5-1 Conservation of massMass flowrate m : the amount of mass flowingthrough a cross section per unit timeAcrosssmallareaOm=pV,dASm(kg/s)pV,dA.mAcross entire areaAControlsurfacedAUse Vavg, then(kg/s)mDVavgA
5-1 Conservation of mass • Mass flow rate : the amount of mass flowing through a cross section per unit time. 6 Across small area Across entire area Use Vavg, then
5-1 Conservation of mass· Volume flow ratee y : the volume of fluid flowingthrough a cross section per unit time(m/s)7Vn dA.= VavgA,= VAcVavgAverageVolumeflowratevelocityV=VavgAcCrosssectionRelations of m andVm = pV=
5-1 Conservation of mass • Volume flow rate : the volume of fluid flowing through a cross section per unit time. • Relations of and 7 Average velocity Volume flow rate
5-1 Conservation of mass Conservation of mass principle: the netmass transfer to or from a control volumeduring a time intervalis egual to the netchange in the total mass within the controlvolume.Total mass enteringTotal massleavingNetchangein massthe CV during tthe CV during AtwithintheCVduringAtmin-mout=dmcv/dtmin- mout= AmcyIn rate formMass balance
5-1 Conservation of mass • Conservation of mass principle: the net mass transfer to or from a control volume during a time interval is equal to the net change in the total mass within the control volume. 8 Mass balance In rate form
mout=dmcy/dtminChange in CV:EFordifferential volume:1dm0dm=pdvdAControlvolume(CV)Total mass within the CV :Controlsurface(CS)dymeRate of change of mass in CV:dmeydpdvdtdt'Cv
• Change in CV: • For differential volume: • Total mass within the CV : • Rate of change of mass in CV: 9
=dmcv/dtmoutmiMass flowin or out of CV:VEFordifferentialmassflow rate:ndmSm=pVndAVn=Vcose=V.n0dAControlSm=pV,dA=p(Vcos0)dA=p(V.n)dAvolume(CV)Controlsurface(CS)Netmassflowrate(overtheentirecontrosurface) :o(V.n)dASmpV,dAmnetCS'CsCsmoutmin10
• Mass flow in or out of CV: • For differential mass flow rate: • Net mass flow rate (over the entire control surface) : 10