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1、7708d_c05_204-2977/23/019:56AMPage204Ajetofwaterinjectedintostationarywater:Uponemergingfromtheslitattheleft,thejetoffluidlosessomeofitsmomentumtothesurroundingfluid.Thiscausesthejettoslowdownanditswidthtoincrease(airbubblesinwater).(PhotographcourtesyofONERA,France.)7708d_
2、c05_204-2977/23/019:56AMPage2055FiniteControlVolumeAnalysisManypracticalproblemsinfluidmechanicsrequireanalysisofthebehaviorofthecontentsofafiniteregioninspace1acontrolvolume2.Forexample,wemaybeaskedtocalculatetheanchoringforcerequiredtoholdajetengineinplaceduringatest.Or,w
3、ecouldbecalledontodeterminetheamountoftimetoallowforcompletefillingofalargestoragetank.AnestimateofhowmuchpoweritwouldtaketomovewaterfromonelocationtoanotherataManyfluidme-higherelevationandseveralmilesawaymaybesought.Asyouwilllearnbystudyingthechanicsproblemsmaterialinthis
4、chapter,theseandmanyotherimportantquestionscanbereadilyansweredcanbesolvedbyus-withfinitecontrolvolumeanalyses.Thebasesofthisanalysismethodaresomefundamen-ingcontrolvolumetalprinciplesofphysics,namely,conservationofmass,Newton’ssecondlawofmotion,andanalysis.thefirstandsecon
5、d1lawsofthermodynamics.Thus,asonemightexpect,theresultanttech-niquesarepowerfulandapplicabletoawidevarietyoffluidmechanicalcircumstancesthatrequireengineeringjudgment.Furthermore,thefinitecontrolvolumeformulasareeasytointerpretphysicallyandthusarenotdifficulttouse.Thecontro
6、lvolumeformulasarederivedfromtheequationsrepresentingbasiclawsappliedtoacollectionofmass1asystem2.Thesystemstatementsareprobablyfamiliartoyoupresently.However,influidmechanics,thecontrolvolumeorEulerianviewisgener-allylesscomplicatedand,therefore,moreconvenienttousethanthes
7、ystemorLagrangianview.Theconceptofacontrolvolumeandsystemoccupyingthesameregionofspaceataninstant1coincidentcondition2anduseoftheReynoldstransporttheorem1Eqs.4.19and4.232arekeyelementsinthederivationofthecontrolvolumeequations.Integralsareusedthroughoutthechapterforgenerali
8、ty.Volumeintegralscanaccom-modatespatialvariationsofthematerialpropertiesofthecont
