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    Chapter 3Pressure and Fluid Statics

    Solutions Manual for

    Essentials of Fluid Mechanics:

    Fundamentals and Applications

    by Cimbala & engel

    CHAPTER 3PRESSURE AND FLUID STATICS

    PROPRIETARY AND CONFIDENTIAL

    This Manual is the proprietary property of The McGraw-Hill Companies, Inc.(McGraw-Hill) an protecte !y copyri"ht an other state an feeral laws. #yopenin" an usin" this Manual the user a"rees to the followin" restrictions, an if therecipient oes not a"ree to these restrictions, the Manual shoul !e promptly returneunopene to McGraw-Hill$ This Manual is being provie onl! to authori"epro#essors an instru$tors #or use in preparing #or the $lasses using the a##iliatete%tboo&' No other use or istribution o# this Manual is per(itte' This Manual

    (a! not be sol an (a! not be istribute to or use b! an! stuent or other thirpart!' 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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    Chapter 3Pressure and Fluid Statics

    Pressure, Manometer, and Barometer

    3,.CSolution e are to iscuss the ifference !etween "a"e pressure an a!solute pressure.

    Analysis The pressure relative to the at(ospheri$ pressureis calle thegage pressure, an the pressure relativeto an absolute va$uu(is calle absolute pressure.

    Discussion Most pressure "a"es (lie your !icycle tire "a"e) rea relatie to atmospheric pressure, an therefore reathe "a"e pressure.

    3,/CSolution e are to e/plain nose !leein" an shortness of !reath at hi"h eleation.

    Analysis 0tmospheric air pressure which is the e/ternal pressure e/erte on the sin ecreases with increasin"eleation. Therefore, the pressure is lo*er at higher elevations' As a result) the i##eren$e bet*een the bloo pressurein the veins an the air pressure outsie in$reases. This pressure i(balan$e (a! $ause so(e thin,*alle veins su$has the ones in the nose to burst) $ausing bleeing. The shortness of !reath is cause !y the lower air ensity at hi"hereleations, an thus lower amount of o/y"en per unit olume.

    Discussion 1eople who clim! hi"h mountains lie Mt. 2erest suffer other physical pro!lems ue to the low pressure.

    3,3CSolution e are to e/amine a claim a!out a!solute pressure.

    Analysis No) the absolute pressure in a li0ui o# $onstant ensit! oes not ouble *hen the epth is ouble . Itis thegage pressure that ou!les when the epth is ou!le.

    Discussion This is analo"ous to temperature scales 3 when performin" analysis usin" somethin" lie the ieal "aslaw, you mustuse a!solute temperature (4), not relatie temperature (oC), or you will run into the same in of pro!lem.

    3,1CSolution e are to compare the pressure on the surfaces of a cu!e.

    Analysis 5ince pressure increases with epth, the pressure on the botto( #a$e o# the $ube is higher than that onthe top'The pressure varies linearl! along the sie #a$es. Howeer, if the len"ths of the sies of the tiny cu!e suspenein water !y a strin" are ery small, the ma"nitues of the pressures on all sies of the cu!e are nearly the same.

    Discussion In the limit of an infinitesimal cu!e, we hae a flui particle, with pressure Pefine at a point.

    3,2CSolution e are to efine 1ascal6s law an "ie an e/ample.

    Analysis Pascals lawstates that the pressure applie to a $on#ine #lui in$reases the pressure throughout b!the sa(e a(ount. This is a conse7uence of the pressure in a flui remainin" constant in the hori8ontal irection. 0ne/ample of 1ascal6s principle is the operation of the hyraulic car 9ac.

    Discussion The a!oe iscussion applies to fluis at rest (hyrostatics). hen fluis are in motion, 1ascal6s principleoes not necessarily apply. Howeer, as we shall see in later chapters, the ifferential e7uations of incompressi!le fluiflow contain only pressuregradients, an thus an increase in pressure in the whole systemoes notaffect flui motion.

    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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    Chapter 3Pressure and Fluid Statics3,CSolution e are to compare the olume an mass flow rates of two fans at ifferent eleations.

    Analysis The ensity of air at sea leel is hi"her than the ensity of air on top of a hi"h mountain. Therefore, theolume flow rates of the two fans runnin" at ientical spees will !e the same, !ut the mass flow rate of the fan at sealeel will !e hi"her.

    Discussion In reality, the fan !laes on the hi"h mountain woul e/perience less frictional ra", an hence the fanmotor woul not hae as much resistance 3 the rotational spee of the fan on the mountain woul !e sli"htly hi"her than

    that at sea leel.

    3,4Solution The pressure in a acuum cham!er is measure !y a acuum "a"e. Thea!solute pressure in the cham!er is to !e etermine.

    Analysis The a!solute pressure in the cham!er is etermine from

    kPa68=== &:;&acatma!s PPP

    Discussion e must remem!er that acuum pressure is the ne"atie of "a"e pressure 3 hence the ne"atie si"n.

    3,5ESolution The pressure in a tan is measure with a manometer !y measurin" the ifferential hei"ht of themanometer flui. The a!solute pressure in the tan is to !e etermine for two cases$ the manometer arm with the (a)hi"her an (b) lower flui leel !ein" attache to the tan.

    Assumptions The flui in the manometer is incompressi!le.

    Properties The specific "raity of the flui is "ien to !e 5G < +.&=. The ensity of water at *&> is ?&.: l!m@ft*.

    Analysis The ensity of the flui is o!taine !y multiplyin" its specific "raity !y the ensity of water,

    &

    * *5G (+.&=)(?&.: l!m@ft ) A ' l!m@ftH O . = = =

    The pressure ifference corresponin" to a ifferential hei"ht of & in !etween the two arms of the manometer is

    in+::

    ft+

    ft@sl!m*&.+A:

    l!f+ft))(&@+&ft@s)(*&.+A:l!m@ft(A

    &

    &

    &

    &*

    == ghP

    Then the a!solute pressures in the tan for the two cases !ecome$

    (a) The flui leel in the arm attache to the tan is hi"her (acuum)$

    a!s atm ac +& A + &? ++ :: psiaP P P . . .= = = 11.4 sia

    (b) The flui leel in the arm attache to the tan is lower$

    a!s "a"e atm +& A + &? +* ;? psiaP P P . . .= + = + = 14.! siaDiscussion The final results are reporte to three si"nificant i"its.Bote that we can etermine whether the pressure in a tan is a!oe or!elow atmospheric pressure !y simply o!serin" the sie of the manometerarm with the hi"her flui leel.

    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.

    *-*

    Pabs

    Patm

    = 92 kPa

    24 kPa

    0ir

    5G< +.&=

    Patm< +&.A psia

    & in

    Patm

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    Chapter 3Pressure and Fluid Statics3,6Solution The pressure in a pressuri8e water tan is measure !y a multi-flui manometer. The "a"e pressure of airin the tan is to !e etermine.

    Assumptions The air pressure in the tan is uniform (i.e., its ariation with eleation is ne"li"i!le ue to its lowensity), an thus we can etermine the pressure at the air-water interface.

    Properties The ensities of mercury, water, an oil are "ien to !e +*,?'', +''', an =' "@m*, respectiely.

    Analysis 5tartin" with the pressure at point + at the air-water interface, an moin" alon" the tu!e !y ain" (as we

    "o own) or su!tractin" (as we "o up) the gh terms until we reach point &, an settin" the result e7ual to Patmsince thetu!e is open to the atmosphere "ies

    atmPghghghP =++ *mercury&oil+water+

    5olin" forP+,

    *mercury&oil+wateratm+ ghghghPP +=

    or,

    )( &oil+water*mercuryatm+ hhhgPP =

    Botin" thatP+,"a"e

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    Chapter 3Pressure and Fluid Statics3,..Solution The "a"e pressure in a li7ui at a certain epth is "ien. The "a"e pressure in the same li7ui at a ifferentepth is to !e etermine.

    Assumptions The ariation of the ensity of the li7ui with epth is ne"li"i!le.

    Analysis The "a"e pressure at two ifferent epths of a li7ui can !e e/presse as ++ ghP = an && ghP = .Tain" their ratio,

    +

    &

    +

    &

    +

    &

    h

    h

    gh

    gh

    P

    P

    ==

    5olin" forP&an su!stitutin" "ies

    &Pa../=== 1a)&(m*

    m+&+

    +

    && P

    h

    hP

    Discussion Bote that the "a"e pressure in a "ien flui is proportional to epth.

    3,./Solution The a!solute pressure in water at a specifie epth is "ien. The local atmospheric pressure an thea!solute pressure at the same epth in a ifferent li7ui are to !e etermine.

    Assumptions The li7ui an water are incompressi!le.

    Properties The specific "raity of the flui is "ien to !e 5G < '.=. e tae the ensity of water to !e +''' "@m *.Then ensity of the li7ui is o!taine !y multiplyin" its specific "raity !y the ensity of water,

    ** "@m=')"@m'('.=)(+''5G&

    === OH

    Analysis (a) 4nowin" the a!solute pressure, the atmospheric pressure can !e etermine from

    * &

    &