sin(e)-Msin(e)2nr绕圆柱无环量流动和有环量流动流线分布图一、绕圆柱无环量流动由均匀直线流动和偶极流的流函数可叠加得绕圆柱无环量流动的流函数方程为W=vroo相应流动的流线方程为：rsin(0)-Msin(9)=C(常量)2nr不同C值对应不同的流函数曲线，将极坐标形式变成直角坐标形式:Vy-』—=C(常量)82nrJx2y21.V=10,M=500,C=10,-10,0,20,-20oezplot('10*y-500*y/(2*pi*(x"2+y"2))=10')holdonezplot('10*y-500*y/(2*pi*(x"2+y"2))=T0')holdonezplot('10*y-500*y/(2*pi*(x"2+y"2))=0')holdonezplot('10*y-500*y/(2*pi*(x"2+y"2))=20')holdonezplot('10*y-500*y/(2*pi*(x"2+y"2))=-20')holdonB4Z--4-146a0Wy-500y/(2vi(x2+/)>-202.片20,M=520,C=20,-20,0,40,-40ooezplot('20*y-520*y/(2*pi*(x"2+y"2))=20')holdonezplot('20*y-520*y/(2*pi*(x"2+y"2))=-20')holdonezplot('20*y-520*y/(2*pi*(x"2+y"2))=0')holdonezplot('20*y-520*y/(2*pi*(x"2+y"2))=40')holdonezplot('20*y-520*y/(2*pi*(x"2+y"2))=-40')holdon42-6-6-2014620/-520沁(/十/)戶-403.片30,M=540,C=30,-30,0,60,-60ooezplot('30*y-540*y/(2*pi*(x"2+y"2))=30')holdonezplot('30*y-540*y/(2*pi*(x“2+y“2))=-30')holdonezplot('30*y-540*y/(2*pi*(x"2+y"2))=0')holdonezplot('30*y-540*y/(2*pi*(x"2+y"2))=60')holdonezplot('30*y-540*y/(2*pi*(x“2+y“2))=-60')holdon642-6-5024630y-540y/(2(x2^y2))=-S04.片100,M=1000,C=30,-30,0,60,-60ooezplot('100*y-1000*y/(2*pi*(x”2+y”2))=30‘)holdonezplot('100*y-1000*y/(2*pi*(x“2+y“2))=-30')holdonezplot('100*y-1000*y/(2*pi*(x"2+y"2))=0‘)holdonezplot('100*y-1000*y/(2*pi*(x"2+y"2))=60')holdonezplot('100*y-1000*y/(2*pi*(x“2+y“2))=-60')holdon642011-246100y-1(XX)y/{2TT[x2+y2))=-0O5.片10,M=100,C=30,-30,0,60,-60ooezplot('10*y-100*y/(2*pi*(x"2+y"2))=30')holdonezplot('10*y-100*y/(2*pi*(x“2+y“2))=-30')holdonezplot('10*y-100*y/(2*pi*(x"2+y"2))=0')holdonezplot('10*y-100*y/(2*pi*(x"2+y"2))=60')holdonezplot('10*y-100*y/(2*pi*(x“2+y“2))=-60')holdon二、绕圆柱有环量流动由均匀直线流动、偶极流、点涡三者叠加后的复合流动，流函数方程为W=y(r-兰)sin(G)+丄ln(r)8r2n相应流动的流线方程为：(r-竺)sin(9)+rln(r)=C(常量)r2n不同C值对应不同的流函数曲线，将极坐标形式变成直角坐标形式:V(Jx2+y2-)+rlnjx2+y2=C(常量)8Jx2+y22n1.V=10,R=3,r=0.1,C=0,10,20,30,408ezplot('10*y*(1-9/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=0')holdonezplot('10*y*(1-9/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=10')holdonezplot('10*y*(1-9/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=20')holdonezplot('10*y*(1-9/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=30')holdonezplot('10*y*(1-9/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=40')holdon642-■6-2024610yexp(sqrt(x2V)y(2^)=402.y=20,R=2,r=0.1,C=0,20,-20,40,-40ooezplot('20*y*(1-4/(x“2+y“2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=0')holdonezplot('20*y*(1-4/(x"2+y“2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=20')holdonezplot('20*y*(1-4/(x"2+y“2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=-20')holdonezplot('20*y*(1-4/(x"2+y“2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=40')holdonezplot('20*y*(1-4/(x"2+y“2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=-40')holdone420-2-024620y(1-4/(x2^y2))+0.1exp(sqrt(x2^y2))/(2町=403.y=50,R=4,r=0.1,C=0,10,-10,20,-20ooezplot('50*y*(1T6/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=0')holdonezplot('50*y*(1T6/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=10')holdonezplot('50*y*(1T6/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=T0')holdonezplot('50*y*(1T6/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=20')holdonezplot('50*y*(1T6/(x"2+y"2))+0.1*exp(sqrt(x"2+y“2))/(2*pi)=-20')holdon62€--250y(1」创exp(sqrt(x2+y2))/(2TT)=-204.V=50,R=3,r=-0.3,C=0,20,-20ooezplot('5O*y*(l-9/(x“2+y“2))-0.3*exp(sqrt(x"2+y“2))/(2*pi)=0'，[-66,55])holdonezplot('50*y*(l-9/(x“2+y“2))-0.3*exp(sqrt(x"2+y“2))/(2*pi)=-20'，[-66,-55])holdonezplot('50*y*(l-9/(x“2+y“2))-0.3*exp(sqrt(x"2+y“2))/(2*pi)=20'，[-66,-55])holdon54320---224650y(1-9/(exp(sqrt{x2+y2))/(2-.7)=205.V=1000,R=5,r=-l,C=0,20,-20,40,-40ooezplot('1000*y*(1-25/(x"2+y“2))T*exp(sqrt(x"2+y“2))/(2*pi)=0'，[-66,-55])holdonezplot('1000*y*(1-25/(x“2+y“2))-1*exp(sqrt(x"2+y“2))/(2*pi)=-20'，[-66,-55])holdonezplot('1000*y*(1-25/(x“2+y“2))-1*exp(sqrt(x"2+y“2))/(2*pi)=20'，[-66,-55])holdonezplot('1000*y*(1-25/(x"2+y“2))T*exp(sqrt(x"2+y“2))/(2*pi)=40'，[-66,-55])holdonezplot('1000*y*(1-25/(x"2+y“2))T*exp(sqrt(x"2+y“2))/(2*pi)=-40'，[-66,-55])holdon2iW：--202461000y(1-25/(x2+y2))-1exp(sqrt(xz+y2)X(2TT>=-40
