Fluid Mechanics

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1、SJPOTrainingFluidMechanicsChikChengYaoJuly12,2014Contents1FluidStatics21.1PressureandPascal'sLaw......................21.1.1Denitions..........................21.1.2PressureinaFluid......................21.1.3Pascal'sLaw.........................31.2BuoyancyandArc

2、himedes'Principle................41.2.1Buoyancy...........................41.2.2Archimedes'Principle....................51.3SurfaceTension............................91.3.1Denition...........................91.3.2PhysicalInterpretation....................91.3.3Ma

3、thematicalTreatment..................92FluidDynamics112.1ContinuityEquation.........................112.1.1Denition...........................112.1.2Mathematicaltreatment...................112.2Bernoulli'sPrinciple.........................122.2.1Denition........

4、...................122.2.2Derivation...........................122.2.3PhysicalMeaning.......................1211FluidStatics1.1PressureandPascal'sLaw1.1.1Denitions1.A uidisdenedasasubstancethatcontinuallydeformsundershearstress.Therearemanykindsof uidswithdiere

5、ntproperties,butwewillmainlybestudyinginviscid(non-viscous),idealgasesandliquids.2.Pressureistheforceperunitareaappliedinadirectionperpendiculartoachosensurface.Usually,thissurfaceisarealsurfaceofanobject.But,inthecontextof uidmechanics,pressureatapointina uidrefe

6、rstothepressureexperiencedonanimaginarysurfaceplacedatthatpointwithinthe uid,thatmaynotactuallybepresentinreality.1.1.2PressureinaFluidWhenaliquidisplacedinacontainer,the uidatthebottomexperiencesahigherpressure,duetotheweightofthe uidaboveit.Fora uid(withnoextern

7、alforcesotherthangravity)ofconstantdensity,inarightcontainerwithcross-sectionalareaAand uidtoheighth,theweightWofthe uidisgivenbyW=ghA(1)AndhencepressurePisgivenby:WP==gh(2)AExample1.1.2.1.BloodpressureisusuallygiveninunitsmmHg,thepres-sureexertedbyacolumnofmer

8、curyonemillimetrehigh.GiventhatHg=13:6g=cm3,ndtheequivalentof1mmHginSIunits.21.1.3Pascal'sLawPascal'sLawstatesthatachangeinpressureatanypointinanenclo