Welty solutions-manual-1

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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 u 1.2 'V = ji X d-:.1 ( 1+ e.-"2.)'; 2.. L~

    -to ~r\1 ( I - i:,2.);1 ~

    ::Tc, (O.CJ~:l~; + .1?23 ~)

    1.>.1 /(Jt",1j) of 'PROB~~/Yf /-10,,"04 t!/l1c.ouS.

    p~;;J O~ PEo13I..~/IIf 13 )lO/f!OtS UV't! ocrs/ 12 -:E. ::: [ l\of '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 IJ ID 'PROP.Rrlz. s : /z./I1?:RA7U..e / D:E,A..)SIT~

    PRS.5 U. REI =':>Pfl:.CII=IC J.I EA0 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

  • 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 e ax - (x 2 + 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 +(5 ine.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 =>- V f = /-x r?s f'sVs +,4 V; Vs -X P

    2

    = fJ/i. 1'>

  • 1.13 1p:= A,. sinB (I - -Fi ) a) V'1p:: d 'I' ~ + ~ ~ ~9

    ()r r r ae

    :. -vP = AOSil1e(1 -~) a r~ e

    WHIC.H REQUIRES -n-tAT

    *-1 V7p/ = ?e I vlf'/ = 0 ~lvVI = 0: - 511'12.e (I-t-~)

    +C05~(I-~:) = 0 (I)

    ~ I \lIP! =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[ J i de 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 I O~ \~~$ 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

  • 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

    ~., g t d, j 5'H ,.0'" Pa {d4 ~ +a~~9HJ ~ -~ :: (1-!i 1-~) ~ -(2 ):02 A

    (2'Z \2-

    ~- Ps= Z44,7pgf :: 1.70 ps I 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

    2 JI F -= '? A - '?o..~A == ,oj 11 -(fR2 e.G.

    PH:J O= 1000 I

  • 2./2 ASSlJh1ING, ArlY1()SPHERIC AIR. TO 13HAV' I DEALL ~

    &- -~Q --ll dg - r.) - "RT

    LET T = a + b~ tJlTH ~/VGN IN FORMI1TION,

    T.: S30 - 2l/ fJ 7;

    dE. - -g dlj -p - ~5 ......:30~--2-J.!tl.ly/~

    fOP .dE -

  • "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 CONTINUS TO BE ?U5HED TO qREATR DE'P~ THE VOLUME OCcUPIED 'BY THE AIR IJEcRASS 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". -= L 6P'S;9'/ilL! + ~ ] alA ~Mo =0

    ~

  • 2.1'1

    F':J = BOUYANT FORcE ON suB-MERGED LO

  • 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>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)D lUe.t1R; \VA~ tbwN~.

  • Po lsT~~~. ~{sT~~~. )(ls~Dt~~

    ~E.~ 10 T~ ~~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~ 1ft l 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

    F oRC.E / UN IT LEI{6rH r: f= f=:: f (p - Pa..n..)a'A ~= C~ 9 f 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 =~

  • CHAPTER L/

    1././ V = IO~ r7x l, AT (2,2)~ {j- = 10 ex rJil ~j A UNIT VEcTOR IN -304 DIREcnON

    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' [112 o.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' (1Jn )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 + 'TrD v-.!:.. 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 = !fl c.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 5 r;;;- ,

    = -~3.S' k 0.39 :;; 6() mt'". /.S'I

    :. ~:: /;/) rniH.-4.....----- c)

    IF THE PLutD VOLUME IS CONSTANT;

    dV/ - dVI de 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 0 di: 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 4 MOVES 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" SR 21T'" 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 vm J. 0 ( 1- Yl J 7 Y? d Yl

    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

    WlHOR\e = f 1.1,; (6d) -f>1I; (3d)

    tit HOR 12-= -;:rll; (.3d)

    . ~ == 21'L b == -2"oL v, b =-v-~t

    ) d ... == 2 W,side = 2 ifnr., d~ THUs -2,aLv + 21' fob v d.!:J=0

    Lv = fob -z.r(y) d~

    a.) -u{ 'f) = !-AVERAGE' A CONSTANT L 1.r = 14:vE b

    "VA VE = L v b

    b) 1T (ej) = c. ':J + Cz

  • 80UN DAR Y CONDITION S:

    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 L V = C -V d~ v~~::: -!:L.::...::v:.--__

    q Lb[t" -(f)jd~ LET 1 = ~b )

    1).,.,"0.)( = --.:L::...::,1/-,--_

    l/ b 1'( t -yt '-J cJ ~ V" ... "'.... = .:2 Lv ,,-"' 2 b

    4.Ju,

  • 4.16~~r--- - -....:.--, t J J

    ----t>- 2 ern I J -I ,Scm , 2-

    I I

    L_~ - - 4crfl....J

    MAss~ ~:: MAaS nPw 0,"

    tQ, 2JAz l12 ~?AiUJ ").

    1~'16~ 1TQ6)2.1~~O-'~ ~

    Uj = B.l5" w.~

    ~ _____ J

    ~AsS ~ lA\ ~ Mm Jtor,.,

  • 4.24 v

    17

    I

    @BaT Vsc:nt (1f(G,~

    ~~ j' 21l'L b V~t-r

    4: Vec,er ~ v l-~ b

    ~~Is~

    lTtJar = 4lT~(~ -Ctr; ~f~~4.'2!2

    ~

    n1.lA7r " f I lfe2'1fLd"( o

    :: 5'! 'iTL blf~ ~

    00 lf~: ~b. 4 b

  • CHJ\PrE'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 (1.0 I V; )" vz -flA v,: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~ =,Pf 1 (v;xf c:/ x+ 2 fv,'dx' -f!r.'~ =f'~.~ . .t + 2V;2. -1/ V;=>J :. ~ "'l1..".:l ( ~,~ 2i I I SJ~CS FROM 5:t~ ~ = 3 vI)

    o -=-(1",)(.,! .,~,)(8OO ~) = 179. g Val

    P,-'P-;a. =t" (J79.e #- ~f'@.o)~ = 189 p~f=J.31p; =9.MJ

  • ~= /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

  • 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") lbf

    -,;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'~S VltAjYi~ 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;(

  • ttl::: I as MIN1MUM .~ FOR "P='P~J v-* =~ ~a.) THE VANE I~ AlTACHeO To A \VHEl of RADI(IS ... ; NoTE TWA1 ALL MAss HITS CA'RT Mj == I'Av-r[1Tc.. (I-'-DSe)vc::ose-~

    :: I'Av-r (/-case X"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 + 5 d~ =0 M = If X T/,'~ Jd~ ::: -~~ (UNIT CROS~ ~EGT10N) flz i +//"i-/iV; =0 X=Vw, ~=-~ ~(1T"",-~) =fl';-~ (I) . MCt'\1ENTUM

    ~ FJ( =: ~ r if-cJM + r ifd.-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;. -;0 1{lA, REA'RRAWGINq

    (P.-~)A, - ~ (A;l-A.) t- p (~-t\) -f'9A 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 A 1=' 0 TO? ",,:l

    v; == 12 tvJ/s R== 12i KPa.~

    A2., = .113

  • 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.~. vd m R= r vdm - ( vd~= Fao~fE.

    OUT )n~ FLUID

    = 2 fa 3Jf'~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:" /.

  • ~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 VE LOC.TV AT 12 RELATIVE To TH E: IMPe:LLE"R =

  • 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 IVs r _______ ~-v. I I

    L

    2F = 1k 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 X 0)

    ~ fcr v. IJdV=O dl: )J) c. v. Cj r

    :. F!j = ,0 Ac. 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"~ ::- f V'j dm F:pv2. h sin ~ b) XMr :: )(0 X O)z dWi

    F"~l = ~ 1!f'Va -~ V";,vb .:: pv2 hsiYloc.R= ~,Pv.J i: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'

  • 5."3D r - - -, USD .. r:; T~ l~ ,; I ~L~j. ; f:~~1

    It: I M=s>A h Vz - n: m, '" gA V : -~ A Ii L _k' Y ~ + *dt

  • ~ 'J' Q -:::.A,V, 'Z 'IT (.08)5 =0.02.51 mi 4-

    rh: gQ :z 2'5_15 tzrs V2 :r V, ~~J '" (2.8 M,i ~ 2 m(V2-~)+~-~)A,

    ~ 2 19

  • CHAPTER b

    I--~ CD I I I.Z..,.= 22 -2 ---, IT '

    P,=:/S-'"~L -t-_J ~:: 175"KR.. 0, =.25 Itt D:z=alS'2 ~

    WORK

    ,. -~ S( et !)d.;,+ ~ rrC..:;{dV o J~S. ~~-

    :. -1r= (et ~J ~ -(e rl), 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

  • 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

    = IOlq" = 0.029'7F '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~l f' 0 j

    Ps = -aws/dt- t'ii tell' -,-LJa (!.jA-~ ) AV 2 Tf- J B

    6.6

    = (-2010 t 3 g 5"0 +- 3CJ 25" -I- q~7 ) == G 702 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?i S-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; ( Cv Tz

    + V.l2 r ~ ) 2 ,.0

    AS T, =- 7;) p, ="P3 e= v T, l' ~ r v,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.{~ -UA 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 - ':i 1. ) ::. 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 = r vi! dtH ;:r \( p(O. Vi) V~dA c.s. -F -Lv' + PA(A = -111 VzlA + ~(o) USE GAGE PRESSURE ~ R~5Um FROM 6.10

    r: := -t.J of- PA/A + m Vz 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-) t\4 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 G t ves lis P= PC VEL.) \viE Do NOT KNOw THE VELO-ern' VARIATION ALON6 THE' LID.

    CD 6.12 Q=6~ AIR

    ~ 'S :lC\LCOHOL fJ= ~J.I:tQ

    "P. -~ = 0.1 WI

  • - -' ) 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 _ V J. '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;2 0 ( I' fig 0 '\

    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. =

  • 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

  • Q = Av =trd:2.Vc. = O.I3i! '(:t3/ 5 ~

    ~ +.. Vc: :0 0 dt: 0'"

    Vc -: y 2'jL - (ho -h) ho=I1@t=o LET 11-h, = z 4h = d~

    I dt dl:

    dZ! d'l...,r dl .,. D~ V 2'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

    A P = (- 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

  • A = ".193 fI'J. ~ v= ~ -= 6.5S fps

    ,+ g: + ':11 = S'Ops,'3 D: Il I"

    CD A = CZT'/., ~2. V, = 3.6'l,f,,!o

    Q::. 1.9 cfs S.

  • ACROSS SECTION ONE J THE VE L-OCITY CHANqS BY A FACTOR OF ABOUT 2. UNLESS THE: MOMNTUft1 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~LCT 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 q 2 % REOlXTION.

    /'.2'1

    tM ='pAh :: f' 7:;r'l. (hfho) ~ = p'TIJt dh d-t .~ dt

    ~t :: ~fi1 vC(At = /l![t.:J."; 29 h

    ~ :: -d 20 \.bur = -d~ i ~Cjh t)2- D~

    C h~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!E N A ~ E

    } -r V.A2 of- ~ 2!A = ~ f Ve;.2. + j rE 2. 2 Pz. 2

    -PE :"Pc: -I;' ~ L2 I ~ = V ~ =

  • 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

  • 6>.'31 tJ~ur;a-U~ TW*~CA f -OFT~ 'JJC1DM~ AI CZ-,1 ~AP T~~ ~TC46 V~~L.

    ~~ '8-

  • 0.33 GJerr(].,f~ NbPrF 16.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/ (Je Z 9.32f;-f~ q 2 A l& ::: f;.CE6roLcfs

    ~.'34-LSvg:; fu (;. \() ~ FOe

    A C. v. &J:I03Wc:fr~ ~p

    -?JA = ~ ?-?~% Ail? at g ~

    = ~ fp'lM:~tR Q -z fr:) Z3Yrm : 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 U

    a --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

  • C1-lAPTEQ 7 7. I ~'lS{~ ~? Aa; ~lN6D ~ ~x. I .

    T OF? ~e I A~ Z6, ) ~ & .0177 G::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

  • 1.'7

    "IV:::: 2,," 1/".2 ~ E' + ,.37 J

  • 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 __ ~ ;?ff6X)AT: - \I"r ()()At= dl4 AJ(~o A>f .1t ax 41: .. 0

    FOR 3-D\M: 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,. =p tr ;;e ar r IJ

    ?J5 H ~1T 1 ~ 1 t i

    'j/t ~h f LL 1 --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.osX 3:t ./O-3)/olS-J7f l"lo""

    .S~2 (3./t)

    = {C07a, f\J

    "lib Fr. = W FROM PREVIOUS PROBLEM

    Fz ::;; v"'}:: 7TDh .I ALSo" Lv' = ;7\9 E

    :. jJ ,/ :u7r D h = I')'t~i e

    1.T:: m9 = b8tJ9.1/-;o-r pif7rDh a5"OU1XIO~~.~

    ".. = o. 7 f:>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 ;

  • CHAPTER g

    t.1 - = 32"uv. Q cJx 0 2 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.) ~ K 041

    Nat: () = rHH -A'f.2= LI'l~ L 1'2 K 1)'1 J K[)'I

    f..I1.P) =. t\1N/a..,1 -.dl,?3 = L.2.3 mN t L J3 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 CONSlOR THE CYLINDRICAL

    SHll ELEME NT

    ~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

    J dv= -.1P (rdr - Sf d,.. :2L.,.u JAr

    V = -.A!:.,...1. _ e,k r + co2 I./)-' L ;U

    "B.C. v=o @ r ="R J r. KR C. & ~ R~(J-I

  • 'Tf.)( = ~ dVt :: ~ l: + c. dr dx 2 ...

    V.{:: -L. 4E r2 t S. .t.-c r + 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.TTR 0= e,Ro-S&

    M

    Va =(JRu'Nf~ @ r= 'RuIHER

    :. w'Ri= C,R; -.. A

    C =# CiRca c, = wI

  • m= pAri = ~7rO~ 41P 02. = 1TD;..oilP 'I L 32r' lli Lp

    = 1J.2

    GOVERNING EQUATION JS

    !L (~)( ) - JfP -= 0 dy dx

    FOR NWTONIAN FLUIDS IN LAMINAR FLO~ -;;x -=fol d ~

    dy V - -'- d? tj~ 1- C, u t C;z . x -:J"u d}( Z;"J

    ae. @ INTR~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

  • BERNOU lLf f='ROM S TO I

    P5 + ~ +

  • 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"

    )(

    (P\X -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

  • SHOWN BELOW' ARE THE' VELO-CITY PROFILES FOR 3 CASES;

    ~ =-1 IS MAX. Ei=1=IClENCY 'RSlh 3

    ~ = 1 IS MAX. FLoW' @ ZERo "'R.Sl h 2 AI=>

    I

    .6

    . tt

    .2

  • B,17 1 \V ~ ~~ -- --~~I- l' A'S S'~ Tul: A1 1- r l' r 'rlrt .. " \ L_ _. 1_ - _ L _I !VET ~lC4L . I I t { j ~'T~ f1..vx.- t ; Ar l I"S~ SO L f::tD

    i:

    W' +- 27f f( f A.t- -1'cr"r'l{ Lxi r.O rt.(r r

    ~~

    \II 2. S(j 111 ( Are 4Fra --rA~w::t lKG LMtT As Ar ~o

    J

  • '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 :. (fiV):: 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

  • 42 = ~o + d r dO + de ;;0 dt ~ di dr" dt de

    ~ = ~V~ t 1" aVe p- + v. ae dr d r ,- ~ r -e r W

    -T Ve~ie dr

    ~ -= ~ ~ +a\j~ +Vt"det"+ Ye~ dB ae I'" ae ~ ae

    ~'-' ,.. ~-:= :;}er ~ = ee~ = 0 dr ~e ar dr

    (}e,. = - ex slY'e t ~ case = es ()6

    SIM'LA~L'" 9e, = 0, dee = -er , d(' ';)8

    HENCE I 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 SlW\ALL 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

    if T Vx~~ T ~~ = '3x -;~ () 0 ()

    :2 :;}~v. 'V Vx =~ = 1 2P

    ~'1~ ,.u 'dX

    ~=J..~Cj+-C dlj j.J. ~ I

    + v'V':Z~

    ~ =-L Q)P ':12 +e,

  • 'V. V= 1..(w"R2)= W'R:ld (,) - 0 r Ole r r- --y:- de r -

    :. CONTINUITY IS SATISF/E!:>.

    'i.j Vp=:! + ~t' = - V~ Dt ~ d

  • 9./3 FoR THE INCOMPREsSIBLE

    LAMINAR CASE)

    OV ".. rli:) J 2-Dt"=g-7+ V 11 FOR 9 NEtSU6~LE') "D V == -yp ... Jv:2v Dt I'

    VECTOR "'PRoPERTIES DETE'R-

    f.lUAIm . 'BY V E VP wHIC.H I ~

    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 oR

    I

    TEN'D To MoVE IN THE

    DtR~CTION 01= D~CRf'AS/N

  • Tw~&~

    ~ (P~3lYi)~ Jqr or 2- 0

    ~IB 2 Sf.t1(.o Tw @ % -lfe e,., ~

    dt r tre :zfCr) ~ trrz~ -z0.

    U-sUKt ~-\6"~/~ T~ TJ.tt5~ \.-sTt5 Lgr W~~(Dg ~Tf4tS E"nlir-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~

  • 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

    J r'Ai9 IN THE' LIMIT,' TAN ~=Z

    G.;Z = li~ .J{r Vgl r+Ar - r ~ r r) ~} .... ~ 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

  • /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 - PC R) -= IZ u..,. 2-

    2

    THU 5.1 "'Pot::) -1(0 J -=,tJ \J w?

    So

    :. U2= ~fP =-~ VtM=126f~

    ,.0 .00200 -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. = P \1'".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" V 2 = Vo02. HENCE J \ Voa I -= \ vel:: 2 \b, si)19 sl~e =.5 .". e%! 30; ! ISOO

    10./0 a)

  • WHEN '-P=O j '1 =0 OR o f:ao Is-W& lwe. 8=6 \.e:Tltl; ~v,;; \( Ax,$'. ~ li_~O (f"~ ~ G:;irr To 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. STRE N6TH

    FREE sTR EAM tp = Vc:o y TOGETHfR tV= Va) g t- ~e

    211"1'

    Vr =! ~tp = VcO C05e +..ttL ,.. a e :.27Y' r

    ~~ r'sine

    Or' =0 @ $=11 AT a =71 r= ~ _ Q.

    zrr P l.4x,- 2'ii~

    lall.{ As ~iP = pDv Dt

    =pBft V(~2)-o. (V'xv~ /WD FLOW 15 STEADY AND lR'RoTA-

    TJONAL I Vp = - P \l (~)

    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 ." mosiY\ede 1~lae . t'ov ~10'.e) '"' (ir

    F~= Jo (1=>~-BYR'5IY\ed8

    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 (-.:tJ 0) '" -I(, e~ 4tT 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

  • C. A.7 Lt~s?~6. ~ ALL Tf; 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'P 5 Ilt8d9 =0 o

    1/: ~TM +~ J(~:-U1-~ LJ:-2'tsm,.g

    Iff "'~D ~M ~~')p.jlf2Ijf s2eJ9 I~T ~ (~. - ~A\1t'\ 'D +.2. O{y"z.. V .,J' ,j (, J ,LV

    ~O\za 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/t

    2) "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; = D c4. Vb fC,)J.; 71i = Ai _ 1-r;rvjJ - 1Rc

    7T;. = DQ, Vb pC: 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 7r cl2J =..L 'Tl'D'2.L 1)~ _ 31 _ 3d

    i/ 3 '4 d 2 - L - 13" :. ~:: (3)~ :: J.I./l/2'" a.) BY 'DIME:.N SIONAL ANALYSIs:

    ~ = 'DQ.w b pC 'P I = La. (Vc)b (MIL~t MJ: ~

    -c 3 '-t=-5'" b:. -3 c=-I

    J

    :. 7(, = _:Po.--_ ,ow3 D5"

    FaR DYNAMIC SIMILA'RITY:

    '"P ( --P I p4.)3"C~ model - ,aW3 D6 proh1:'jpt

    ~=[~ ?fjff.r 3 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 MILAR ITY ;

    ~'" = 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 - fAI p U2 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< MOo I 0 I

    L 2 0 0 0 I -3 , tOO 0 0 0 -2 0

    .: ~ = '3 -..... ------b)

    l= n-r' = Z-3=S .: No. OF" DIMENSIONLESS G'Roups ::- 5' -~.-------

    'iT; -= 0

  • (~) = ~; =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

    TMERATUR NOT GIVEN,!

    ASSUME 'H2o = 10C

    JH,.o = I. 3x/o-6 W1~

    'MR = 2t;OC JAlR ~ ,.": >(105' ~ = 2.'1'l>C10-6 wsl

    ~

    L V I - L vI . u. -, I J L J - IT .. ,..- vF.s. ~ F.s. ~ h~ .J L

    VF,s. m

    Um= 1l,2.4Cf/o-6 .q :: 122.3~ /.3 10-" 5

    F"l. = .0262 h F.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 Voo 2 V'.,. 0:/1 La

    DO~_ 9 L vp* 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. cl 2 a

  • IU2 SYMBoL PIMEW510N

    FLOW RATE" Q. DIAMETER 'P 5HA~SPEE.D N VISCOSITV A 5U L RPM w \ It: VOLUME Q L~/t DENS\TY P M/L3 \I'ISc.oslTY M MILt r=3 Y\::.6 L=6-'3=3

    " J

    CORE (f\RDt)? : "'P"DP

    ~ = -P"''D 1o pc. W

    ~ = -pa.DIIa pc Q

    ~.1:... II. =pD~4i

    'IT = ~ 2 P

  • /I. 11 AS5UMIN:S /NVISCID EQUATiONS)

    ~ DO = -tiP +PS Dt

    MAKIN6 EQUATION DIMENSION-

    LEss: V := +(~ ) t ~ I ~) to L L ~2.

    OR JL = f(>< t~) 'f;L L"J L ~)5IZE" = 2 "" = .005~6 ~

    "360

    VE LOC lTV 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' - J 1.

  • 1\.20

    IN he$r~NT(,~/~ Is W~

    g W=-\7f+)AV?ll~ -I) f.!1t$(~

    l~ o-~ ~ u-/~;\t~ v;,-l/L Ou;~AtJ\C

    r "-

    - ilt: \ QY.E.. ~~z~~+31~~-l) J L/I/ n.+-" .~(5c::Z)W' C 7 D

    o!.-Il .. l~

    T ~ GrO D="THE ~ vrry ~}./\To mt. hpzn~ -rt~t ls

    I \.Z I E 0't cfr2-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 "8 r4

    12_ ~ /:4\.i"2 5 It ~ ~H.&) L. z ('?/~

    m~ d:4:~t~ A- Yr~/z, ~~---~-",-~~-~

    69

    1\.2'2. a (/v\A: ) )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 d J Oy'1) YD ) .J-i~~ /

    X> 3~ ~~ i\\l-g W~$

    D) ~) V f() ~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~lJS T~ ~LD Sf; 4~~ VIA {~(D(;; WE UA~o 0/. 2i ~

    '\) /0 ._A. .-7 L e 6JLt ~r j J;.. ~N h:X7C~ ~ Q 6.111;, , i.Mr Grow ~TAl.V~Q - ~Qh

  • CHAPTER 12

    122 "DRAG = ~ pv2AR C]:) SO

    Df =.!.pV2~C-r 2 ~L>-t

    = ~ (. 002 3"Y1! rfa )(293.33/"( ito f 21100 (.011)(.75') Ibf

    =202b~)(~O~p~} Ib f 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 OF A GOLF BALL 1ReC.R\T1CAl. == 2 lOS" AlR @ 20C 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

    V fp~ 1s

    12 S" ~ 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.\ll163 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 +

  • .: 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/PVaJ2 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

    ~ (" E P v)(~&~ == ~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)~ p V" d~

    = 41' Voo2 X cI ra x"SiYl7i~ d~ 0..2 dx Jo :::zE

    ::: ~p Vco-:J. >< i.. (d"x) '11 0..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 $)( = 11 A 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~(( VXpCOn1tAt~i(: /'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[

    ~ = 51r1 rtr;:i ~:x (S} = 0 VXd 2~ .:J

  • b) FOR A CIRCULAR CYLINDER " 'L WHERE Vx$ = 2 VQ') 51 (\ 0. }

    VxJe2._ 0.'11j)( 5" ~ T - V)(~ 0 V,,$

    s: Sir15(~)d~) = = f S\Y\~~ d~ _ - Si\1 'I ~ cas ~ _! co.; ~ (Z +Slrt 2~)

    5 ,s

    = .! - J. cos. ~ {2. + S;r'l~~)-SiY1\cos~ 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. xa. 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. '29 X I. 22G)(30)

    :2

    = 631.1'0 N

  • POWER = 30m (631.10)= 1095"o.Q\V 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 \ 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' 220 7

    a -, ~ ~ W=~ .2b'RttJ (lOZ."1).?i(25.i3J

    !2:)

    : 19.~ Yp

    b W= gEE ~:: 15.70 tr 5>0

    IZ.Z3 T ~\ F 6 -? "l

  • It.2.4 :} J}~ 0.16.1 /0 ~~ . S'T4rlTtN~

    AT ~ -r7.5'cf I Va 92J~ frs 2-

    1Dz~~V ~~~== V20/$,@

    ~.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

    Ae 2 ~.B{ 1~1. / C,-:% O. 224 ~l)5 gQ ~ L l42

    V

    .Qz{5LO~:: 240 @at/s ~Too kApID.lIJ.t ~ TQ\E.. 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= ~f\J~~~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 ftk o.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 1\7_ ( \ ;: S 7m ~ rlD I.S7/ )

  • x 1Re.x dLJ~ ~~ G4't1 0 0 0 0

    . I 21()5 .111 0.321

    .5" .219 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. (L CL 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(bJ P v2A Cfl: FOR 2 SIDES =(O.~2373X I600XI.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 FLO\J~ 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';;' = a 022 5' f V;< ma.x --~--VXmAX ~~

    FOR THE Y7~ POWER LALJ v = o:Z{? Vmo.x ("PRoB. '-1.12) :. VW\~ :- O. f 16 t\1/s

    ~h1o..x == t:J. 07!J WI 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 EN ERG Y ,,-.J P v3 @1i?e -= IO~ .&- =~S-Jk)CO.2,\

    6L l-s i~ ~~S-J = 2. '3'1

    v= V)f(~) MoMENTUM = pVoo2 f2.(-rJ MOMENTUM nuX' = f 2(iJ

    P ~2 ENERV ~LUX = f3~) Y2f1~3

    LAMINAR;

    M = sin2.(i 1J) p Veo 2 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 -L pV .2 ,~pVco3.

    r3.Q "'ORA6 =CfL ~pv2A -2SIDE5 A = Tl/O2= SbOfP-D= ~(.OO20qqX205)2(S60)CfL

    = 2~" J Eq .eft. Ibf-"IRe. = vL - 205? - 'Z IL/O 000

    1) - 3~6'1'IO-7 - J .I D02.0~

    0.) LAMINJR 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

    =~ IOOOJIC)O''1200 =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

  • 13.11 J; = V, I cl Vxd"i 2) 2 de P 'X d;"t2t e e t-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 - f Pr.x)clx 5~( x>e ~ P(lt} dx c( x

    <

    WHeAl vxr.s CONSTANT ?CX) = 0

    U = Q x -t C..I c= ul ){=o I~J"

    TM:A A~ tSb ~ Tm:.. VIcM~IM~ S1tn>~ ~~ &t~ ~b-r~~ ~v,lk(~~~ ~DtS~~

  • '3.I8VlC'''(~yJ=~O) t ~~./L x

    ~Vx'L 7'l1!...2 d2.Vx'/.f + ~ y + X~ 2 + ;;y 2. 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~"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/i l)( I. Ii) = 2 q 5"

    JJ 8 -Io-S' LAMINAR

    A P _ ,- - 2 rf L V 2 . . = \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

    A P -= \5" ps', Gl)ESS LAMINAR FLOlJ

    g = '32.f

  • GIVEN "PIPE J

    A'P -- .f P V 2 - f iA ~ P

    FoR l=ULL'l' iU~ULE"NT J:'LOW,

    f -= fUNCTlON O~ e/O ON L Y 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;' 12 .- ~ 2t.3J ?o - 7. T..c r -'

    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! -'c J '3) A ~NOZ2~

    :2 u.. ~ PI" _ VEX,T .:.L-+ r --2 T2. A P == V i-xfT _ vp:2 == ~ ~(V~ IT - i" p ~ ~ 2 Vp:1 I)

    C.ONTI N U lTV / Al> Vp -= A\lOiZ ~ VE)OT :. A~::: \.?2.(Ap'2_r p -"2 AN:2 I} ADDIN6 T06ETHER

    ~:: Vp:l fi'"t" 2\( : Llf b + Ap -0 jJ 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;

  • :. 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/6OJ2= 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

  • - P:a. = "S. S I' ~

    '"Pz =-~/q ?sf~ :: -'S~ 'P'$.~~

    IL(./O

    ?>fTWEEN I E 2

    4f"OIA UNE

    '2" 1)IA LINE

    I

  • V= Q = ~ '~'1 :::: 225fps A ~,~

    De = i A~A = 2 '21 -.:: Z'''' = . "6t1 l' '32

    ~ = q~J 3~O ~ -= 0'5 ff

    ~ = L '3 33 ~ :: . 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 '2 II 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 PoWR t = 1.03q~ (~ Ib;Xhl fl75)

    == 301. OS OlL t 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~ = q25"270'bG22~ o ~ D:;2 S rrr2 1)'1

    hL = 22" Q62.!i = 2QO.3 OS

    jl = '30L05" (2QO. '3+ 175') ~r +.JI.(~gO'2'll.lf)

    = S 153 '321 /

  • 0..) SOO 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 .OO?I

    " => t!.~S'1 /MIs 'Re. = :~s ?bSI = 3.03 '/0'"

    10" .

    Q::: O. Z 3:2 IN\3/S

    I

    I'/./f T "~~

    1

  • AP ="?.l-~ = ffj(- ~l. +Ac)

    = fJ ~ ft' v l + Pc) Ai! v= Q = qO *3/5 = 4.S'i "'/5

    A 7r( S..,p. 2j

    ,6i=> = 10 "'f8~. :>. ('4

    T (q :fif? X6h"Z M4j

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