流体力学Chapter5ControlVolumeAnalysis

1、23CSCVsysdAnVVdtVdDtDB=M and b =10dtdMsystemVddmM)system(V)system(Msystem 560dAnVVdtdtMdCSCVsystemCSCVdAnVVdtinoutmmRate of increaseOf mass in CVNet influx of mass70dAnVVdt0dAnVVdtCSCVCSCV0dAnVCSinoutmm8inoutAmmdAnVQmAdAnVVA90VdtCV0VdtCVinoutmminoutQQ10AVmVAm1112Flow is Steady2221111212CSVAVAmm0mmdA

2、nV0dAnVVdtCSCV2121VVSince A1=A2s /ft219.VTpTpV221121RTp132V14Flow is Steady 2/2012max2max102maxuVUuUArdrRruR0dAnVVdtCSCV021102211A2UArdruUAdAnVR212maxRr1uu15t/h 16airvolumewaterwaterwaterwatervolumeairairairCVmmVdtVdtdAnVVdt0CS0mVdtairForairvolumeairairair17)9 . 0)(/1000()/100min)(/34()9 . 0()9 . 0(

3、)5 . 0()5 . 1)(0.6(2322mftLftcmLAmQthmthAmAhmmmhVdtmVdtwaterForjwaterwaterjwatervolumewaterjwaterwaterwatervolumewaterwaterwaterwatermin/3.78cmAj18CVVWV0dAnWVdt. S .CCVdAnWVdtDtDM. S .CCVsys19systemsysBSsysDtPDVdVDtDFFF=VdVdmVP)system(V)system(Msystem20 VbCSCVsysdAnVVVdVtVdVDtDdAnVbVbdtDtDBCSCVsys21

4、FdAnVVVdVtCSCVContents of the coincidentcontrol volume22Determine the anchoring force needed to hold the vane stationary.23zCSCVxCSCVFdAnVwVdwtFdAnVuVdutNVAFNVAFFVAVAVFVAVVAVAzAxAzAxsin54.sin)cos1 (54.)cos1 (0sincos12112111121111121kwiuVzCSCVxCSCVFdAnVwVdwtFdAnVuVdutNVAFNVAFFVAVAVFVAVVAVAzAxAzAxsin5

5、4.sin)cos1 (54.)cos1 (0sincos12112111121111121kwiuVzCSCVxCSCVFdAnVwVdwtFdAnVuVdutNVAFNVAFFVAVAVFVAVVAVAzAxAzAxsin54.sin)cos1 (54.)cos1 (0sincos12112111121111121kwiuV242526dAwdAnVApWApWFdAnVwVdwt22w11nACSCV22w11n21A22w11n2211ApWApW)ww(mFApWApW)w(m)w)(m(mmm21s /kg599. 0.QAwmmm112127N0278. 0.gV)DDDD(h1

6、21gVWN981. 0)s /m81. 9)(kg1 . 0(gmWm6 .30.4/DQAQws /m98. 2.4/DQAQww212212ww2nn22222111N8 .77.)(.)s /kg599. 0(ApWApW)ww(mF22w11n21A 2829AxCSCVFdAnVuVdut2211AyCSCVApApFdAnVvVdvt0FAx302211Ay2211ApApF)m)(v()m)(v(2211Ay21ApApF)vv(m skgAvmmm/150.1121NApApvvmFAy6194.)(221121313222z11CS2221122z11CSCVApWRAp)

7、dAw()w()m)(w(ApWRApdAnVwVdwt212Rr1w2w342)/(12221022A2222122RwrdrwdAwwRrwwR112121221121221334AWARwppApWRApRwRwzz3334N83700.)uu(mAAFFApAp)uu(muAmuAmmFA)pp(A)pp()m)(u()m)(u()AA(pApFApdAnVuVdut122211thth22111222221111th2atm21atm1221121atm22th11CSCVs /kg204.uAmRTp1111113536hbuFbh21bH21RuuandhHForFbh21RbH

8、21hbuHbuFbh21RbH21dAnVu22f22x21f2x22221f2x2CSbH21RRbH21dAnVu2xx2CS37CVVWVCSCVsysdAnWVVdVtVdVDtDFdAnWVVdVtCSCVFdAnW)VW(Vd)VW(tCSCVCVCVContents of the coincidentcontrol volumedAnWbVbdtDtDBCSCVsys38.39.40.x2211xCSxR)m)(45cosW()m)(W(RdAnWW22221111AWmAWmwz22WzCSzWR)m)(45sinW(WRdAnWW.VVWWAWmAWm01212222111

9、141.xzzxwzxRRNRRRNWAWRNAWR122121121tan266.246.45sin101.2.)45cos1 (1wgAW42=+gz2Vu eWQVdeDtDorWQWWQQVdeDtD2sysinnetinnetsyssysin/netin/netsysoutinsysoutinsys43dAnVeVdetVdeDtD. S.CCVsys=+44CVCSinnetinnetcv)WQ(dAnVeVdetvolumecontrolcoincidentinnetinnetsysinnetinnet)WQ()WQ(45othershearnormalShaftWWWWWSha

10、ftWCSCSnnnormalnormaldAnVpdAnVVFWdAnVWCSshearCSinnetshaftinnetCScvdAnVpWQdAnVeVdet46in/Shaftin/netCS2CVWQdAnV)gz2Vpu (Vdet470VdetCVmgz2Vpu mgz2Vpu dAnVgz2Vpu in2out22CSinin2outout22CSmgz2Vpu mgz2Vpu dAnVgz2Vpu dAnVgz2Vpu 2CSUniformly distributionOnly one stream entering and leaving48innetshaftinneti

11、nout2in2outinoutinoutWQzzg2VVppu u mpu hin/netshaftin/netinout2in2outinoutWQzzg2VVhhm49innetinoutin2ininout2outoutqu u gz2Vpgz2Vpinnetinout2in2outinoutinoutQzzg2VVppu u mm m/Qqinnetinnetin2ininout2outoutz2Vpz2Vp0qu u innetinout500qu u innetinoutlossqu u innetinoutlossgz2Vpgz2Vpin2ininout2outoutDefining “useful or available energy”gz2Vp2Defining “loss of useful or available energy”51innetinoutinoutinoutinoutQzzgVVppuum222m )(2222innetinoutinininoutoutoutquugzVpgzVplossgzVpgzVp