ch01 solutionssa

7/24/2019 Ch01 SolutionsSA

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Chapter 1Introduction and Basic Concepts

Solutions Manual for

Essentials of Fluid Mechanics:Fundamentals and Applications

by Cimbala & engel

CHAPTER 1INTRODUCTION AND BASIC CONCEPTS

PROPRIETARY AND CONFIDENTIAL

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part!' No part o# this Manual (a! be reprou$e) ispla!e or istribute in an!#or( or b! an! (eans) ele$troni$ or other*ise) *ithout the prior *ritten per(issiono# M$+ra*,-ill'

PROPRIETARY MATERIAL. % &'' The McGraw-Hill Companies, Inc. imite istri!ution permitte only toteachers an eucators for course preparation. If you are a stuent usin" this Manual, you are usin" it without permission.

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Introduction, Classification, and System

1,1CSolution +e are to efine internal, eternal, an open-channel flows.

Analysis External flowis the #lo* o# an unboune #lui over a sur#a$esuch as a plate, a wire, or a pipe. The flow

in a pipe or uct is internal flowif the #lui is $o(pletel! boune b! soli sur#a$es. The flow of liuis in a pipe iscalle open-channel flowif the pipe is partiall! #ille *ith the li.ui an there is a #ree sur#a$e, such as the flow ofwater in riers an irri"ation itches.

Discussion /s we shall see in later chapters, there ifferent approimations are use in the analysis of flui flows!ase on their classification.

1,/CSolution +e are to efine incompressi!le an compressi!le flow, an iscuss flui compressi!ility.

Analysis / flui flow urin" which the ensit! o# the #lui re(ains nearl! $onstantis calle incompressible flow./ flow in which ensit! varies signi#i$antl!is calle compressible flow. / flui whose ensity is practically inepenent

of pressure (such as a liui) is commonly referre to as an incompressi!le flui, althou"h it is more proper to refer toincompressi!leflow. The flow of compressi!le flui (such as air) oes not necessarily nee to !e treate as compressi!lesince the ensity of a compressi!le flui may still remain nearly constant urin" flow 0 especially flow at low spees.

Discussion It turns out that the Mach num!er is the critical parameter to etermine whether the flow of a "as can !eapproimate as an incompressi!le flow. If Ma is less than a!out '.1, the incompressi!le approimation yiels results thatare in error !y less than a couple percent.

1,0CSolution +e are to efine the no-slip conition an its cause.

Analysis / #lui in ire$t $onta$t *ith a soli sur#a$e sti$&s to the sur#a$e an there is no slip. This is 2nown as

the no-slip condition, an it is ue to the viscosityof the flui.

Discussion There is no such thin" as an inisci flui, since all fluis hae iscosity.

1,CSolution +e are to efine force flow an iscuss the ifference !etween force an natural flow. +e are also toiscuss whether win-rien flows are force or natural.

Analysis Inforced flow, the flui is force to flow oer a surface or in a tu!e b! external(eanssuch as a pump ora fan. In natural flow, any flui motion is cause !y natural means such as the !uoyancy effect that manifests itself as therise of the warmer flui an the fall of the cooler flui. The #lo* $ause b! *ins is natural #lo* #or the earth) but it is#or$e #lo* #or boies sub2e$te to the *inssince for the !oy it ma2es no ifference whether the air motion is cause!y a fan or !y the wins.

Discussion /s seen here, the classification of force s. natural flow may epen on your frame of reference.


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Chapter 1Introduction and Basic Concepts1,3CSolution +e are to efine a !ounary layer, an iscuss its cause.

Analysis +hen a flui stream encounters a soli surface that is at rest, the flui elocity assumes a alue of 3ero atthat surface. The elocity then aries from 3ero at the surface to the freestream alue sufficiently far from the surface. Theregion o# #lo* in *hi$h the velo$it! graients are signi#i$ant an #ri$tional e##e$ts are i(portant is calle theboundary layer. The eelopment of a !ounary layer is cause !y the no-slip condition.

Discussion /s we shall see later, flow within a !ounary layer is rotational(iniiual flui particles rotate), while

that outsie the !ounary layer is typically irrotational(iniiual flui particles moe, !ut o not rotate).

1,4CSolution +e are to iscuss the ifferences !etween classical an statistical approaches.

Analysis The classical approach is a macroscopic approa$h, !ase on eperiments or analysis of the "ross!ehaior of a flui, without 2nowle"e of iniiual molecules, whereas the statistical approach i s a microscopicapproa$h!ase on the aera"e !ehaior of lar"e "roups of iniiual molecules.

Discussion The classical approach is easier an much more common in flui flow analysis.

1,5CSolution +e are to efine a steay-flow process.

Analysis / process is sai to !e steadyif it inoles no $hanges *ith ti(eanywhere within the system or at thesystem !ounaries.

Discussion The opposite of steay flow is unsteady flow, which inoles chan"es with time.

1,6CSolution +e are to efine stress, normal stress, shear stress, an pressure.

Analysis Stressis efine as #or$e per unit area, an is etermine !y iiin" the force !y the area upon which it

acts. The nor(al $o(ponent o# a #or$e a$ting on a sur#a$e per unit areais calle the normal stress, an the tangential$o(ponent o# a #or$e a$ting on a sur#a$e per unit area is calleshear stress. In a flui at rest, the normal stress iscallepressure.

Discussion 4luis in motion may hae aitional normal stresses, !ut when a flui is at rest, the only normal stress isthe pressure.

1,7CSolution +e are to efine system, surrounin"s, an !ounary.

Analysis /system is efine as a .uantit! o# (atter or a region in spa$e $hosen #or stu!. The mass or regionoutsie the s!ste( is calle the surroundings' The real or ima"inary sur#a$e that separates the s!ste( #ro( its

surrouningsis calle the boundary.

Discussion 5ome authors li2e to efine closed systems an open systems, while others use the notation system tomean a close system an control olume to mean an open system. This has !een a source of confusion for stuents formany years. 65ee the net uestion for further iscussion a!out this.7


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Chapter 1Introduction and Basic Concepts1,18CSolution +e are to iscuss when a system is consiere close or open.

Analysis 5ystems may !e consiere to !e closed or open, epenin" on whether a fie mass or a olume in spaceis chosen for stuy. / closed system (also 2nown as a control massor simply a system) consists of a #i%e a(ount o#(ass) an no (ass $an $ross its bounar!. /n open system) or a control volume,is a properl! sele$te region in spa$e.

Discussion In thermoynamics, it is more common to use the terms open system an closed system, !ut in fluimechanics, it is more common to use the terms systeman control volumeto mean the same thin"s, respectiely.

Mass, Force, and Units

1,11CSolution +e are to iscuss the ifference !etween poun-mass an poun-force.

Analysis Pound-mass l!m is the (ass unit in English s!ste( whereas pound-force l!f is the #or$e unit in the

English s!ste(. 8ne poun-force is the force reuire to accelerate a mass of 1&.*9: l!m !y * ft;s&

. In other wors, thewei"ht of a *-l!m mass at sea leel on earth is * l!f.

Discussion It is notproper to say that one l!m is eual to one l!f since the two units hae ifferent imensions.

1,1/CSolution +e are to iscuss the ifference !etween 2"-mass an 2"-force.

Analysis The unit kilogram(2") is the (ass unit in the 9I s!ste(, an it is sometimes calle kg-mass, whereas kg-force(2"f) is a #or$e unit. 8ne 2"-force is the force reuire to accelerate a *-2" mass !y


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Chapter 1Introduction and Basic Concepts1,1Solution / plastic tan2 is fille with water. The wei"ht of the com!ine system is to !e etermine.

Assumptions The ensity of water is constant throu"hout.

Properties The ensity of water is "ien to !e @ *''' 2";m1.

Analysis The mass of the water in the tan2 an the total mass are

mw=V=(*''' 2";m1)('.& m1) @ &'' 2"

mtotal@ mw+ mtank=&'' A 1 @ &'1 2"Thus,

&

&

* =(&'1 2")(


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Chapter 1Introduction and Basic Concepts1,15ESolution /n astronaut ta2es his scales with him to the moon. It is to !e etermine how much he wei"hs on thesprin" an !eam scales on the moon.

Analysis(a) / sprin" scale measures wei"ht, which is the local "raitational force applie on a !oy$

lbf#%&%=

==

&

&

ft;sl!m1&.&

l!f*)ft;sl!m)(D.:(*D'mg

(b) / !eam scale compares masses an thus is not affecte !y the ariations in "raitational acceleration. The !eam scalereas what it reas on earth,

lbf1%0=

Discussion The !eam scale may !e mar2e in units of wei"ht (l!f), !ut it really compares mass, not wei"ht. +hichscale woul you consier to !e more accurateE

1,16Solution The acceleration of an aircraft is "ien in g>s. The net upwar force actin" on a man in the aircraft is to !e

etermine.

Analysis 4rom =ewtonFs secon law, the applie force is

&

&

* =B " (


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1,/8

Solution The preious pro!lem is recalculate usin" 5. The entire 5 solution is to !e printe out, incluin"the numerical results with proper units.

Analysis The 5E)uations winow is printe !elow, followe !y the Solutionwinow.

W=m*g"[N]"m=5"[kg]"g=9.79"[m/s^2]""The force balance on the rock !els the net force act!ng on the rock as"#$net = #$%& ' #$o(n"[N]"#$%&=)5"[N]"#$o(n=W"[N]""The accelerat!on of the rock !s eterm!ne from Ne(ton+s secon la(."#$net=a*m"To ,%n the &rogram- &ress #2 or cl!ck on the calc%lator !con from the alc%late men%"

SOLUTION

ar!ables !n 0a!n

a=2.2) [m/s^2]#$o(n=1.95 [N]#$net=)).) [N]#$%&=)5 [N]g=9.79 [m/s^2]m=5 [kg]

W=1.95 [N]

The final results are W< 7'8 Nan a< /8'/ (=s/, to three si"nificant i"its, which a"ree with the results of the preiouspro!lem.

Discussion Items in uotation mar2s in the 5 uation winow are comments. Jnits are in suare !rac2ets.

1,/1

Solution Graitational accelerationg an thus the wei"ht of !oies ecreases with increasin" eleation. The percentreuction in the wei"ht of an airplane cruisin" at *1,''' m is to !e etermine.

Properties The "raitational accelerationg is


8/13

Chapter 1Introduction and Basic Concepts1,//

Solution +e are to estimate the wor2 an power reuire to lift a crate.

Assumptions 1The ertical spee of the crate is constant.

Properties The "raitational constant is ta2en asg@


9/13

Chapter 1Introduction and Basic Concepts1,/E

Solution +e are to estimate the rate of heat transfer into a room an the cost of runnin" an air conitioner for onehour.

Assumptions 1The rate of heat transfer is constant. /The inoor an outoor temperatures o not chan"e si"nificantlyurin" the hour of operation.

Analysis(a) In one hour, the air conitioner supplies D,''' #tu of coolin", !ut runs only B' of the time. 5ince the

inoor an outoor temperatures remain constant urin" the hour of operation, the aera"e rate of heat transfer into theroom is the same as the aera"e rate of coolin" supplie !y the air conitioner. Thus,

( )'.B' D''' #tu * 2+* h 1:*&.*: #tu;h

* = = =

0)888 Atu=h 8'657 &@3

(b) ner"y efficiency ratio is efine as the amount of heat remoe from the coole space in #tu for * +h(watt-hour) of electricity consume. Thus, for eery +h of electricity, this particular air conitioner remoes


10/13

Chapter 1Introduction and Basic Concepts1,/4

Solution +e are to calculate the useful power eliere !y an airplane propeller.

Assumptions 1The airplane flies at constant altitue an constant spee. /+in is not a factor in the calculations.

Analysis /t steay hori3ontal fli"ht, the airplane>s ra" is !alance !y the propeller>s thrust. ner"y is force timesistance, an power is ener"y per unit time. Thus, !y imensional reasonin", the power supplie !y the propeller musteual thrust times elocity,

( ) ( )thrust * 2+ *.1:* hp*D'' = DD.' m;s*''' = m;s * 2+

# + = = = = 6/'3 &@ 111 hp3

where we "ie our final answers to 1 si"nificant i"its.

Discussion +e use two unity conersion ratios in the a!oe calculation. The actual shaft power supplie !y theairplane>s en"ine will of course !e lar"er than that calculate a!oe ue to inefficiencies in the propeller.

1,/5

Solution +e are to calculate lift prouce !y an airplane>s win"s.

Assumptions 1The airplane flies at constant altitue an constant spee. /+in is not a factor in the calculations.

Analysis /t steay hori3ontal fli"ht, the airplane>s wei"ht is !alance !y the lift prouce !y the win"s. Thus, thenet lift force must eual the wei"ht, or#@ 138 lb#. +e use unity conersion ratios to conert to newtons$

( )* =

*:D' l!f'.&&:* l!f

,#

= =

4)38 N

where we "ie our final answers to 1 si"nificant i"its.

Discussion The answer is ali at any spee, since lift must !alance wei"ht in orer to sustain strai"ht, hori3ontalfli"ht. /s the fuel is consume, the oerall wei"ht of the aircraft will ecrease, an hence the lift reuirement will alsoecrease. If the pilot oes not a?ust, the airplane will clim! slowly in altitue.

1,/6

Solution +e are to etermine a positie real root of the followin" euation usin" 5$ &x10 *'x'.D0 1x @ -1.

Analysis Jsin" 5 software, copy the followin" lines an paste on a !lan2 5 screen to erify the solution$

2*4^')*4^.5'*4 = '

&nswer$ x< /'840 (usin" an initial "uess ofx @ &)

Discussion To o!tain the solution in 5, clic2 on the icon that loo2s li2e a calculator, or Calculate-5ole.


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Chapter 1Introduction and Basic Concepts1,/7

Solution +e are to sole a system of & euations an & un2nowns usin" 5.


4^'^2=7.75*4*6=.5

&nswers$ x< /'8,y< 8'38.


1,08

Solution +e are to sole a system of 1 euations with 1 un2nowns usin" 5.


2*4'6=5*4^262*=624*62*=

&nswers$x< 1'11) y< 8'6137) z< 0'303'


1,01

Solution +e are to sole a system of 1 euations with 1 un2nowns usin" 5.


4^2*'=)4'*^.564*='246'=2

&nswers$x< 1) y< 1) z< 8'



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)e*ie+ roblems

1,0/Solution The "raitational acceleration chan"es with altitue. /ccountin" for this ariation, the wei"hts of a !oy

at ifferent locations are to !e etermine.

Analysis The wei"ht of an '-2" man at arious locations is o!taine !y su!stitutin" the altitue "(alues in m)into the relation

==

&

&B

m;s2"*

=*)m;s*'1.1&2")(


13/13

Chapter 1Introduction and Basic Concepts1,0Solution The thrust eelope !y the ?et en"ine of a #oein" 999 is "ien to !eD,''' pouns. This thrust is to !e epresse in = an 2"f.

Analysis =otin" that * l!f @ :.:: = an * 2"f @

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