Solutions Manual To Accompany Fundamentals of Momentum, Heat, and Mass Transfer, 4e By: James R. Welty Charles E. Wick
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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 ,
IF ,)IE: Co/VVcte.S/ON rr'1C70R/
je
1.1 n = L/ 10 /i,,;, V::''''; J< ~ R-r = /.32 x 10'" il1/5 >(
r(
A=
16 3
I
USe.D,
csk35 j.
~LOl.J PROP~RT/g s:
I.S
;.,,/-
IS
~ ~[
20
SrR~S5 /
lg
,:. NA = -'- n OA = 1.04 x IO /s
PRE.S5UR.~
($~ADIE./v~
II~LocrrY.
4
= j~pi
1.2 'V P
cv'PCQJ b) = f'c
u
+ dP
II
d-:.1 L~ -to
(
~r\1 ( I -
::Tc, (O.CJ~:l~; + 1.>.1 /(Jt",1j) of 'PROB~~/Yf
12 -='
O~ PEo13I..~/IIf
)lO/f!OtS UV't! ocrs/
-:E. ::: [ vz
l\of 'S a
f~
~ ;:( ~!,\" = -sin
'l
J
e);
+
e ex
+
I~ IS! e.~ GOes.
e
~j
Q. E. D.
9] -
i:,2.);1
.1?23
e. s =-cose'" __ de
1.2 WILL IF
O~
Pfl:.CII=IC J.I EA0 SPEED o f Sou/1/D.
J
-
([.r
Q.E. D .
~''(\
e'"
(
RI
"M
1p:= A,. sinB (I -
1.13
a) V'1p:: d 'I' ~
r
()r
-Fi )
+~
~ ~9 r ae
:. -vP = AOSil1e(1 -~) r~
~lvVI
~~
=
ffE? de
_.J.
= ?e Ivlf'/
=0:
-
- 511'12.e (I-t-~) +C05~(I-~:) = 0
5i"e case
FRo;n (2)
r'"
FoR. a;l 0"
(3")
(I)
..
oC
if
I O~ \~~$ l,v 9 / A lO'r\~EA$E IN PI~ ~o
fOe
0;' sin e cos e =0
t.l7
(3)
2
1-
1'5
(I)
a~
r2.
(1.01):' 3CCD:; 217 AiM
AT Co~~ntNTlEMP,) .?""' \/
\1 m W"'~ m MOL&:::u...A12. Wi;(ah'T. ;.tr
DEJJSrry::
2.~Q:;()'-, wt ~ W1~ \~ . ~ (lAwf>
:. 0
n
a=f"
,:: n
CS).L
IS
C/.)AJDIT/ot1JS
=0;
?2SO,,~1
j>s. l-
=2.5'·10" ~(e~
IhI PasS/SL ~ ,
.e
Ji
L\(o
(2)
2~,,~
:.
r2;(l[ L 3
L-
- ...
?= '3001
. L/a"4 = 0 r':4
0" _7r
IAlTO
G)=O:
v: 2..
------------lAKE R =- i AnA. Wrm s:'&, : 1.01
-~.
,-,15
-(1- ~:YJ::o
. e --
LJ
2 r
=0
~ I\lIP! =0 : "!>lrleCOSe[C1 +~ f
••
A-
fL.2 -
-jfJv;.'-[~~r] ~
REQUIRES -n-tAT
WHIC.H
*-1 V7p/
ae
ln 3
.4Rs.
~lc;H
i=a...
AL.TrT'UDc
Utrt~ IVf\~
G Is CVr~~. n~ L~'(O·~
3
CHAPTER
dP....
V'P=PS j
2./
~t... clP
R='Po. tP"" 5(\:2");
2
-pc.?At-JDHS(2 _
/0']
+6
o.lI'c..,
fps.
fp:..
= :Y.. /0 V;= .of,., .,.
C j
=
q1r
)oRq(l- n) :2'rrrd~= 0
=I 2
R:2. (f-.,"- -I) ~
..
11 (1.5"~
$ fps
l/.'1
l/. 2 {} = 10 ~x + 2 x .~'J
0.) ~ = ~
(I-fi)
)5('.s/,Cv.MdA = )fA/,(v.r1)dA
~~
e· v-- (Y3" 1 lZ:s 2" eN -2
= 5"13 -
'i
+ ~~A1P(V-·~)c:lA
COMPoNeNT IN
=
k fVdV =0
f)c.s.f'(v.nJdA ...
V =IO~ r7x l,
AT (2,2)~ {j-
SHOWN;
[J'--'-____
;::w
(2, I) .'. c = ~
=0
He.s. f'(v.n)dA::" ))Ai f' (1J·n )dA + »),40 f' (V-. n)cl A
= - f)A', fJvdA
(1,0)
Q= IT
~.
=,q, , it - ,/ lie - ..,
.~
V;
.
)(
Q
,.,,3
::.
r- - -
i~-
JJA.
= -~/J"Ah +~1.T~s30"A)o
)~2J
Yl
+ (( pvcos30acJA
~ CONTROL I VOWME:
-- +-~-r!'
L.. _ _ _ _
J
12
= Ao A:
,,;;. ("D~"30 •
= 1/6. /9
= Avo = o. S'S-S' fI?,s
=0 fps
:. ~ T dt
•
S
••
=Al 'LJ + 'TrD v-.!:..2
2.
V-
= V-(-n:~1 +1J' 0 L)
2L
• '
= ITrO,,/q 'XV;) ==
V;
"irDa
~
=
1
- 3. iLl :: 0
-,q.:z.t)
=~(l-e.J;iI
Z33 I~
M=
I='O"R t = '00 ""i"" S = 15'0 Ibrt\ ..
V
I + "'D
r~
let. 2 5 M
-t: =:>
F'OR
=
0..)
oJO
S I 6 b. 6 Ib"" .. (t.l (S::z _ _ d;.,..s_ __
1.1-1 ~/s
= Js
Jl; dt ,
b)
3. ~q - 19!.3 s tI\
I
= -1:1 £.,.. ,Q.4
t 1 -t I
.
3.Zl/ - ~ 5:, M
'3.!q -
= -~3.S' k
IQ.2 5 r;;;,
0.39 :;; 6() mt'". /.S'I
:.
~::
/;/) rniH.-4.....----- c)
",(
L( ~~S-)4-G~tl + .•• 1)"=
Q
A
l{. -;
IF THE PLutD VOLUME IS CONSTANT;
Q = 12.1" cf~
6)
a.)
J
=
12.1(,
'7r(fft
I
IQ.2 '2
o.:l
(1Y-)= 0 ?lfl /
0.2,
-¥.
~
r
=
5'( 6l/)
= 320 fpsl.
1/.9 STEADY I=LOW
M:" 70TAL MASS IN TANK 5:: SAL7 IN TANK AT ANY TIMe"
If~s.,o(fJ'.n)dA =: /9.2(F) - 2(f. 92) M
ffL
A., (
r
.r. Jfc.tCv.n)dA:.O oR JJc.s (r d (p-.rft) = 0 . pA =c.onsi. )
~t
~ c.v. pdll =
=
V; (~
11;.:: 2 ( ..;fr) 2. = 127 fps
••• .2.M=o IF-"
cit 2
-
AI if. = A~ 'Vi 1.1,. : V; ~ =
ffe.s. ,o(o-.n)dA + ~ 5f{~dV ~ 0 fL:$.,a(v.n~ = mout - w'irt =
dVI
dV/ de
== 5.~~ fps
d (evA) ~ V-A
!fl
= cJA f EY-r.:!..E:::. '0
:. Q. £D.
13
A
"IF
,0
p(v.¥\)dA +
[
~
rrvpdv= 0
~c.~
Cos,
o
'STEAOy F~w
K ~(-o-.n)dA = -1'11; (6cO + lb.,. 13J
WtHoRlc.
• ~. d M di:
+ Jr nees d rn =0
:.
~ E• 0•
+ 2.
'"to
'1.1/
~ l~",-; v. =0 ~LIIP.
Vi
WlHOR\e
=f
tit HOR 12-
=-;:rll; (.3d)
1.1,; (6d)
o
jl ]!;. .ydy =0 3d
-f>1I; (3d)
I"' -;( ·1 • 'j "I
fls.pCi/".n)dA
-1"
;~av ~O
o CONTROL VOLUME IS FIXED TO WAVE FRONT MOVES WITH
4
VELOCITY v,.., TO THE R If$HT. -,.0. A~ T~ A (v-m -1I;.J
=a
:. 112 = Ym ( I -~)
v =f
'/./2
r
= ifmo.x"
'11 R~
LET
;z
.
-vdA
~ == 21'L b == -2"oL v, b =-v-
SR 21T'" L'rt - R'J,..lY7 dr
~t
0
=%
de = d
('
) d ... == 2 W,side = 2
YR
I
v-= 2~Jo ~(I-zf' de LET
q = ,- &
". = - 2 vm
J.
0 (
J
d 7.
Lv =
1- Yl J 7Y? d Yl
a.)
=!1.J.v: (,0 ma;x
.·0 l/. 13
V
nr., d~
-2,aLv + 21' fob v d.!:J=0
THUs
=-d ~
if
fob
-u{ 'f)
-z.r(y)
d~
=!-AVERAGE' A CONSTANT
L 1.r = 14:vE b
= o. ilt'1I"mc.x
••• "VA VE
~I
b) 1T (ej)
=L v b
= c. ':J + Cz J =~,~
#-
...
+ V b\o..cl~
r - - - -'"1 ".5"~
I
f
~f'@.o)~
= 189 p~f=J.31p£; =9.MJ Ibf
caltlTROL VOUJME MOVES AT
V= 4.S- ~
e.x.
MEASURE nUID
.: THE TENSION IN TIlE ROPE
VELOCmES RELATIVE: TO TANK
~9
= COs30~
= FoRCE' O~ FLUID BVTANK
~I='x = 2.. ((( v~M + (( VKdm dI: J))c.v. J)c.~.
Bx
P, A, - fi A2 + I='x
FLUID IN TANk #-lAS 0 VEL/JC.ITlI R~LATIVE TO ~~
'"'-
I
=~A2
MaM~NTUM
~
IAA_
OF MAss!
So
(I)
(p-aJAA ~o -dP _pgclY -=..ov-cIv .1
:. dp of-;nrdv- t-~ dY :: 0
r
~ FJ( =: ~ if-cJM + ifd.-H
:::?t (~x&)- V;tf~ = ~ ~ l.C ~1f4 =~A (vw -zr) "Pa-Pa
FROM (I») ';;,.02 (~-~s)
.:1i-P,
=A' It,1..[
CD
-A~1&
2.1
A1=' 0 TO? ",,:l v; == 12 tvJ/s
A2., = .113Vold
P~A.:z.
FoRcE o~ CVLlNDER.:
o-A +"R1"m (A 3 -A~) - F)(=O o-A =Fx.-RiMtAs + Pc-mtA:z. o-A::
m(Vj-v;,).,.(p~-Rn.,)A3
S'Jt
~-'P~)A.2
o-fJrof.)=E!'
(33ao) t U:~~(:l~t ~
3!U
-
SECTlON
o;-A, ~
0.) AIR:
lfw
~
= 1130 fps slc..c.gs./Pf3
=Pal.{." ~ :(.OO:131XIl -
N02lLE
-R=l't{/J
-~--
tJ;=10fps
A'P= ~ -P.
psi (COMPRESS/Otl)
A.UID
~
1'= O.0023?
- SHi. ~ ~(12)· 0--= I Z2/
....
(MOMEN1UM OUTSIDE'
®
SEC.TION
~
--;l, V;; 2 bd
t-f'ifo.l3ol
=:26.KQpsf
)(,q
30
= O. 116 'i!ps;
b) \VATER: VW = 11100 fps p:" /. ..
-f'Ac V~ (-ve.)
. .
&~)fc.v.
V)C
pdV=:. ('(Ae Vs
:.FK::f'[Ac.V;Vc I)J
1I
f= 11 cotcX
:-Aj~')(O)
2
-Aj1f2.]
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
=,0 Ac. vs:z.
. FORCE OF FLUID ON CAR"
2 h sino(.
R= -~
24-
H2 = h~
+ 2 v-:1 n/9
H -= Yh~+(2V~hY9
R=
? (h2 -L:a)-f'h~(1J[ -I)
529 Q,~j)()ny
V. h( =Vz h-zM.o~UJ-.1
~h.I~n.Z= ~Al)~
?"'
So hjz ,~ =5'0 h,h
Wt,AlilC
:z
Jv, hi (V2 -V,)
~
~.-i~~" ~V.hJ (V2 -V,) ~GNnw(rr V2. 2~h/h~ 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
~1... ~I-Ya.
h.: th, h~- 2 v,\~ =0
~~h2
~l = ~ (~-"("'-~f gh,\
-0
~ ~U1i).)vrrY
p=: ~ ~i"c:X 1. )
-P. -=1' A h Vz -
; f:~~1I It:
n:
Y
m, '" gAV: -~ AIi L _k' ~ + *dt. -
SS
.3Yb KW
-,0 t!i '4 A3 ccs.G
P,-~ 6.i ENERGY EQUATION - STE.ADV ,..:" hOI + 1IM31103 = Wt:z ho :{
v,AI(CvT. + ~~ t~)
A'S p=c/
t
V3 113 (C",
+ V.l2 r ~ 2
AS
73 + ~3~ t ~3
)
= ~ A; ( C vTz
)
+
,.0
T,
=
p
=- 7;) p, ="P3
r
~2[43~ • VI
-2
I ... Ihv3
~
2 b, c.osB A.
A,V,
e= v T, l' ~ v,A, f V:.A.3) t A, v,3 t"A!.vf ,u
-
2:2
=V:zA2 (C 7i ;'2 +- ; ) t
v
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
6.9
:2
Z6.
CAN ELIMINATE
C v (72 -T,) = P,-'f;i ,.0 _ V.14
+ V. .!:1,.2 + AJV] V3~ 1f:2 A;:~.:l
T So Cv(-r; -T,) = P. -P:a. r'
+
It
+_~-_~ A-!lI3 V:::)" --v.M( 1+ l
A3 ~ tA, v..4
;;.
I
I
1I,;\
A3~ 2
«Yc.'S. p(et~)(v.n)dA=O ,lL ~
ve,
A,V,
It 3 11:):1. 3
V ':1 -:4 2
+ U13
- £.lit t
"Ps - ~ ;z>
=3. B2
:::a
0
VA ::= Q
= 3f1o/s
Us =
=/fg ~ tI~ = '-IlI.4 =15.28 fl;ts
AA
A,'if
Q
Ag
~ -~
I'
PA -~ 109
701 (19-):1
=
Vs:l. -'{12. + c.{~ Z
10','" -:2 (3J. J =?'I)
+ . liSP.
fI'/s
-U A
~-""B3 =
fCj
~
=
2./S'
Q.
Z f1- + 2. IS
= 4.15
w-
r
Z~r = vi! dtH
of flt.\id
A of
-F -Lv' +PA(A
flt.\ic:I
c.s.
= -111 VzlA + ~(o)
r:
:=
of- PA/A
-t.J
w:: p Q
+ mVz fA
VOLUME
-= 6:l.l./nr~~.s +'lI) ( ~S-7" j.'1
!/rIA = lIi
~:l:: lI.JI V4
F
~ -~ -{if:: f{(er ~>,(V. n)cM o 0 t. 0 t +~~C.S.pdV o
~ -'PH + VA :l.fJ
Vl.'2.. t
=1399
ON FLUID
/39'K
Ihr 1
b) THF FORCE ON THE LID IS THE INTF6RAL 01= THE' PRFSSURE
OVe;K THE' AREA O~THE WHILE "'BE-RNOULLIS
G tves lis P= PCVEL.) \viE Do NOT KNOw THE VELOern' VARIATION ALON6 THE' LID.
~ (l1A - ':i 1. ) ::. 0
Ibf/f+ 2 ) + y2( 1.11-"7.3)
CD
6:2.'1 lh""/f+3
6.12
~G
+ "32. r;L/ (-;" 1 -:! 0 y2 = 1'/2.3 y
16[
52.lrl(
LID. EQ UAT7 0 N
'C.v.
.L
(IO./l/L/
'!!.1.+ 62.'{[,3S'X3r..,
FoRCE oAt LID IS
FaR TI-I~ COlJTRoL VOLUME SHCWN;
~t
10
-;
fps
3Z.6Q
I.{
2
2
t-1T. 1~
t\4
IA ::
=1/1. / /hi
:S'1.51(2.7r'12 '-b-)
IIlAz
F:: -111./ r
"Us =3.gj V 1:!§..'-= 1.:3 V2
VA: 2.1{'5'"Y
p(O. Vi) V~dA
USE GAGE PRESSURE ~ R~5Um FROM 6.10
at flu.lcl.
...-I:t!.{ ----=-t
6.JO
;:r \ (
®
Q=6~
AIR
~ :lC\LCOHOL fJ=· 'S
= 13.5" ~
"P. -~ =0.1 WI
U2..:Z
I
2
M,
~ 0: 2+hL%~
kl-~D}lo ~l£,
J
t52
%
@.::: (4,0 Mt
M:: yAUC :. Ill§) ~ ~@ h~'%()J ~
L1:2~ A~A~ }
~
z
1.6
L(O~
~ I'!L "3~
}.b ~
~V~tfz
0"2. '" ~ '" .g,291'V1i; 10/),:6,(£
~
Z%,
~% cfI/~f~)
~ ~
20
S(3 ~a
'%
ht...2.~% 3th
2
AJJ.t>
1-
z
l3~ ~
Lce6lz~
~.3B
~~L'-r ~-----.- .10-5 Q32 /4M - (,34::).IC- 5
G::O
.0177
QIM) ~O.~2
80
.{){)70L
ICO
.cor28
T OF?
~e A~ I
41'32
~b~z-(3~~!
7.4
z
.r.m
=N c
= No. OJ='
4
CROSSING
W =MOLECULE'S
I
t
ORDER OF l-AR~E :; MAI{"BE
SI6~IF1C.AklT COM1=>AR~D TO THE
REMA/NltJ~
,..
~'-'
~-:=
~e
dr
7eRM5.
~ = ee~ = 0 ar dr
:;}er
(}e,. = - ex slY'e t ~ case = es ()6
SIM'LA~L'" 9€e, = 0, ,
dee
d('
';)8
= -e r
HENCE I i'
~ = ;;Vr dr dr A
:
=
i("
-t dVe
ar
e
P
Dt
if
T
Vx~~ T ~~ ='3x -;~ 0
()
+ v'V':Z~
Q
:;}~v.
:2
t-V0 ~
FoR Q.? To BE 'D V ; ~ = Vr
de d+:
~ = ~ - 1. V'P + J V:2 0 ()
(~ - Ve)~r i-~~
dt
dt
bt
'V Vx =~ = 1 2P ~'1~
=-L
B.C.
.•. -:g2 ::. ~ -rIV('dVr- -t!!dV,. _~~ ~~. dr r ~ rtr
,.u 'dX
~=J..~Cj+-C dlj j.J. ~ I ~
= w =rVe
~=O
Q)P
2)-' ~X
':1 2 +e, JT/NUITV:
VECTOR "'PRoPERTIES DETE'R-
V E VP
f.lUAIm . 'BY
I
~
wHIC.H
ARE IN"ITRDFPENDENT; i.e. CAUSE i, EFFECT. MLJST LIE IN SAME -PLAN~
.:
La')
~E'7E?M'NE'D
0"1
-\JP~
p (~ + V)C ~ Va~: :tf l'cu ax) ax
.c ~(()kJ A~
y.!WS z direction
Dt
J, HAS
=0
t
t
Dv
9.1" Usu:4TwG;
:x (p'lx)
~rTtVG 'O:wAl ~ L1?~20 AND ~:: r) EC( E - ~
IN ABSENC.E O~ V/SCO()S
FORCE'S
MOMENTUM:
~t
.~
(a"-
Pes/TIVE SENSE 6lVEN
~
ai)
1¥or+ ~2'J r- +, ~z +pg,+/J- [-1-a (av,) 2
,
=-
"BV -VP OR DIRECTIoN Ot=' DE'CREASIN6 -PRESSURE
v.
PWc+ v7a r +~+v,-r; r ar
ar
r
0
-b)
SIMILARLY" ANY FLUiD.... '5TA11C
OR MOVINq.... HAS nils SAME'
'N~WENCS TEN'D
e WILL I
MOtIF oR
To MoVE IN THE
DtR~CTION
'PRE'SSVRE
01= D~CRf'AS/N
11.'3
1)~ _
I = La. (Vc)b (MIL~t MJ:~
5"-'3: 2
CORE GROtJP
V
d2 -
'4
3
J. 3
(P.I 'OJ w)
tC4
l.)p:.
=
3-$'~
3-2/q
O. 'T13 ........t - - - - -
1:,)
11.5"
MODEl
D
,,1>
D
V
V
p
20 knots
p
p
A
).t
M
F
/Olbf
A
1)2
Cmo.x
"PRoTOTVPE
fJ
9 1
.~i
b~
KWl5Tl~ ~tt &-r~ T~~R.u~ ~Nor-~.
Buz.
.\0 -t;
I
ak.1?O ~ \4}ffi)
~vt;_~~T~
NOTb. T~-rUi;
O~C:1~ _(O.-t; !t~
(S
lW~dN fu ~mLt; DJZ
'~:2.
os
ftk~
V45 ~ '~57 _\O-s .ft~
t.~,.~( V~2'(JtDV)
~
Nor 'Stow ~1Z.L~ \)J ~
~f\J~~~jh/(Ja>
I=
I~ .. '
155
77
£
~
z
(§ \ ; : S 7m rlD I.S7/ )
1\7_
x
1Re.x
0
0 2·1()5
dLJ~
~~ G4't1
0
0
.5"
.111 .2«19
I 2
.352
0.321 I. Jt' 2.0'3
.'1Ql
3.SQ'
.I
I
= J+n
TRAHsmON Pol NT
'I
~=2'ltfi
FOR TURBULENT FLO\J~
d' _ O.3'g1 X - (""Rc).2
=
Lv J}
2.
= (Y2)( LlO}3 = \-:l~ ZOO
13"'7 .7
v= AQ ==l((.u;)4. .~b = 0. 3'1 Hot/s T
.Isq .,0-
0.) TlJRBULENT FLOW
CALCULATE ~t
Cfx -=
1';;' = a 022 5'f
O.OS?6
( ';f2(x) 0.7.
efL
=J. (L CL ax =O.o!;".f' (L L..Jo
f
Vt
V; y+ >S'
30
AY
= I.?SI./
.: ~~)C
Mtti\
= 1.~'2. ~tH
1'5"-I.?£" = 73.25'" ......... 13.&' MOMENTUM ,- pV2
P v3
EN ERG Y @1i?e
,,-.J
-= IO~
.&- =~·S-Jk)CO.2,\
l-s
6L
i~ ~~S- J
= 2. '3'1 MOMENTUM
P
~2
ENER§V Y2f1~3
~LUX
M E
~pV~3 ~ ~L
0
.1 .3 .5 .1
=
.~:z
.1./92
.126
.5S3
.3f1S.4112
./68 .2.10
.601 .6QO
• 5/2
.:25:2
.61~
.5SQ
ON 6RAPH: \) MoM-LAM 3) MoM-TURB 2) ENER6.Y-LAM q) ENER6'1-TlJRB
2(iJ
.q .2
= f3~)
OL-~~~--~~---
() .2 .'1
M
pV• .2
= SiY13j~ 1r) \-CL 2 0
~pV~
.~ol
.Oqq
· ?O1'
• SOO
· Zq
.195 .t/f
.355" .?aK .'i7
J .00
Ibf-
"IRe. = vL - 205·?
1) - 3~6'1'IO-7 -
0
· 'I5S'
l. 00
= 2~" JEq .eft.
E
.OO3E
1.0
-2SIDE5
D= ~(.OO20qqX205)2(S60)CfL
.021./1/
.qq
£-L ,~pVco3.
A = T·l/O·2= SbOfP-
.J5'b
.q
.6 .8" /.0
r3.Q "'ORA6 =CfL ~pv2A
L
..M~It{~ rrt) pVoo2. &1- Z
• ~6b
J.o .X .6
sin2.(i 1J)
0
0
.ofq
LAMINAR;
p Veo 2
0
.2S1
=pVoo2 f2.(-rJ nuX' = f
~f'V~3
• CJ()l/
v= V«)f(~) MoMENTUM
PV~'2.
0
c) CORE
~
M
~
q
'Z
• D02.0~
0.) LAMINJ¥R CfL
=1.32X' = 0. OOL/65' ~
D= 11.26 Ibl
/.00
b) TURBULE'NT O.OS'1&
cfj( = (vx/lJf2
79
J
IL/O 000 .I
4L::
0.072
eft = 0.0000664
:: O.Oo2QQ
~.2
L
D= 265"6 N
$:.
5".2,0
=. S'/O-2~
::" . 5"em
fl/·/oJ
=\0"
13.10 ~)< COM"PA'RE'
13.12 0.)
C" ~ CfX a) LAMlNAR ~:: S"x
J"~= 1,(1- ~.&)cl'j
fi& •3?6 ~
TURBULENT s:" _ '1" -
C;- _
.3=1€,'ii"".).3 ~ If"e ::
1Re.X • 2
LET
-
b)
LAMINAR Cfx=
~ s: (1- ~) d(~)
~ = t{
J~ (. ~1 ~ = )0 ~ -(1J d~ = 1-
LJ ':UJ
~
TURBULENT CfJ(
=
-"T7
I
lti;-
~tt I +YI
=.OS''7~ 'iRe)( .2
Cfr _ . 05'76 ~.3=
ef£. -
S:'17
.66'1
1"3.11 Tl1R13ULENT:
o _ o. 3~
X - "Re".2
C _ o. on. tt. - ~L..4.
=
1Re -
V.L L-7
c) 2
T= 2oD C, J=IO-b ~}§
'IRe 2D. =
Lj./OT
V1
(rt+lX (lt2) .
+ .E! =
e
==
2
D= fPV 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
2
+(21X"H'2) (~)CV\)
2
+
~ Vl
T\-IE SOLUTION \5
u=
eSA{
= e- fPr.x)clx 5~(x>e ~ P(lt} dxc( x 13.1£1
J; = V, I cl Vxd"i2t 2) P
de
2
d;"t e e t-Vxcr G&
'X
~ - ~ = (Pow£R) 1t cH
\RQ. = \) V = V.l2'1/i l)( I. Ii) = 2 q 5" JJ 8 -Io-S' LAMINAR AP _ ,- - 2 r L V2 . £. = \6 --"L - )~f -1) ) 't ~ P 0.0'2
\ 'P'~E
GIVEN "PIPE J
A'P --
.f PV 2
-
V 2. ~ "i:) \J 2~+~=rpt~
f iA~
:z.
P
fUNCTlON O~ e/O ON L Y THUS ~?_ ~2-
P
B
.:1 'D
_
1°2 .-
'3) A ~NOZ2~ :2 u.. ~ PI" _ VEX,T .:.L-+ r - -
;:;0%
\'2 (~\~ 6:2.'1 - ,'" ~"nc;' ~ 2t.3J ?o - 7. T..c r -'
2
AP
,
1~.5
2
t; = ~PlZK or 'It! -'c J
P.
t..~2 = A'PIIo.O (~02.J p..... wHa,o
I
\lp :z. ~
A~ =ZK~~+t(f.f~~~
THE \t)EA 'BEHIND WATE~ CAL IB'RATION IS A'P. :: ~,~
w.~
p
3.20 KM
T2. == V i-xfT _ vp:2 == ~ ~(V£~ i" ~ ~ 2 Vp:1 I) IT-
Al> Vp -= A\lOiZ ~ VE)OT \.?2.(Ap'2_
~= 6."1 '/0- 6 jlM2/s
C.ONTI N U lTV /
p.: ZOo I
:. A~:::
K~ I ""~
v='.1~/5
'D
e =
\~~3 /
L:: 32q
p~
DOO~
~=
~:: jJ
.005'12
~~
I}
Vp:l
2
fi't:"t" 2\( :
Llf b + Ap
-0
:f 0 Aw?' . 'J
t)/e. == ·'=1¥:J,·5'fOb) = I~
::: ~(.OO51:2)(32q ~) (l.I):2. \: ,-:rl J ~Y()7
~y
•
M
Vp2 ==
~ = M~L:: Z'D11L (.'1/)2(1.1) S"~1.1{ ~
=lq41 KW
r
AN:2
K := !/ f! L~ ID 2K =;; -a:; t 3.1 +1.5 == 155
= l/t~1~ t>
:: 5".1
-"2
ADDIN6 T06ETHER
~e.:= llbJ Doo
~ = 13,Q"? ~
p
D=.l"~
e = . 000 ,5 ff-
t#o
2) 6."PFRtc.notJ
P ~?2
-=
p
f -=
T
,a
A'P.
FoR l=ULL'l' iU~ULE"NT J:'LOW,
So
+- A ~ + 6 'ij
~
'"
1'1.5;2
.:.
=2-' -lOS f
~.'OS' V2.+ D
VP
WlJs
L£
!)~
~.h.. Q~ '3 pS
=
II
•
= .Oo4~5
/1 r L Q,'J. "1"t"~ D 2g (~"D2)'J.
-
=22Spsf =1.S'Tp~i
;SO~
~
Q -= O.O/erg »13/5
=1.6l! ·/oS
2 ... CAST I1 3..23 ""'/5
~S/OOO OK, v~ '3.Cb
1Ke.=
t,.'P ='-I~OOb'3(:'X.2! ~X'3I."3)
1..-.
00
~5
V= '3. 2;2q
-
L. :: 21"3 t>
~e- ~
~= . DOSO
FoR 200
Of
l..\lt:; 0
~/~
4 IS ~ \A-~~TlC..
~=l~S ~t; == 1':> \~~
WlN'OWJ
f,w ::- ~~ %01'0 ~H
~\
(J44)
'?f r;y,,~S
(ct)
ce
I)$,~~
v~-WMJ..., \)\~\
-=
-
~,f\~ r;J..~ ()C\~ \,4)
~""'" It> ~1Itt\t-l(" \JJ~'J = ~'Lf1.6ot,~ tr t\~_T'2-4) ~ ~~Mb. ~ I'l uj -= At ,\\" ~ IS
',,1. t\!\ =
~lllil\. 1 ~ 1,,, r: f!J. ,,) :L
= a~b}1 ~~(l-)( ')5(j_)~.i-
24./ /
[)A~ =-
..6
(J"c10IJ5t T3/:L[~ I- ~e. r'l;2. _ _ _ _--..:....It-
p ~i
:::
MW
Gi-k
1.9
q7
3.,{J7
2,-14 (~)'~ )'d1("W)3 3