Solution Manual - Fundamentals of Fluid Mechanics (4th Edition)

Instructor's Manual to ACcolnpany

FOURTH EDITION

Fundamentals BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics

THEODORE H. OKIISHI Department of Mechanical Engineering Iowa State University Ames, Iowa, USA

John Wiley & Sons, Inc. New York

Chichester

Brisbane

Toronto

Singapore

TABLE OF CONTENTS

INTRODUCTION ................................................................................................................... 1 COMPUTER PROBLEMS .................................................................................................... 2 Standard Programs-File Names and Use .................................................................... 2 SOLUTIONS Chapter 1

Introduction................... .......... ............. ..................... ....................... 1-1

Chapter 2

Fluid Statics......... ..... ...... ........ ................ .......................................... 2-1

Chapter 3

Elementary Fluid Dynamics-Bernoulli Equation .......................... 3-1

Chapter 4

Fluid Kinematics... ...... .......... ......... ..... ................... .......................... 4-1

Chapter 5

Finite Control Volume Analysis ....................................................... 5-1

Chapter 6

Differential Analysis of Fluid Flow ................................................. 6-1

Chapter 7

Similitude, Dimensional Analysis, and Modeling ............ ............... 7-1

Chapter 8

Viscous Pipe Flow............................................ ................................ 8-1

Chapter 9

Flow Over Immersed Bodies ........................................................... 9-1

Chapter 10

Open-Channel Flow...... ...... ......... ....... ..................................... ...... 10-1

Chapter 11

Compressible Flow ......................................................................... 11-1

Chapter 12

Turbomachines ............. .................. ................................................ 12-1

Appendix A

Listing of Standard Programs .......................................................... A-I

INTRODUCTION

This manual contains solutions to the problems presented at the end of the chapters in the Fourth Edition of FUNDAMENTALS OF FLUID MECHANICS. It is our intention that the material in this manual be used as an aid in the teaching of the course. We feel quite strongly that problem solving is an essential ingredient in the process of understanding the variety of interesting concepts involved in fluid mechanics. This solutions manual is structured to enhance the learning process. Approximately 1220 problems are solved in a complete, detailed fashion with (in most cases) one problem per page. The problem statements and figures are included with the problem solutions to provide an easier and clearer understanding of the solution procedure. Except where a greater accuracy is warranted, all intermediate calculations and answers are given to three significant figures. Unless otherwise indicated in the problem statement, values of fluid properties used in the solutions are those given in the tables on the inside of the front cover of the text. Other fluid properties and necessary conversion factors are found in the tables of Chapter I or in the appendices. Some of the problems [those designed with an (*)] are intended to be solved with the aid of a programmable calculator or a computer. The solutions for each of these problems are presented in essentially the same format as for the non-computer problems. Where appropriate a graph of the results is also included. Further details concerning the computer and their solutions can be found in the following section entitled Computer Problems. In most chapters there are several problems [those designated with a (t)] that are "openended" problems and require critical thinking in that to work them one must make various assumptions and provide necessary data. There is not a unique answer to these problems. Since there are various ways that one may approach many of these problems and since specific values of data need to be assumed, looked up, or approximated, we have not included solutions to these problems in the manual. Providing solutions, we feel, would be counter to the rational for having these problems-we want students to realize that in the real world problems are not necessarily uniquely formulated to a have a specific answer.

One of the new features of the Fourth Edition of FUNDAMENTALS OF FLUID MECHANICS is the inclusion of new problems which refer to the fluid video segments contained in the E-book CD. These problems are clearly identified in the problem statement. Although it is not necessary to use the CD to solve these "videorelated" problems, it is hoped that the use of the CD will help students relate the analysis and solution of the problem to actual fluid mechanics phenomena.

Another new feature of the Fourth Edition is the inclusion of laboratory-related problems. In most chapters the last few problems are based on actual data from simple laboratory experiments. These problems are clearly identified by the "click here" words in the problem statement. This allows the user of the E-book CD to link to the complete problem statement and the EXCEL data for the problem. Copies of the problem statement, the original data, the EXCEL spread sheet calculations, and the resulting graphs are given in this solution manual. Considerable effort has been put forth to develop appropriate problems and to present their solutions in a manner that we feel is helpful to both instructors and students. Any comments or suggestions as to how we can improve this material are most welcome.

COMPUTER PROBLEMS As noted, problems designated with an (*) in the text are intended to be solved with the aid of a programmable calculator or computer. These problems typically involve solutions requiring repetitive calculations, iterative procedures, curve fitting, numerical integration, etc. Knowledge of advanced numerical techniques is not required. Solutions to all computer problems are included in the solutions manual. Although programs for many of these problems are written in the BASIC programming language, there are obviously several other math-solver or spreadsheet programs that can be used. A number of the solutions require the use of the same program, such as a program 'for curve fitting, or a numerical integration program, and these "standard" programs are included. For those requiring use of one of the standard programs, there is a statement in the problem solution which simply indicates the standard program used to solve the problem. A list of these standard programs, with their file names, follow. The actual programs are given in the appendix. Most of the standard programs are, of course, readily available in other math-solver or spreadsheet programs, and the student can simply use the programs with which they are most familiar.

Standard Programs-File Names and Use Curve Fitting EXPFIT.BAS

Determines the least squares fit for a function of the form y=ae bx

LINREG l.BAS

Determines the least squares y=bx Determines the least squares y=a+bx Determines the least squares y =do + d JX + d 2x2 + d 3x3 + ... Determines the least squares y=ax b

LINREG2.BAS POLREG.BAS POWERl.BAS

fit for a function of the form fit for a function of the form fit for a function of the form fit for a function of the form

Numerical Integration SIMPSON.BAS

Calculates the value of a definite integral over an odd number of equally spaced points using Simpson's rule

TRAPEZOLBAS

Calculates the value of a definite integral using the Trapezoidal Rule

Miscellaneous COLEBROO.BAS

Determines the friction factor for laminar or turbulent pipe flow with the Reynolds number and relative roughness specified (for turbulent flow the Colebrook formula, Eq. 8.35, is used)

CUBIC.BAS

Determines the real roots of a cubic equation

FAN_RAY.BAS

Calculates Fanno or Ray leigh flow parameters for an ideal gas with constant specific heat ratio (k> 1) for entered Mach number

ISENTROP.BAS

Calculates one-dimensional isentropic flow parameters for an ideal gas with constant specific heat ration (k> 1) for entered Mach number

SHOCK.BAS

Calculates normal-shock flow parameters for an ideal gas with constant specific heat ratio (k> 1) for entered upstream Mach number (Ma)

3

t. t

I

1..1 Detennine the dimensions. in both the FLT system and the MLT system, for (a) the product of mass times velocity, (b) the product of force times volume. and (c:) kinetic energy divided by area,

mASS

;( ve/oc;'& .:.

(;VI ) (L 7-

1 )

-

F .:. M L T-.2

Sinee.

Fr

=

( b)

./oree

J(

Y&/I/ml!

-

_

(~

)

F L3 (ML T-2.)(L3) _ /'1L if T-Z.

J::,;'e/:'G e ne r.!~ t:l

reL /'1T

/- I

-2.

/'2

1.2

Verify the dim~nsions, in both the FLT and MLT~ystems .. ofthe folioWing quantities which appear in Table 1.1: (a) angular velocity, (b) energy, (c) moment of inertia (area), (d) power, and (e) pressure.

= a 1'19 tI //1 r c/'spkce/?'J()~';' -time

( 0.)

(.b)

..!.

e he 1'"1:J ~ C.a.;aci +!J 01 b~cJ!1 1-0 do w()rk Since.

Wt?/'"K

= I()rce;(

d/sl-tll1tt:..)

~nerJ!J tJr

~if;,

;

FL

F _' /11 L T- 2

e. n erj tj ~ (M I- T -2) (L) == M L 2 T - 2 cc) /7l{pmfl1t 0/ inerlltt.~V'ea.) =

sec~l?d /nl'Jme/}f

. (1.:2-)(L~)

=

+-()rce

-

.£

,

~

LZ.

. L= F

=. L If

2

J..---------- - - - - - - - - - - - - - - - - - - - - - - -

/-2.

D/

t:lff?l

1.3 \. ~ Verify the dimensions, in both the FLT system and the MLT system, of the following quantities which appear in Table 1.1: (a) acceleration, (b) stress, (c) moment of a force, (d) volume, and (e) work.

a cc-e/e ro.:tt'tJl1 :::: ~ t-r-<

eS5

(C)

=

./C)Yce

/?1t:J/)')t"l1i ,,{

0. rea..

(£

Ve.JDC.I+~ .:=

+/me F. == L;" -

(-kyce

=

.force.K dlsftln('~

=f/1LT-VL ...: (a)

volume

(e)

Work -

Oen~f-h) 3.-:.

2

I1L T-

L3

--

!=L

/- '3

.-: 1= L Z

/''1

I I I

I

1.4

If P is a force and x a length, what are the dimensions (in the FLT system) of (a) dPI dx, (b) tf'Pldx\ and (c) JP dx?

dP

ra..)

-

(b)

d 3.f

dJC

dx:. (C)

-. --Lp- -. .

:::r

3

jPdx

!= L- 2

F -. -L3

-.

-"'

1= L-3

PL

I i

I I

I

/.5

I

1.5 If p is a pressure, V a velocity, and p a fluid density, what are the dimensions (in the MLT system) of (a) pip, (b) pVp, and (c) p/pV 2?

(a. )

1> _ --f

--.

f.1L-'T-Z.

(ML -3) (LT- I )

.

Z

--

'--_ _ _ _ _ _ _ _ _ ._........... _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _......J I-~

/. ID

I

1.6

If V is a velocity, fa length, and \I a fluid property having dimensions of UT-I, which of the following combinations are dimensionless: (a)

vr", (b) VC/',

v.R -V

(1:, )

(d)

V ).11

- L~ T-1 ,

. LOr"

(Lr')(L)

-

V 2 -z)

(C! )

I

V'" (d) VIM

V J. -zJ .:.. (L T -'j(L)f1. z r)

(a.)

j· 7

(e)

( dimension /ess)

(L'2. T I)

-

(L T-) "(L • r - I) ~

-

.

(LT - 1 )

{L )(L' r

-

')

mol dlm.nsienle,s)

L~r3

-l.

(oof dimfnsl'oIl!ess)

(not

L

dlfnen sion!e>s )

Dimensionless combinations of quan1.7 tities (commonly called di mensionless parameters) play an important role in flu id mechanics. Make up five possible dimensionless parameters

by using combinations of some of the quantities listed in Table 1.1.

Some possible

e" Q mpl e~ :

u C( e Ie r,,-/-'M " f 1m e ve /OCI f '1 frefllenc'j ;(

hme

(ve!oci+!j)

2.

/ t'179 f !? x. 1i< visUJ~if:J

-

1- 5

I

/.~

118 The force, P, that is exerted on a spherical particle moving slowly through a liquid is given by the equation P = 37CJlDV

where Jl is a fluid property (viscosity) having dimensions of FL -2T, D is the particle diameter, and V is the particle velocity. What are the dimensions of the constant, 37C? Would you classify this equation as a general homogeneous equation?

.p =- 37T;

sa -/-1 's.f." C6"t/, ',,,()~

"n r)

.ta -f If b = - I (.£. :!iJ 1-, ~ I-y ~Y1 dJ/o'" "" L) a. =LZ. tlnt! /:; = - ).2. So

c = ~i0:

-tn..-f.

Thb re.5u

1+

/s

1

~nsisl-f"r /AI;-!/1

:5peed ()j2- 5DUJlJd.

YeS.

1- 'j

the, sblltlt/J'p

~rIl1U/A

-kr 17te

I,

/2.

I 1.12 A formula for estimating the volume rate of flow, Q. over the spillway of a dam is

Q

= C v28 B (H + V2/2g)3/2

where C is a constant. g the acceleration of gravity. B the spillway width. H the depth of water passing over the spillway. and V the velocity of water just upstream of the dam. Would this equation be valid in any system of units? Explain.

5/~ce ea.c;"

I:errn ,i1 ~e .e.Su.Lf/~H rnus-t- ha.ve +he SQ/7Ie dimellsi{)l/s -the ~11.sb1l/i C VI must:- he cilmeI15/!)/J )e~s. Thtls; -tnt!.. .et(f~tltJH is a ~-ene r-a I htPl1IP ,e/ledJ t(J eg Ua.,tIOJl -1'n¢,f WOf,{ /~ 411'1 e4)A~/sl:ent Set: of (,Iilif.s. Ye~.

be. v t).. //d

I»

/. / if

I

(c>-)

1.14- Make use of Table 1.3 to express the following quantities in SI units: (a) 10.2 in.lmin, (b) 4.81 slugs, (c) 3.02lb, (d) 73.1 ft/s2, (e) 0.0234 lb·s/ft2 •

1t),2

:;;'1 - (;0. 2 - i-.

;,;J (Z,S*;t/O-",:'.) ( ~;;n)

'a2. .;c It)

[ h) If. 9/ S/fA l' =

('I:?/

( ~ ) 3. tJ:L /b:::

(3. ~ Z / b ) (

Cd) 73. J :Efi

-3 /W1

s

=

sill!> ) (;. 'f$f' ;< I () If. If'If

f1 ).=:

tf. 32.

T

sju~) =

70, 2 ). ff

/3. If AI

:

ce) CJ, tJ23'1 Ib·s

~

ff~

(0. ~Z3'f ITt.)

('/,7.?1;tIO

N· -': ",.,1-

lb. s -ft'l-

-

I, /2

N·s M'J'l.

1-/0

)

/./.5'

I

(b)

1.15 Make use of Table 1.4 to express the following quantities in BG units: (a) 14.2 km, (b) 8.14 N/m 3 , (c) 1.61 kg/m\ (d) 0.0320 N·m/s, (e) 5.67 mm/hr.

o o.llf.

!!..3

,11'I'f

" (g. 'If ~

)

(~3U;(/O·3

':3 )

= 5'. IF)( 10'2

,,",,3

(

l I.

Cf Iff) )(. /0

-3

SJUjS)

W

=

~

~~

(d) 0.0320

N-1'H1

-S

--

(~, 0 j 20 N ~ I1f1

)

(7, 371P;( /V-I -il-·Ib ) oS

N·/'M

-

2.3b)(JD

- s: 17

)1.10

-2

-to

/-11

.{.f·/b

-

-1-1 ...5

oS

-

oS

Pt.

/. /(0

I

1.lG

Make use of Appendix A to express the following quantities in SI units: (a) 160 acre, (b) 742 Btu, (c) 240 miles, (d) 79.1 hp, (e) 60.3 OF.

IfpO a. ere

(6)

7tf2 137U

=

6'1-2 sru) (.°£,;') L

2/1?1 ,,-]

I-i ~

-ft 2 bJ

rnu//-'/0

Thus)

fo

(/

9.

= 0, () q 29{)

'2'i{)

£ - 2. +0

/H1

~

t!trJnvfrf

/ffI :2..

II;) /

slugs/.ft.3 b!:J 57 IS-If

Thus) mu/fipJ'j

E of 2. ;'0

CtJl'Jtlfrl

-to Ie? / /I'n ~ (I!)

If-

/

fj ) (~. 30'/; jJ)~

= (/

Thus.) muillpl!) Ills -I: 0 (d)

bIJ

3.0'le f - / -1-0

cOl1vert

/s.

/t11

I JIz - (I !l ') (If. 't'l12 !!..) [ I Ii 3 3 l If 3 - l' -It 3 ) l ~. /j, ( 0, "3 () Iff) /W1 3 J

-= TfJlAS)

fo

m

IA

IV /57, / ;;;;

If/pI:;

#/;m3

/ b/R ~

4

/-/if

b!:J /. 5'7/

}; -t 2

-10

t'e>ntlfY't

/,/9

.J

-

--

1..1 q

For Table 1.4 verify the conversion relationships for: (a) acceleration, (b) density. (c) pressure. and (d) volume f1owrate. Use the basic conversion relationships: 1 m = 3.2808 ft; 1 N = 0.22481 lb; and 1 kg = 0.068521 slug.

(a)

Thus) m""/+ipllj tt/ .J.t / .5 J.. (b)

I ~ ~ = (I ~3 ~

1111

""

-

I

040

. 1

')

x /0- 3

N

'2. () g r i. I D

-.2.

"='

Thu5) m/,.{lfip/~

N/rrn l

(3. ZFO~)3

-f1:: 3

J

/. qLfo E-3

~J1t/fri.

to

l (3.IlfOg) ft l J (M1.

2.

1.

Ik

f.t1b~

;;'.Ogq

E-l fo ~~n()fYt

/ h / f.t :L,

1::-0

7

3

==

T h US)

+(/

h,!j

tn1 2.

/'I't1 ?

1m,3

S l u ~~ f-t3

(I !:!. ) (O,2.2lfgl ~)f

I Ji ::

(d) /

T;

\ (

Th ~S.i m ul.f.i pJ'1 ~J/tt113 -1:0 S /u~/.ft 3. (C)

slugs) [

(0. oft> f/5:L/

(I ~) [cg, 1.KOS/~:l= rn f.,( I t

ifl':J

3

1»1 /5

b~

ft 3/s.

------------~~-

--------

/-/5

35". 3/

fr'

3. 531 E+ I -1:.0

rlOl1Vfyt

/.2..0

J

1.20 Water flows from a large drainage pipe at a rate of 3 1200 gal/min. What is this volume rate of flow in (a) m /s. (b) 3 liters/min. and (c) ft /s?

( ()...)

f./owrat e =

757 ;