 -S.319E-02 0.3S , ,I 35 -S.27lE-OS -8.337B-02 0.10-----_._ .. ---._-----_. _..
  • 241.
    /1 111/ luil;;;/M / I r'/ ,'I ~ -'1 i. Due Iz> ,sfflCl/; {J;;t' r'U,s/c// 1(/ 1)( If) if ") ClrJd /tJnJ d,.s/Qn~/ /h/6' CL. .5C>ff/I:'- II? hY71 Ie' dl / /JIS fa n ~J1:. :::; n ir.e) t;- !,//f6 ~ dl:2. @ f:.:[) ) c14 :: CAd =() a~:J t~, Cit:; ~s (j) ~::CJ Cf'W ~ CA~ "" /) ~7,3 z.::. 6"cm::- c::? cPSJ11 S.,... t =: 72. h;p" ::: ~,,$"'/ '!< /0 .s o.o5m '2 i(/,/: ~-v",~1J.,5f:'/~fG- s ::: /,0'53 erfUp);. eyf{I,?'5"3) -; OJ '11,)" {Its -Cit ::: ;Z1- Y1 ~ (/.. Cf1t2....· ('lis -L,4 :2.1-tJ C .=- cJ, £ 15' m,j/e,j,yJo ~ ~-==---.: J) ;::bY' fir/I fe 6/)t(l1~dhJ c!dl1rJ;-i/dt)s.; ()nf?-,/;mef7•.<)lollt;? I tlll<;<Pticlr-5 J-~le./ v COr1tt!C')71f"'4 ,1;£)/; rfJrLl/;k hI" /;JeI'7.;f("7F1cf dI5StJ/I/'C"/ III (j}llfr:-r-s't1 ft1tC'lled .5cti//.$ jli/eh bj/ PROBLEM V.3 EXCEL SPREADSHEET A - benzene (m water solvent "B") T- 293.0 K M... • 78.00 kgll<gmole OM- 1.00&09 rrf~ w= c.... _ 24.0 gmoIe,b!' t - 2.592H+05 sec t- 7200 h C... & 0.675 gmole,b!' iI Term Summation %OJange 9.98&02 9.983&02 3 9.85&02 1.983E-Ol 49.67 5 9.59&02 2942&01 32.59 7 9.21&02 3.864E-Ol 23.84 9 8.72E-02 4.736E-Ol 18.42 11 8.15&02 5.551E-Ol 14.68 13 7.50&02 6.300E-Ol 11.90 15 6.79&02 6.979E-Ol 9.73 17 6.05&02 7.585E-01 7.98 19 5.30&02 8.115E-Ol 6.S4 21 4.56&02 8.571E-Ol 5.32 23 3.84&02 8.955E-Ol 4.29 2S 3.15&02 9.VOE-Ol 3.40 V 2.52E-02 9.522&01 265 29 1.95&02 9.717E-01 201 31 1.44&02 9.862&01 1.46 33 1.00&02 9.962&01 1.01 35 6.36E-03 1.0038+00 0.63 37 3.35E-03 1.006B+00 0.33 39 9.686-04 1.0078+00 0.10 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 -8.32&04 -212&03 -2.97E-03 c3.45E-03 -3.63E-03 -3.60E-03 -3.4OE-03 -3.09E-03 -272&03 .2.32&03 -1.93E-03 -1.55E-03 -1.21E-03 -9.186-04 -6.686-04 -4.636-04 -3.02&04 -1.786-04 -8.71E-05 -234E-05 1.86E-05 4.37E-05 5.64E-05 6.04E-OS 5.86E-OS 5.33E-OS 4.62&05 3.86E-05 3.11E-05 243E-OS 1.84E-05 1.006B+00 1.0048+00 1.0018+00 9.975E-01 9.939E-01 9-903E-01 9.869E-01 9.838E-01 9.811E-01 9.788E-Ol 9.768E-01 9.753E-01 9.741E-01 9.731E-01 9.72SE-01 9.72OE-Ol 9.717E-01 9.715E-01 9.714E-Ol 9.714E-01 9.714E-Ol 9.715E-Ol 9.715E-Ol 9.716E-Ol 9.717E-Ol 9.717E-01 9.718E-01 9.718E-Ol 9.718E-Ol 9.719E-Ol 9.719E-Ol 0.08 0.21 0.30 0.35 0.37 0.36 0.34 0.31 0.28 0.24 0.20 . 0.16 0.12 0.09 0.07 0.05 0.03 .0.02 0.01 0.00 0.00 0.00 0.01 0.01 O.ol 0.01 0.00 0.00 0.00 0.00 0.00 1.00m 0.05m 1.00m 0.0 gmo1e,bl'
  • 242.
    2. "J, 4- ..0- n~~OA-8-t4:4 ell-CAS _ 1- ~ .LSinlr11t'~'e /' -trLh LI-/ CRt)- 'its Y/-I tvhere "'X1:::'l::....:::: / m')... A Cit::: /. 00/llm3 fiJ i£':;:- XI Iff 1/,15 (JtJ'l'7l; a/I /he 5"/l/1 /5 c!tJnftlmlnaftJd bect1t1.5("J' tji (,b11116e dl In I i1) 1"I''I/.IIrA., /I /IScJtJer/VY}~ Ilt);1 ttJ.as u~r?J ~f1 aitdc/;edt'prn(JtI/t!Y' sJJt'~(Jd- ..5h~e tj l:.lfI'l~ thi/lle J'pt!'.5'st!d I Iert!7 f; /.Ie1'1 ct n 1-/) C'tl::: j,().h ttl:e::. XI" ./ 1+1 3 A~ benl;tf'ne (,n wa/-t'f"'.J'tJ/ven.f 8) r= ~93 1<' XI:::' ~ ;:: /1~tJft1 MA-" 1 !,~ al?fYI~/e' ~.:::; IdJM Oil"'" /x/~~rm"/$ w:: Id) frl 1,/"3 ,..~ Cill A o:f! C>. tJ gl1'l()Je/rYl c,q~::: ;2f,~ !m~/~/IYI'] "<1 n Tenn Summation % Olange ~1 1.16E+OO 1.160E+OO 3 -1.84E-Ol 9.763E-Ol j18.8 : 5 2.50E-02 1.001E+OO 2.5 7 -1.92E-03 9.994E-Ol 0.2 9 7.67E-05 9.995E-Ol 0.0 11 -1.53E-06 9.995E-Ol 0.0 13 1.50E-08 Q.995E-Ol 0.0 15 -7.19E;.11 9.995E-01 0.0 17 1.67E-13 9.995E-01 0.0 , 19 -1.86E-16 9.995E-01 0.0 21 1.00E-19 9.995E-01 0.0 23 -2.59E-23 9.995E-01 0.0 25 3.21E-27 9.995E-01 0.0-~'-'--- -----.....:..........--.---.-----~-- f(e~u/red t ;:::. 43s:5: da,!f..s ').41 n Tenn Summation % Olange : 1 1.17E-01 1.168E-01 3 6.79E-02 1.847E-01 36.7 5 3.18E-02 2.164E-01 14.7 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 1.65E-02 2.330E-O1 1.00E-02 2.430E-Ol 6.70E-03 2.497E-01 4.80E-03 2.545E-01 3.60E-03 2.581E-01 2.80E-03 2.609E-01 2.25E-03 2.631E-01 1.84E-03 1.53E-03 1.30E-03 1.llE-03 9.64E-04 8.43E-04 7.44E-04 6.62E-04 5.92E~ 5.33E-04 4.82E-04 4.38E~ 4.00E-04 3.67E-04 3.38E-04 3.12E-04 2.650E-01 2.665E-01 2.678E-01 2.689E-01 2.699B-01 2.707E-01 2.715E-01 2.721E-01 2.727E-01 2.733E-01 2.737E-01 2.742E-01 2.746E-Ol 2.749B-01 2.753E-01 2~756E-01 7 Itt t:::. 6.to'I. /0 s -:.. ~/OVe..ar'$) mI'l .::;:..5I~ ,!i.ttlfrJ ,:: 7.1 4.1 2.7 1.9 1.4 : 1.1 0.9 0.7 0.6 0.5 0.4 : 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1
  • 243.
    I:/. I g CAl>':=I K /0 tihJl11S/ CWJ CIfG ::: :<. X JO~/ Cl.f~ms/CmJ t: .:. / At" :=. 36c:Jtl 6 -1 Z~ {)...Jr1JeY'c:JI'')$: j.l<ltJ em Dl9-d =5x /tJ- 13 cm% ;2l7 cp == 111.4:11 Vt;'(£l ("-1 Y' f Ih /.7J 17 fJ-L f5f tCS) 3~()tJ tPI13 7fl:L 10,; 7,,64 1~(t1 dJ eY'fctP) 2.551 0,99904 I /.? 0, <Ii91 /1 " 0,91'3 J,4- 0,95),3 I,l 0/1103 I 5' ~ 0~~J /,0 0.1+:<'1 ,0 ;u ~~O 0, 9(,~:<' 0. !:.fp;;., t(hr' / 2- 3 4 5 t, o. 911r = erf ((f )2 q'15i I ,i ::' cP:= ;2,R 7-.tDAfJ1; Z: = 5.''' JSx IO-13~2-#~) :::: 3.9[P0 )(, /~-t;it;) Z: UYI t r lCtnJ Z iJ.Y7f:.f (h1tcrOf1s) 36tJ(J :)./34,7/-;1 ~tJ1~ 7200 -1 3, ~~() xI~ 3;-;6 lC!;i~/) f'//~>t I~: 4;IJ~ 11j11JIJ 4.75)( ItJ 4,7,j I~OtJ(} 5:3/ 'J./o-1- ~11 -1 s,r.2 ")~(p~~ 5:g~ y. J()
  • 244.
    6) eNS;:::' ~,Ox /O:W a/oms Icm3 Clio':: I. x IC/~ aftll1'ls Iem] C,q.;::' / x 10 IgQhJlJ1slcm~ if: := :z 'I- 1(;-"'clYJ erf(cP)~ O,9?5" J cp:::';(rO " -f 2,():. C .:::. :t."j. ItJ tfY1 .l~D~1; ;z.i~/tf IrC,;-{t S- a ::.70, 71J,) 1:-= 5tJ()/J.s f -4 Omtkln PIn wal'er @ Jx/ocm !!!fl ~ L~ v;i~ Si!- c- ~ If~ =:...1.: 4 Fi~~~--:":i"""k-;xt-65-'""-!J~) >< :2 ~ (0 ~m qr oS - - )(. (Q,)( l()i~(JIIfJJ..s) tJm3 =5.~4:lx. If) '~fplYIslcfl)3 ii!rt =- rflIIIv !!!.!J. -I- m5 ; V V _ S;61~ x10J9af-tJfns(.3tJ.17fJ- CI1)3 irfomJ ---I--=- - ... (~k1:< l( to ;X3t1,'17) +(f),xitlt;ll.07) - /'~4 x 10-3
  • 245.
    ::27,/() 011'/14,)/113 hm cJl7e.;a~e t ;:::./Ohr = J't Of}{}s , j , /)J/rt>'= o. UJrrs os a0I '1:.(' ~ (.;'hlcKYie~s):r 2. (0.5'mICf'df1) =1n1lcr()y1 =- I ~ ItJ"' 4 CI'J? VAS::::' /,5";< /~-13Cm2~ ... / g , X-::: 'Dl1e! ~ (I,5')f./()crrfI;.XJiP,}o.!S):::0,51 1, (I )(: IO-4cm)~ as t ~/fXl.l Cft -''')0- t',4$ q'1d mA~PlAf fnlrf -:;:::. C,4.$ y7lf(S-:: 0.110 "'3 Cd, ft; I-q! tim"tthl aJ fraf1.5 it:rrc!) Info 3el bead h1 ..: IJ n r;. a, 5" i (n: 4); OIP..1} 'Ita,;):' 0,2.1 Y(VI :r') :::. (}/~:4 W,4s -tUff ::::. 0. 21 .::: /J,()/-tVA WftS-i'Ilfio 0.01 -tJ tJllt -==- '"r;, x. /P- 3 ) 0, 7~ % :J-J,II --CAs'::: tlt / fYJeJ/e/m 3 Cit;::: K4ts;:' /5/;{eJ, I) ~ /bmtJ/ e /m 3 CAD ~O (a~~~~d) fZ :::: 0, 'J.,5'em -/: mA (1;) :::. J NACt)d-l: o 6 Q/) I ( - ~6n~rr7:/{(it) n· 1 2 3 4 5 =:: mAf -.z.l n;. I-e 11' n=-I . ' I: I. .fJ- .1- -Qt/r Z- (/1 -, n;t.J " /_ m~l.£:);:. f. ~ ~ eDItBn27t~k2. rtJlI f 11':t /.., n ~ .,. n:::;1 .YUl'Ylmaflcn ca/ctlkhons are i I vel? in ctJl"rlptltr!3 r spY'eadshee t:. Term Sununation % Change 1.03E·OI 1.031E-Ol 2.80E-05 1.678E+OO .93.9 ' l.44E-lO 1.678E+OO 0.0 9.88E-18 1.781E+OO 5.8 i 8.I8E.;27,oI7B':: -:L)( !{[{,em%- '-.~~-~ 1.?81E+OO ___Q~O1 Cf~ - ~ _ 1!:::..!2;::: £1.20 t~-Cfh?- /5 n::.. () a ' y'}1 :;:: 0 ...:../:j!}_t - (;, ;).,:2. , 1<2 - a 2;), r<..:t l.to< ' )~{ ..... ~__,_. J ::: 0,:2,2, (o•.!t ,;;,(! fI'1 ;;;. b 9(}/Js Q ----;.-(i----T~- ',4e ~. >(to (:»11S - - t -:: 7J.O()s :; d.....Ohr /- m(? (t) == o,{){':5 mflf m;4 ,;:: (), 10:3 t~!l2l -CA :;:::;. is'JS It'il/emil_=--~~7!":;~.~=_~_,!:,:,!":::'=::::--=:,:,".....
  • 246.
    I ; I ! i 0.0 72iTime, t(s) ITime, t (h) 0.0 0.020 WA (gmo1e/sec) 1.0 1.0lE-09 WA (J.unol/h) 0.0 3.65E+OO Series Term n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Series Term n = 20 5400 1.50 3.45E-11 1.24E-01 9.78E-Ol 9.13E-01 8.15E-01 6.95E-01 5.66E-01 4.41E-01 3.28E-01 2.33E-01 1.59E-01 1.03E-01 6.38E-02 3.78E-02 2.14E-02 1.16E-02 6.00E-03 2.96E-03 1.40E-03 6.31E-04 2.72E-04 1.12E-04 7200 2.00 1.94E-11 6.99E-02 1.82E-01 1.03E-01 1.09E-03 1.12E-04 2.16&07 1.29E-09 1.41E-12 1.58E-16 ' 3.04E-19 2.05E-25 2.17E-27 2.80E-36 5.09E-37 4.07E-49 3.95E-48 6.25E-64 1.01E-60 1.02E-80 8.56&75 1.75E-99 2.39E-90 3.19E-120, 2.20E-107 6.17E-143: 6.70E-126 1.26&167! 6.72E-146 2.73E-194 I 2.23E-167 6.27E-223 Ii 2.44E-190 1.52E-253 8.81E-215 3.92E-286 II 1.05E-240 O.OOE+OO I 4.13E-268 O.OOE+OO I5.37E-297 O.OOE+OO....;;..;.~--- 180 360 , 720 1800 3600 0.05 0.10 0.20 0.50 1.00 6.06E-10 4.0lE-10 2.56&10 1.27E-1O 6.25E-11 2.18E+00 1.44E+OO 9.22E-01 4.58E-01 2.25E-01 9.45E-01 8.93E-01 7.97E-01 5.66E-01 3.21E-01 7.97E-Ot 6.35E-01 4.03E-01 1.03E-01 1.06E-02 6.00E-01 3.59E-01 1.29E-01 6.00E-03 3.60E-05 4.03E-01 1.62E-01 2.63E-02 1.12E-04 1.26E-08 2.41E-01 5.83E-02 3.40E-03 6.73E-07 4.52E-13 1.29E-01 1.67E-02 2.78E-04 1.29E-09 1.67E-18 6.17E-02 3.81E-03 1.45E-05 7.99E-13 6.38E-25 2.63E-02 6.91E-04 . 4.78E-07 1.58E-16 2.50E-32 1.00E-02 1.00E-04 I.00E-08 1.00E-20 1.01E-40 3.40E-03 1.15E-05 1.33E-10 2.05E-25 4.18E-50 1.03E-03 1.06E-06 1.12E-12 1.34E-30 1.79E-60 2.78E-04 7.75E-08 6.01E-15 2.80E-36 7.86&72 6.72E-05 4.52E-09 2.04E-17 1.88E-42 3.55E-84 1.45E-05 2.10E-10 4.40E-20 4.07E-49 1.65E-97 2.79E-06 7.76&12 6.02E-23 2.81E-56 7.92&112 4.78E-07 2.29E-13 5.23E-26 6.25E-64 3.90E-127 ' 7.33E-08 5.37E-15 2.88E-29 4.45E-72 1.98E-143 1.00E-08 I.00E-16 1.01E-32 1.02E-80 1.03E-160 1.22E-09 1.49E-18 .' 2.23E-36 7.45E-90 5.55E-179 1.33E-I0 1.77E-20 I. 3.14E-40 1.75E-99 3.07E-198_._------ :27.13 ' /'/' l. ~ fal Y&lfeof Cd l11'e fa / ItJJI} rlUx. //JTO 5fhe Y';'cal jel 6e4d.f't>r ti4o==' () etua/s , t1ND -418 n~rr ').-1:/1<. ~ W!',{t,)';;; ('fiCAs ~e~Ie ::;er/es 5"d/J1mof/CJI1 CP/CLl/t:1 //t'J/)S (.if r& il ven ;'n above C() tr7f u1eV' sf! relld.s/)eel:. Ilrf~r :J. hV') va lu~s /;,y ~ are ve r:l /tJw,j Ir) ellac:r/-/rJ£ l)ul'll);e. fJ e / 6e~d C1)t1S SCif-wYa fed t,/.ul" a bSt.'H,beJ Cd..
  • 247.
    '*$== :;',0 moles1m..! @;l:.::.. 5'mm·;;::' (}." 1)'CIn J f1 i == ¢ ,) ~~::: O. '. /.' :... ", , cp:;:ItI" s" =- ;C_ :J. Jq,.(3 t; 7:.::: /'/~5(;1.)~ ft -:::: O,Scm ~,33 (J,xli'JIJ:z.{£ =.. d,.5ch1 t.:::. 4tt;J 05cJ.!.. r;,.h'lsre,.. lYON? OJ'l/y Ode hce X, =- ~(f/;IC/O?~>'ti).::-I:lml11::=: ;:2~1'17 y::: WI)-s - ~;::::: 0 - at;o~-:!5':. If.. 0334' W)}-s -t01o 0- 0,0/ ~o':- U{,egt.///· fj)lfd::< () tJ)tt .:: (/. dl aJf1et-v;/ y:: (k~s -1:0; ~ W",.~ - aJ/it1 /bINI- &/hlCh C2:SSl/l';r.;>S allr;oa>arls CUll! be Ie.>,:;; IA:1!J pI" '1,,{I6</1,:;. 1% aJl// iJr !Je't1r .f/lf"7aC!~ i!.1.;::' 3mm tJ.:::j,tJ 1)1:::: tJ, H CJpy&, ;:(1) Xp:" :2,~ := J21l!il d Xl J,fh/s/t!17 <:1111: aile' .,6ee.J X.:.: 'U'IJ"t ::;: a,6 CI't/ I OJ " t-";; ::;10 ({j,~t'fnJ- -= Z':;' )(10.5 I )(.IO-7~~1$ - - f/ /;'h~'r;;eled t!!lfi'ClPl ~ frr..<I 10/ I ' " //b C ' dfIp be less / /tJ ~-t/./p"" '. L fapsdr If("e,' ~:;:£?_; f , fw,' ;17,/1 - ...r7" j [ / # ' /~.f/ ;'n/6 {tftJll/d tie fe 1:11/-'/1'/ /./j';l/t:C I?--;t!?c:.!;Yin" .:/./"" -.al, A "'-oo{ -- ~"S' .•~ .:;: Vi t7 "" , :::: {J;5:L.!, tJ}~:; - ttl,:;I'i O,.o:t -(J,t}tJ J ,,J ...t /~;'.~-.,li ,..".{) erf (r:PJ~ (J, 5';)· {, (b "~, ,/'",1:::·::::·" .::: IJ, ,tfj/f~ :2 V011{j. Ii
  • 248.
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  • 253.
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  • 254.
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  • 262.
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  • 263.
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  • 264.
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  • 265.
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  • 266.
    :::. 314/( '1< II W, ----?t ~ .•, t :vv"- Re ;;: "tV [ -:I.., V m)!:::..-.- =- :l ,;;)(10m ,t}5 S jJ I, '115"x IcTsmo/s ~"ft,5 x /61- y -s- Se .:: ....-.::::. 1.1-15'1./0 mo/5 OilS s,4- )<.10 - {; m:J/:s ;:::J., 0J.. '. 1.13 ~h Sc :; C;l, ~:2.) :=: j,9() --lee. Cf/~ A -3 ;::u::: ::. ,.;:::. £/.00:5 :: /,5%;< If) (10 5c ~ I,'to cit ~!lL-..:::. '3~ ;S f< T (-:--8-,:-"31=-=1?~;-,m-<<=51-';:;.-e3-/<.) elf s 2?,30, I'YIdj.J< =I,~ 7'5 >< 16-.1J.I.?drJ13 115 dev'el"~6'd /n 2f1.:J..9 %~L:;/~[!~-"- }/v;;, efl:, - C~cP '- I<e':- JJ'5';<. It/' t;.t...:; 0, !JtJ3 :2.. Sc ~ ,::(, &. ~ 5~ 213 :: /, 'ItJ ~ _ Cf/~ -3 v;. - Sc. ~3::::: /,5'i x /() -3 'I eft$ == 1,~75 'x /0 Jrrlo/lm3
  • 267.
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  • 268.
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  • 269.
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  • 270.
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  • 271.
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  • 272.
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  • 273.
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  • 274.
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  • 275.
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  • 276.
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  • 277.
    --- ((eL.. = il{QJ==:: (0, '5 ~)(tOm). :f )/ /-,-_/ _....-..':::: 3,,1 x It) ':?/xloiJm"Y,s ItI r~;tt ,&J') l %c;:- 0, ~610rt3 sj~ f~e~:;' La {)3t5 ~ 5, 1/3 (12 '1-1.,- £/:'/5) f- ,__ 1913 c. ..... eJ.. - t; j -~---L-'-------'- -~-.----- n ~ / 5' /: I. e:t:::: l;J. ,[J x /0 ) /.4.::: 41-7 Re:lS' = (;).,0 x fOS'/I/s'.::;: 1!J-111 f(e:!I:>;:::; (8~JI;<I/)~)-1/S"-,- ~t:,J053 /J 4/!> 0 +.&- feL. - I'.€" -::::. <E'1:1- .;) -~ u S'c. == 46:: /. '5'1x II) nus;:: O.Sf/Lf 2..,5'4 xllJ-s-mYs Sc. '/3 -== (O,,:),?1) 1/,3'::::: tJ. J'41 _~ I lc:=: (/~/P~1o..5'1;<./~'t~o,r1iX147) /01'1'1 f 0, 03~5(2. S'1 x/O~:f~.J'1itlft,-1-:;)_____.5.._______ _ )CJ m 4zc. ::: 13, () ~ x /02{ mh 30,3 - 6f :::. 29~ +.3lJfI::::. 30o/c )J~ 1,f)'~rx/os--mo/5 D/}g-e ;;",31 ~ (~(4 /,tJllx/IJ'lJ.. J..Cff) :::: 2,(,3 x.1t5~1n7S R.e ..,. L tV"ao ::: (Im)(;. II1/S) .J) 1,5£grxI3,!i7n % = /,27 )I f05" /omi"n&?I" ;- _' 16 ~ -4!c - 0, be,1 4eSc. f<eJ.. L , ,.-5' ~ (Sc/7::. ~ =- /~Sl.fr)(lo IJ1 $.:::: 0 b/) 11113 '~/C,3 x/o$'IJ1~1s ' ( )~ I )~5c ..;::; lO,Wl ::= 1J.843 Re~ :::: (/,27x.IOO)'/:4.:::.35t,1- - -~ i.e, ::: 0, J,{,1(;;..'3)< It; ~~,813)(}5't.f) /h'? :=: 5.:25x. 10 3 m/.s
  • 278.
    Nfl :::. lee..(errs - Clfoo) C - ~(J 2d 00 Pc....tr.s --::::.. R r (5: 511 Po.. m 3 '{:iff2 k) mole'I< =: 0, y()t. mol!: mg Nf'J :: O, I7k ~m~)eA/dlJl)--3;<.k x L hr- I~'} ~ 3{'(;~s Im2.. -::: :21'23 x /0.3 fZ11) It;. #)2.,5 WI II use FVoeS5/;1/ e!tJt.'rfion. 'l':t ~ ~aD ::: ~," r-c);5'52. (r?e) cs-~) DItI3 ~ '/3 -::: .2.I ~ +- 0'. 5.52.. (I<¥-'O5'J.(I,(pI) ;;:..30, .,to - 3 ...3 I (, Cj, ~.r/')de_ ~ ) ~" 2"3 X /0 mol .:: S;;.5X It) YIlt:> t! d_ () m3 ()tl j.c:: '3t),-1 t, ~ f3 D . -. fYs) 2. m'1.. s.. {~ltf'If1 ,5 111 3 / CA ;::: a106 ~ ::: ~A!>O 011> m~ fiT /PA e (j,4tJt, ~ (8,.3/1 Jt,,!lX36K!<)U/,JiX) mE mal"./< ;::: /O-4(} ~ 30. -1 fI1 :::- 0, /2..3 SCJIv'l?n 1-. j- jr'y-3 V .::: (), 12 ti • s-''/T'(0. bc.Yr,!;(. ~ em3 .3 /00.0d- =- {P,~K x IO~ V0t..Ax -::: A.c (C,4,t -Q:rllb)4 rrr'A. -5" @2/lfK) Va'i"'=- 1.55'/x/()m:Z1s D148 ::: ~'2 x 10 6 m t Re:::. 0::::(O.o/;nf3 m/.s) -;::; IQ31, /, 5!J!~ lti5"m'Y6 -:::: 3d, 4~ ('!. C, /l y. J0 fYI S f)~O I yn = [J,/J:l,93 fJ16 e.0 4- Clls =: ..-!!-.;: /':l1A /0 &... «T (E:"5J1 f'a. l m3 :)(~9f/K.J Ino/,KM ::: 5, / J.. h?~1 m3 j, ~ ..A)<,.-::. COd):t1J ;1s;J:< ~)4tf(p,OJ.5uY " m3 ~ 3, '3 X I~~1tJ/s -5" t :: l!1-:::: t,2f'~ I~ /t1 10 ~ ,Ax _ t'L ::: 7S 11 3, 3 )( /0 (.Ae3/$ =--,
  • 279.
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  • 280.
    A ::: Waf4+h (;t)B nt> MWA :::: 11$ 1/amp)e fA_ ~ ~ Wft: ~ CA-s 4tr~'l. Mvlft dt flt_ 1/1f~:J. r1B ~ .lee Cfts -4 rtf<.~ MI1' elf:; fi ~::. CA~ dt Mfr ..ftc. I -~c. flt-: 11,1$' '64,3 _O,55/; 16 m()le-=: ~f1(; ~ fI1/* _ . ItS m3 I ~ f Ib/lbmd/p J?,4' G F, 90'1. Ie! rtJ(:J~1m3 :::: h 4 xI~, MITe,.s I. 2OJ;./0-3Wlo/elm'S . P..~ I: (7,1 i. (O~)j fc ~ Et ~ b (CL) 1<, «'I.. (0 em) o~ID'J,m f<.e &Wl6. 'lk 3,7fJ I, 7~'- ,7~" D,() I () t, 9"1 7,S" I,:) /5'1:3 o,o/ltJ fa lo,S 1,3 13/.2 o. o/~4 7 I/), 5',S" /, I 1110 0, O/3~1 73, ,38 0,815' 883 Il, ~I5"1- c,LJ. t:: (Z4y..ltJ(.jO,35tJS') ::: :;',5'1 )( I~'S =- 720 hys
  • 281.
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  • 282.
    Ibh 3 t::: ~1.(P'If (0. CJ~:U:L7) J~ (1.91 )(I(l'(~e) ff~ -=- 75': 33 :> 5 - ,,~ IJ. t;::: /1,5' fj (15', 35s) - 'Uoo :5 ~ 13,/f? H 30,8 O:.:.O~08 m Wit :; J(7 (fitA.- !/tv] M,./;0 L 0. '56 ~& P(S,,) -:::: (), J,.81 -r;;;- P.eo.1 - 5" ;)./ )/::./,178')< /0 "'IS k - ~ O,;ZJ'/ f.r - P R.l·':; 5l'5" ::: ~/~5~ I~:J.tfi-~~/e ~ O. 2- 8'I // ~ 13" 10 5 Pt>- (5"1.~Xt,J-4~) =:2;38'XI'i7~~ H1.2. s.Pa., IVA'" 4 ~ V .h.L~ "~/,I/X /O-<~8/.s h (" .36tJOs VV~'" it&- CJ~tr'- J~~) fV~lr'1J f- I./Ix /o~_ (;;Z138'J(tD~e )(3,J}(.I~fa.-O)" ~ n~~SIP4 )({7g ~ ) 'Tr'{o. p8Ill) LeM) ~wJoft1 30..1' tr?A'" cJ. I) ~ S"(J/t/~nr~ t( 01.- CfYl-Z. =: .tJI ~ ( rrXI.O ~ty1 ';(l.1th:m) ~ 3/,2. _(p Or?74 m~ foJ/s ( 290) ~ 7:13 x. 10 !!).2. I.OI3xltlr & ;J.'ff' .s Cf}tI:2. /tJOtl d .:: 0,63774· AlA -:: k6- (rftfA.- - OJIf«:» ft"VL •Mil -k -0.28'1 GJVI I G ~ P R.-r-;;a.6"6
  • 283.
    I j -$ @27f? J<. .J1t)t'"::- /-5".5/ >< III mo/s ~ I r ~~ hi (fS- ~3j1Y)3 -6 ~/ £4,13== 9t~:2.xl() m7S Re = 1)~ = (d.o Irn)(/mlr;J =- 015"" J/ ItS'SI'j. /oS"'h12/s l<e6 ,4-=- /.3.3 -s- Se = JL = J,5"5/ x t~o/s -=- /,1,.1 DI'1t3 9,(,).. x /0 -t;, IJ1% CSc)f),$t;, =: /,3'0£ 6M .:: -1foo.f!.:: (Itnls)(1. I t$ k;/m3 ) Mit 10,4 Iefi/k,J rYl",/e :::; /, I f5" ~ h?{jJ~ M/4 vn fl.. S mrr:= 1.6-(frt;..-oXrrlJL)M/1 -1 :'; 1,8I?)( to (1,1.7'1.)/Po..)ff(o.Olrn}(IYfI) 110. Mf'r fJ ~ 7,5"1)<. J;S'~/s I -t --= ml'T =- 0,0 3 h:~ _ -== 5{){) s 'm~ 7,f:)4 1t/O-sk3fS 30.10 f)~1 fe':: :Z.GJcm Ir 1m fhlck: tJ,/enl Dt.· .flow:::.;,gCW1 v-= 311 Cmo/:; A)( ..: 710,,' ~ ir{l,rcm~ =- :2151ot~ -4 4 ~.:- 314 CI"/lls :: 123 Cm/~ ~,s15'~~ -~ -:t, ~ ffP ;2}13k.. ~c/"O.1r5x)0 ~.2..-=- O/i'ltixlfJ ~m "1"'1 / - r :2,/ v/lI6':;- /'::2., )t. 0 h1 7S , Q ~ :::. (j.8crn)[J'J.3 ewJ/s) Re =:. j/ ((J,'195](/~zcrno/s) = 2:<...) ~ Reo, ~3.: -1 "5'8' - ~ ;;L 5c -- .JL. = (), r95"x /b mY:> ;:: YJ..-r OfJl'5 / .. Z )( 1(J-9m:21s ~ Sa .:::. 9,37 1_ 0,;3 ~ ~ :: tJ,tJ:l3 Ke Sc. '(.}1+6 -$" z )eL. = (J,tJ;(S (4/)5'5)(1, -:'7)(,,)., ;(/IJ~ ) /' gam -~ /;:: S:!3xlo C'ms ./J.$/t'Jg Pi':: 2,0 {f W) Ca-}JCnCo3 remo-red) A')(..::: 3J4cm:1.. ~ ::; /tJ(J em/.:) l2e:: .2q; Iat} J L == 1~ g:<.. x JO~Crr71.s ;[L. "::: .s:t3y. /(J-"'.,- 1,r.:z 'IC_Zi3cmh ~ '= S;32.S-x 10 3 em/s
  • 284.
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  • 285.
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  • 286.
    ~ =1.5£ :.:.;.).,:..:;..0.::;...(;,_---: C(l:: t<e c:J.:515.5G ~/;J =- (0, 7;<.. ~) ()., Ot:,) =-a111 J (O,7Sj(:2.1. 7)(0,711) 30, /3 ~ltrsc;¢ 0.000I fjfls ::: 0 ;j-u-1t><O ..:. (), O{k1J ~rs = 0 C;::; !r =: /,();3 x I05'Pa..- .= (S;~5 ~ ( f.314 ~. m!J Xf()f)K) W1 • m"le,J< . /rI~ ) ellr-s =- CIr, ::: CU(IO-= (15.%3 ~a)tollJ~<1J OQ 00 <11 :: /.S;Z xltr?? :;~ hJr /rl me Ihdl ff'd//iL/M @ f/Ot)J<' 1-12, AS VIC $'.686 cw;.o/s. ~ Ott!! ::: 1,55 em Is 5~::. ~ =5.6; g~ tm~S~ 3',{,7 VIIS /,5S- cm:t.ls @ ~co -1 em.) lertdII?J 8dIe Sh x -=-0 4z.t::. 0 tV/ir =- 0 ~ ~.:: rc~ (fr(J1'tI ex4W1(jJe ,) Re~:= ~ X ~ (tao ~)(jem) )/ S; ~¥' em.Xis, :c- 15%,3 5h x = K,375' _~ .J<C;( -=-1/f1 ~ ;: 1144 )(/" trfs /Vtt ::: kx.(cr; Czs) -5 :: /,14)1./i;l~ (115r2J<./tJ;:) -15 lc ~ 2..,J'1 ~ /(j ~ mZ.s N11y,::: kc){ (Cftoo - C~$) . :::: (/,(14-11< Jii:l.~ )(1,'51.)1. IO~;t-) -5 A ;:.... /,59 x (0 ff)1) ~ fY12..~s
  • 287.
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  • 288.
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  • 289.
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  • 292.
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  • 293.
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  • 294.
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  • 295.
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  • 296.
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  • 297.
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  • 298.
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  • 299.
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  • 301.
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  • 303.
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  • 304.
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  • 305.
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  • 307.
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  • 309.
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  • 310.
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  • 311.
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  • 312.
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  • 313.
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  • 314.
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  • 315.
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  • 316.
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  • 317.
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  • 318.
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  • 319.
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  • 320.
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  • 321.
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