作业-流体力学张鸣远

ν×ω()2212inininoutinDMFVFADVADLDDµδωπδ=====−()3220.510.8822inininoutininoutinDDMDLDDDLNmDDωµπωρνπ=−==•−µ.δ()2cyyuδδ−=yumax=4m/s0dudy=()2002ducyyydyδδδ=⇒−−=⇒=2yδ=max2224/16/cumscmsδδδδ⎛⎞−⎜⎟⎝⎠==⇒=()22ducydyτµµδδ==−160,0.0481920.004cyPaτµδ===×=16,0.0481920.004cyPaδτµδ−−===×=−G=190Nd=152mmD=152.02mmL=200mmµ0.62Pa.sU=39mm/s()/2duUFAdLdyDdµµπ==−2UGdLDdµπ=−µ()()190152.0215232.1/220.623.141520.2GDdUmmsdLµπ−−===××××()()190152.021520.51223.141520.20.039GDdPasdLUµπ−−===××××i1.4κ=1.461112221213403.236100.2VpVpVppPaVκκκ⎛⎞⎛⎞=⇒==×=×⎜⎟⎜⎟⎝⎠⎝⎠()10.461.42225113.23610402735963.410TpTKTpκκ−⎛⎞⎛⎞×=⇒=+=⎜⎟⎜⎟×⎝⎠⎝⎠5511.43.4104.7610vEpPaκ==××=×6621.43.236104.5310vEpPaκ==××=×0khρρ=+kρdpgdhρ=0khρρ=+()0dpkhgdhρ=+202kghpghCρ=++0,0hp==0C=202kghpghρ=+ρ12apghghpghρρρ++=+()412136000.48000.310000.59.814.60610ampppghghghPaρρρ−==−−=×−×−××=××pm=2.45×104Pah=500mmh1=200mmh2=250mmh3=150mmρ=13600kg/m3ρ=843kg/m3()2121231345436256mHOHgAlBHgpppghhppghppppghppghppρρρρ==++=+==+=+=()()21123mHOBHgAlpghhpghhghρρρ++=++−()()2411232.7410BmHOHgAlppghhghhghPaρρρ=++−++=−×10Ddy=−xcDCCIyyyS=+12Cym=3132123xcIba==12102.11xcDDCIydymyS=+⇒=−=510009.8112249.40810CFghSNρ==××××=×l=200mmh=100mma101010pgygappaxρρρ∂⎧−−=⎪∂⎪−−∇=⇒⎨∂⎪−−=⎪∂⎩(),ppppxydpdxdyadxgdyxyρρ∂∂=⇒=+=−−∂∂00dpadxgdyρρ=⇒−−=ayxCg=−+0,xyhCh==⇒=ayxCg=−+,0xly==()204.9/ahlhagmsgl=−+⇒==()24.9/ahhagmsgll=⇒==23Vyzixzjyk=++323363xyzuuuuauvwxzyztxyzvvvvauvwyzxytxyz∂∂∂∂=+++=+∂∂∂∂∂∂∂∂=+++=+∂∂∂∂∂∂∂∂=+++=∂∂∂∂2,,0uyvaxw==−=a2dxdydxdyuvyax=⇒=−222122ayxC−=+222axyC+=22222,,342zuxyzvxyyzzwxz=++=++=−−+yxlhayxlhaga2(3)0uvwdivVxxzxzxyz∂∂∂=++=+++−−=∂∂∂()()()()1111222211115022322222222wvuwvuVijkyzzxxyzyyzizzjyykyzijkω⎛⎞⎛⎞∂∂∂∂∂∂⎛⎞=∇×=−+−+−⎜⎟⎜⎟⎜⎟∂∂∂∂∂∂⎝⎠⎝⎠⎝⎠=−−+++−=−++−22,,0uxyvxyw==−=220uvwdivVyxxyz∂∂∂=++=−≠∂∂∂vV=0.6m/sD=24cmQ=0.2m3/s()220.244.42/43.140.24QvmsDπ×===×V=0.6m/s0.6rVV=−x()()224rFvVQvVDπρρ−=−−=−−()223964WFVvVDVWπρ==−=VVV=5m/sD=100mmd=20mm()2222100050.10.0237.7/444mVDVdkgsπππρρ=−=×××−=yxF2222sin4544322xFVdmVVDNππρρ=−−=−0.3m30mm15m/sy3150.30.030.424/QVRtmsππ=•=×××=ydsy220sinsin24050yydFVRdtVFVRtdVRtNπρθθρθθρ=••⇒===∫UθVU=V/3rVVU=−x()()12cosxrrFQVUQVUρθρ−=−−−()12rrrQQVSVUSρρ===−()()21cosxFVUSρθ=−−x()()21cosxRVUSρθ=−−y()()22sinsinyrFQVUVUSρθρθ=−=−VxydsθFxFyyxy()2sinyRVUSρθ=−()()21cosxWRUVUSUρθ=•=−−()()()()()()21cos21cos30(0)(3)0dWSVUUVUSVUVUdUVUorVUρθρθ⎡⎤=−−−+−=−−−=⎣⎦⇒−=−=V=UU=V/3x2uaxby=+zyvaby=0v0uvxy∂∂+=∂∂2222()0,0()02uvuaxbyaxaxvaxyfxxyyvfxvaxy∂∂=+⇒=⇒=−⇒=−+∂∂==⇒=⇒=−2,,uaxyvbyzwcyzdz===+2,,2uvwuaxyayvbyzbzwayzdzaydzxyz∂∂∂=⇒==⇒==+⇒=+∂∂∂0uvwxyz∂∂∂++=∂∂∂200,20aybzcydzacbd⇒+++=⇒+=+=°°°3320/88.89/,1.226/pppppVkmhmskgmRTρ====120mLpLCL==ReRepppmmmpmpmVLVLρρµµ=⇒=,,pmmppmpmTTppρρµµ==⇒==1777.8/pppmmppmmpmLLVVVmsLLρµρµ=•••==3288,140016.94/mmmmmpTKpkPakgmRTρ==⇒==128.66/ppmpmpmpmmLTTVVmsLρµµρ=⇒=⇒=•=33999.1/,1.13910mmkgmPasρµ−==ו51.78510pPasµ−=ו139.2/ppmmpmmpLVVmsLρµρµ=•••=pmpmmmppVVFrFrgLgL=⇒=3.162/ppmpmmLggVVmsL=⇒=•=THρQωη[][][][][][]331122:;:;:;:;:MLHLQLttTMLtρω−−−−⎡⎤⎡⎤⎡⎤⎡⎤⎣⎦⎣⎦⎣⎦⎣⎦η,,HQρ[]222222000331112,HQMLtMLLLttαγβαβγηρω−−−⎡⎤⎡⎤⎡⎤⎡⎤Π=Π=⇒=⎣⎦⎣⎦⎣⎦⎣⎦[][][]230312222222:0:101:3303MHtHQQLαωγγρωαβγβ−⎫=⎪−−=⇒=−⇒Π==⎬⎪−++=⇒=⎭[]333333000331223HQTMLtMLLLtMLtαγβαβγρ−−−⎡⎤⎡⎤⎡⎤⎡⎤Π=⇒=⎣⎦⎣⎦⎣⎦⎣⎦[][][]331233323333:011:202:33201MTHtHQTQLααγγρραβγβ−−⎫=+⇒=−⎪−−=⇒=−⇒Π==⎬⎪−+++=⇒=⎭32,,0THHfQQωηρ⎛⎞⇒=⎜⎟⎝⎠23QHTgHQρωη⎛⎞=⎜⎟⎝⎠Qd[][][][][]31312:;:;:;:QLtdLMLpMLtρ−−−−⎡⎤⎡⎤⎡⎤∆⎣⎦⎣⎦⎣⎦[]31312QKdpLtLMLMLtγβγααβρ−−−−⎡⎤⎡⎤⎡⎤=∆⇒=⎣⎦⎣⎦⎣⎦[][][]:01:121/2,22:33MtLβγγγβααβγ⎫+=⎪−=−⇒=⇒=−=⎬⎪−−=⎭1/221/22pQKdpQKdρρ−∆=∆⇒=1230,15dcmdcm==80,10Hcmhcm==2211221222pVpVzzggγγ++=++21zzH−=()22221212HOHOHgHgHOHOpghpgHghppghgHρρρρρρ+=++⇒−=−[phone]VdVdVVππ=⇒=()()22222221121.284/215HgHOHgHOHOHOghghVVVmsggρρρρρρ−−−=⇒==23110.0907/4QVdmsπ==110dcm=25,3,4.5dcmambm===2200550522pVpVzzggγγ++=++050054.5,0,zzbmVpp−====529.4/Vgbms==2551234212.35/dVVmsVVVVd======2200110122pVpVzzggγγ++=++2010111,02761.252mzzVpVPaρ==⇒=−=−2200220222pVpVzzggγγ++=++2200221,032191.252mzzaVpgaVPaρρ−==⇒=−−=−2233111322pVpVzzggγγ++=++131331,2761.25mmzzVVppPa==⇒==−2200440422pVpVzzggγγ++=++2400241,041383.752mzzbVpgbVPaρρ−=−=⇒=−=2222AABBABpVpVzzggγγ++=++22,4.5/9.18/AABABABdzzVmsVVmsd==⇒==()22132044.92ABBAppVVPaρ−=−=()21006.24ABFppdNπ=−=()()22333,31/,21/VAxyiBxyjAmsBms=−=•=•223,,3,2uAxyvBxyAB==−==22230uvAxyBxyxy∂∂+=−=∂∂223,uAxyvBxyyx∂Ψ∂Ψ===−=−∂∂()()233AudyfxxyfxΨ=+=+∫()()()()33322203AxyfxxyfxxyfxfxCx∂Ψ′′′=+=+=⇒=⇒=∂23xyCΨ=+2320uvAxyByyx∂∂−=+≠∂∂ψ()()()2222ln1ln12QxyxyπΦ=++−−+()()()()2222222211211211QxxuxxyxyQyyvyxyxyππ⎛⎞∂Φ+−==−⎜⎟⎜⎟∂++−+⎝⎠⎛⎞∂Φ==−⎜⎟⎜⎟∂++−+⎝⎠()()200,06.37/,0,003.14Qumsvπ====()122QθθπΨ=−()()2122arctan41.56/22QQmsθθπππΨ=−=−=−()()20,40.375/,0,40217Qumsvπ⎛⎞===⎜⎟⎝⎠2222xxyΨ=+−1.12kg/m3pkPa2222xxyΨ=+−222214444xxxyyy∂Ψ∂Ψ=+⇒=∂∂∂Ψ∂Ψ=−⇒=−∂∂22220xy∂Ψ∂Ψ⇒+=∂∂4,41uyvxyx∂Ψ∂Ψ==−=−=−−∂∂()()44ydxfyxyfyΦ=−+=−+∫()()()4411xfyxfyfyyCy∂Φ′′=−+=−−⇒=−⇒=−+∂()44ydxfyxyyCΦ=−+=−−+∫()()()()21221,248/,1,2415/899,6424/,9,64137/1945uymsvxmsVuymsvxmsV−=−=−=−−=−⇒==−==−−=−⇒=()22211213760.642ppVVPaρ=+−=sin2gyuyhρθµ⎛⎞=−⎜⎟⎝⎠v=w=00ux∂=∂z0uutz∂∂==∂∂()uuy=220sin0cos0dupgdyxpgypzµρθρθ⎧∂=−+⎪∂⎪⎪∂=−−⎨∂⎪⎪∂=−⎪∂⎩()cospgyfxρθ=−+,ayhpp==()cos0apfxpghconstxρθ∂=+=⇒=∂0,0