Chapter12FluidFlow

12-1TheBasicEquationofSteady-Flow12-1-1TheConversationofMassA：Crosssectionareaofflowductc：Velocityoffluidv：SpecificvolumeoffluidDifferentialform:

12-1-2TheConversationofEnergyDifferentialform:

12-1-3ProcessEquationUsuallythefluidflowstoofastinaducttoexchangeheatwithitssurroundings,soitundergoesanadiabaticprocess,then:pvk=constDifferentialform:

12-1-4VelocityofSoundandMachNumberFromThenTheVelocityofSoundisdenotedby

MachNumberMaisdefinedas：

ErnstMachwas?bornonFeb.18,1838,d.?Vaterstetten.HefoundanexperimentalprooffortheDopplerEffect(Christian?Doppler)andbyinspectionoffastmovingprojectsproposedtheMachsprinciple.TheMachNumbernamedafterhimdescribestherelationofabodysvelocitytosonicspeed.Hisattitudewascharacterizedbyempiricalthinkingbasedonscientificfindings.OneofhisstrictestopponentsandcriticswasM.Planck.AfterretiringfromtheUniversityin1901hewasappointedtotheupperchamberoftheAustrianParliament,apostheheldfor12years.Hediedin1916

12-2TheFluidFlowinDuctDuringthefluidflowinaduct,thepropertiesoffluidchangesalongthestreamline.Inmostsituationsthiscanbetreatedasaone-dimensionalflow12-2-1ThePressureandVelocityFromconservationofenergydh=-cdcdu+d(pv)=-cdcdu+pdv+vdp=-cdc

Fromthefirstlawofthermodynamics:δq=du+pdv=0Then:du+pdv+vdp=-cdcvdp=-cdc-vdp=cdcToincreasethevelocityoffluid(dc0),thepressuremustbedecreased.ThiskindofductiscalledNozzleOrtodecreasethevelocity(dc0)offluidtoobtainahighpressureinaductflow.Thiskindofductiscalleddiffuser

12-2-2VelocityandTheCrossSectionAreaofDuc