流体力学Chapter7DimensionalAnalysis

1、234),(VDfp567VDVpD28000212432TLF)FT)(TFL()L/F(LVpD0002124TLF)TFL()L)(LT)(TFL(VDQWhhQPPvhhhhhhWWWnetidealssssPTnet)()()()()(41212134211011)u,.,u,u(fuk3210)u,.,u,u,u(gk321120)u,.,u,u,u(gk3210), , , ,(or), , , ,(rk321rk3211314234/3163215or2151617)V,D( fp1812243LTVTFLTFLLDFLp19202122cba1VDp1c , 2b, 1a0c

2、2b:T0c4ba3:L0c1:FTLF)TFL()LT()L)(FL(000c24b1a321VDpcba2VD1c , 1b, 1a0c2b1:T0c4ba2:L0c1:FTLF)TFL()LT()L)(TFL(000c24b1a2DV224000000200000021TLMTLFDVTLMTLFVDp2425DVVDp2), , , ,(rk32126VDVDp2VD22728),(VhwfD13112LTVMLTMLLhLwMLTD29301, 2, 202:031:01:)()()(0003121cbabTcbaLcMTLMMLLTLMLTVDwcbacba221VwD0, 0,

3、10:031:0:)()()(000312cbabTcbaLcMTLMMLLTLLVhwcbacbawh2311c , 1b, 1a0b1:T0c3ba1:L0c1:MTLM)ML()LT()L)(TML(Vw000c3b1a11cba3wV332wVwhVwD,2233343536373839E, d, f ,Df212223TMLE,FLETML,FLLdLhLDL40DE,Dd,DhDDE,Dd,Dh,D432144332211ba4ba3ba2ba1EDdDhDD4142VDVDp12VDVDp22)V,D( fpSelecting D,V, and as repeating vari

4、ables: Selecting D,V, and as repeating variables: 43VDVDp12VDVDp2244321,2223211,b3a22All are correct45VDpVDVDp22VDVDp22VDVDp12Selecting D,V, and as repeating variables: 46),(VDfp12243LTVTFLTFLLDELp47pFcancelsTLTFLFLp-224-3TcancelsL1LTTLVp1221148 LcancelsLLLDVp021 21DVp 00014222TLFLLTTFLTFLVDVDVDp249

5、 54232505132222gLLVgLVFrgLVFr52*s*s2ssssdsdVVVdsdVVdtdVassVVV*s*smdsdVVVF*s*s2IgVgVdsdVVgVFFrF2*s*s2GI53VVRe545522VpVpEu562vrV21ppCa221vrV/ )pp(572VWe585960C1where C is a constant. The value of the constant must still be determined by experiment.6162),(VdfDrag 12FLTVTFLLDDragVDragDCDragCDVVDrag163)(

6、2164321,6566676869),.,(321nThis equation applies to any system that is governed by the same variables.70),.,(321nmmmm71nmnm33m22.m1172), , ,(n321), , , ,(nmm3m2m173nmnm33m22.m1174mmmm12m2mmmDVfDVF),V,D(fFprototype122VDfDVFprototypeelmodVDVDprototype22elmod22DVFDVFVDfDVF12275V, h,wfDprototype22Vw,hwV

7、wDmmmmmm2mm2mmwV,hwVwDVwwV,hwhwmmmmmmm2mm2m2mm2mm22DVVwwDVwDVwDVw,hwVwD22767735m/kg23. 1, sm/kg1079. 13water3waterm/kg998, sm/kg10178TFLTLTVLHLDT22411FL79VDVDDHVHDVDVDcbacbacba32180VD,DHVDmmmmmmmmmDV,DHVD81mmDHDHmmmmDVVDmm60.DDHHmmsmVDDVmmmm/79. 4. Hz0 .29.DDVVmmm822m21m1m2m121mVVmVm8384m22m11m11852

8、/1ppp2/1mmm)g(VFr)g(VFrppppmmmmVReVRe2/1pmpmVV86pmpmpmVV2/3pmpm2/1pmpm87888990V,i91mmiimmmimimmmmmmmmmVVVV/VVVVmmm1mm92VVm/VVVVmmm19321Vpm2mmpVVpmppIn general9495V,iModel of the National Bank of Commerce, San Antonio, Texas, for measurement of peak, rms, and mean pressure distributions. The model is

9、 located in a long-test-section, meteorological wind tunnel.9622DV21DCThe dependent pi terms would usually be expressed in the form of a drag coefficientmmiimmmimim97mmmmmmmmmmVVVVm2m2mm2m2mmm22DVVDV21DV21D/VVVVmmm98991/mVVm100101102The effect of Reynolds number on the drag coefficient, CD for a smooth sphere with CD = D/ AV2, where A is the projected area of sphere, d2/4.103mmmmmcccVcV1