SOLUCIONARIO WELTY 4°EDICION

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<

Dv _ -V? --.fJ

I:>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<

MOo

I

0

I

L

0

0

I

-3 ,

tOO

0

0

2

0

0

-2

0

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

.:

F

(bD)2

f3 M L

0(

l= n-r' =

Z-3=S

FOR DYNAMIC 51 MILAR ITY ;

.: No.

~'" =1~;p

G'Roups ::- 5' -~.-------

Dvpl ==

)

~:: Vp(~

,u

v~

'iT; -=

.fI;. .¥t)= 6v

,

.:

rtf

DVfJ( A- ?

.= I 20

=M LJ., ~ c C¥MX I =M~ Lb (LlP')c M L)lt ~

I

Krto-t5

a.)

0.

a. = -1

1TS

ALSO FOR DYNAMIC 5IMlLARm' £u.~

r?::

J

=C

10= -/ I'Mtl.X

~Q.Lb~cf

;

fAI? F,.. (}t. %. ti)= F~

71S = twf' Lb~ c 'R

~

:. Fp = IOlhF

L

3b

J.ri.

11.'1 IRe = L V J, 1) "llIa.,....

= (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 )(1021.3¥?6

M

L p 9 1<

oJ

a.)~ASE'D O~ LEN~TH

/I.' VAR tABLE

S

= I. '2..&, 70 ~L .10-5' ,..,45 @ 2iOK (~'1.6°F)

~

0(

11~ = 1::1175 ="R-c.)

; V"

I

= -/

ML~

1lq =

C~o.x

C

I

=EtA?·

ELA-I p m -U2

112 =/3

0:' p~NbbC,L{

t -l

:. nD'W = t ( LID) G

'112.=

,

L

0 \

P

-= P N1)

COR E" GRo()~

0 0

L 1)

L= b - 3 = 3

J

M V\

~ -pa.DIIa pc Q

'IT = ~ 2

P -t

rfa)(293.33/"(itof

= ~ (. 002 3"Y1!

21100 (.011)(.75') Ibf

=202b~)(~O~p~} a)

WHEN

V= 500

(SEA L.EVEL)

P =A,

l.bS

/1'-

1<

2-

rax"SiYl7i~

Jo

:::zE

d~

i.. (d"x) dx

COLLecrrt-lq 'iE'RMSj

.: 8" -= ttxo.lS.... ----------0.) ~

4p"&1{~x) = qreU ~ ')( + 2I'Voa2d(&~ Q. :1 a. t 0. :z olJC - zpv«!..?)(

"fret

7rc..'" $)(

= 11A

d- (bx) &x

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 12.13 ;(

G

X'+dX

XF~(( VXpCO·n1tAt~i(-t-~~tr:(trm~V)

""" O:(1~3r) I.,O.I (Iae~ 2:91t0e i~~

%

-1."--

15.3 2CJl3A:z 044~ ·{o'2. cPs -1.

V~d.>* ~ ~-k2 =- 14524

-

4- ~ ~ l5~ L +- lSi,t.

o.44It3!t~

T~(p

v.~

~~t~tJ... V)+ l( ~~J".. ~') Tug Clt~ ~ TD V

a.~" ~7ft(z)(r4S2) ~14('87 t!>.~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

<

Vd f.

O.022S

In

\ V)C~ (mIXr1t2)B

= vx~ d

lJxJ"(2+3"\e

,dx

11

MULTfPL Y eY

j

ekI

+-

)~

v~ de dx

AND NOTE

eX! de = %Je 5N dx

\14

=0.0225

n} clx

rS./~ LET eS-lt = U EQUATIoN 15 OF J="oRM

WHERE Q(x):

=QU()

(

~.

IhQ\~

"tl)(m-2)j Ux~

l)

~} = ~(2t-3"\dIAtVxi Li Yl"} r).y.

~O.022S

tvxiJ

MAy VARY WITH X

EQUATIONO) J5 KNOWN AS A L1N~AR

FIRST ORDER

DIFFERENTIA L EQUATION

?CX) = 0

U

=Q

x

-t C..I

c= ul){=o

I~J"

TM£:A A~ tSb

~v,lk(~~~

fr~+I~(Y1tiJ~ (~J~

~ + 'PC)() U

CONSTANT

~ Tm:.. VIcM~IM~ S1tn>~ ~~ &t~ ~b-r~~

;L deSfil + e5~(2 +3,,') d v'x~ 5'

vxr. s

WHeAl

~DtS~~"R

~ vx ~ v""

c;1~

~'1

ttl<

~ == ~o...~

CHAPTER ~

ru

V

Q == O. 56

= ~ = '0 ~'~~o.J ·~s ~ (o~~'f

=~V +ffCe.-rfrM.it o

P:: ~ [\/2. +u 2 z + 3.. p 't 42 J 2 2

-Or +~dt,+U.,~

A?:: 2 (.OSq:;J~ (1.II)2(SV

R-'2.

32.2

q .b3 ps~

a

~ /~3.

o

:: 0.0542

= 66-=1 tbf

Ml\2.J!:>

~ - ~ = (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<

qG.. 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

P

32.

L

= ff Q2.

~ + V¢ +eA =~ + ~+Z'g -rhl.. ~ ~

7b~

a.) "'D

:=.

= 12.5":2.'°5

Y:2 'I

fASSUME

2."S 0'/"

..../

ffQ:J

iRe..

=

=I."6Q _/06Q

hL

2.2.,.,

1..3 =l!'...

= 3.65"7

.3S

- --v'l. _ ~

= .00 1I~).

30

v = IJ. .b'8 Kifs

.Z7~4.~

kJow Q=ALJi,

~

T~

~K\

~= - (06 r\~~,· ~ ~:,H r.--vv---~

fLo

1"11'-. R.\ \1, \1

12.\:;- 15'-..1. \- /'(IJ 4l\~-

""-

'R 0-'- 4-Ti'fo'L~ l -."

(D" ()

\1 1/ lOS - /0, ~~ N~u::c.,'\6D ~ \/~

?.

(

h~ ~ ~:: ~ ~~1S O'~~l~ l' LLl t ~'~)'4.T'lj

t\

~M..

~ ~'o -;~ f.o~

K.

~\~L. -= 0 l~,\-2- ~ V~ 'lo,4"'~ fi-,--~ ~/(2. ~ '}.~\

O,m)11 Cp,o(W,01t;x..ss;

\sULf"::. '3'60\(. -\ ~'1,"'ISL

\~ -= ~1S\( \ S== ~S:o\l}(3/~\3 A) -:. 0lltS'S Y\OIo'N\7..../s r,-~ o/toG\ V\J4b\L ~(~ I). ,~o

~

b)

419 N ~-Ar'1~~ ~\l.N ,

\jG2:{\C(}L

2.

h-- kC o/?g,l ~/~ 1 L[0£'21; t D"t (O,v~1"r).1)

k =(').l,S,\ l'-161~,(5jStbS'0-'~") ~ IJ-,CZlo~

'f.. \09

h-: \";C; (

IN/ v/!. ~ \--~t~w'N I ~1 ~ o,on (lL0 ,L~-(O, Ip

6 f'("

~ \[\\0L':l ~"'J(}\t, ?. -= - 4 (L

,'ill

0(00\\12-

Vo CS\-")

~

o{ L\1 L\--

T~:; '?lO -l()~\~)~()) ~~l

Too? ~~1

~ \'l'i -

Tb~' ' ~\SIS I'~' ~\1:oNJ1i>U T~ ~ [ S~ ~~ '; (

o

o

o

0,2

10 ,':'/1:,1.(;

0,,+

OI~1

0,)204

0,07104-

CI~

l,c ('\4(\ /l.1

0,2 \,0

h~1: . . 1-').So

0,152

~ ,,\L

)

hw~ .. 12SoIt,~( \14\ 'N/JklL

o tit

o ,I~1

V\)/

~l.\~~~~

1).."1 ~

Wr ~oO' )-t-(" ,Ill ~ t."''74

1;'

V,I "\iC\i>\, ~ ~,

3'2.'). \::

~~" (J~ 0--"11"4)

1.38

\f O-I).~ ~

O,lJ.l~ 7.

o/)..\~

2 O,'2.W'(,:},'l,9, x \0 )

__ '6141 x \0- ~ W

AI

';'~,wc\ \'l0', I~ T\"\6 ~ ~S\Q;,~ ~t: Wi =,~\-

'\UlN\i

~~~ CJ'lrt~~r~4)+~(r--T~)

~, S iCll,,(toD)'1_ £,lal(" (~ ,()'~)~ +3~) \""T- lo(oc~

~(0/~~ ~M

\'l~()~lbr:W\

~.\t>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