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1、03IntegralRelationsforaControlVolume03-2IntroductionPrevioustopicsdealtwithfluidstaticsonly.Fromthistopicon,wewilldealwithfluidsinmotion–FluidDynamics.Threeapproacheswillbediscussedinthiscourse.ControlVolumeorIntegralAnalysis:Alargescaleanalysisfocusingontheoverallfea
2、turesofaflow.(ThisTopic)InfinitesimalorDifferentialAnalysis:Asmallscaleanalysisinvolvingapplicationsofdifferentialequationsoffluidmotiontoanyandeverypointoftheflowfield.DifferentialAnalysisExperimentalorDimensionalAnalysis.Thisapproachismoreaccurate.However,formosteng
3、ineeringproblems,itisdifficult,ifnotimpossible,tosolvethesedifferentialequationsaccurately.03-3OverviewofThisTopicItemsdiscussedinthisTopicA.Flowclassification,descriptionandvisualization.AB.ControlVolumeandReynoldsTransportTheoremBC.ConservationofMassCF.BernoulliEqua
4、tionFNoticeslideIDattheURcornerD.ConservationofLinearMomentumDE.ConservationofEnergy.E03-4Eulerian&LagrangianDescription:EulerianEuleriandescriptionoffluidflowbasically“observe”fluidpassbyapointoranentireregion.Thisdescriptionfocusesonthepressure,velocity,etc.ataspati
5、alpointorregion,ignoringthefateofeachindividualparticle.Moreappropriateforfluidmechanics,sinceformostproblems,weneedtoknowthefluidpropertiesatcertainlocationssuchasthegateofareservoir,thevolumeenclosingtheaircraftwings,etc.Fortheseapplicationswedon’tcareaboutthefateof
6、thefluidparticlesnotintheregionininterest.Wecandefinefieldvariableswhicharefunctionsofspaceandtime:Pressurefield,p=p(x,y,z,t)Velocityfield,V(x,y,z,t)=iu(x,y,z,t)+jv(x,y,z,t)+kw(x,y,z,t)Accelerationfield,a(x,y,z,t)=iax(x,y,z,t)+jay(x,y,z,t)+kaz(x,y,z,t)These(andother)f
7、ieldvariablesdefinetheflowfield.NamedafterSwissmathematicianLeonhardEuler(1707-1783).A03-5Eulerian&LagrangianDescription:LagrangianLagrangiandescriptionoffluidflowtracksthepositionandvelocityofindividualparticles.Moreappropriateforsolidmechanics,sinceweneedtoknowthesa
8、fetyofeachindividualmaterialparticle.Difficultandnotpracticaltouseformostfluidproblems.Formostfluidproblems,wedon’tcareabout
