绕圆柱无环量流动和有环量流动流线分布图

1、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：=V r sin()-M sin()2r 相应流动的流线方程为：V r sin()- M sin()2r =C（常量）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 y-M2ryx2+y2 =C（常量）1. V=10，M=500, C=10,-10,0,20,-20 ezplot(10*y-500*y/(2*pi*(x2+y2)=10) hold on ezplot(10*y-500*y/(2*pi*(x2+y2)=-10) hold on ezplo

2、t(10*y-500*y/(2*pi*(x2+y2)=0) hold on ezplot(10*y-500*y/(2*pi*(x2+y2)=20) hold on ezplot(10*y-500*y/(2*pi*(x2+y2)=-20) hold on2. V=20，M=520, C=20,-20,0,40,-40 ezplot(20*y-520*y/(2*pi*(x2+y2)=20) hold on ezplot(20*y-520*y/(2*pi*(x2+y2)=-20) hold on ezplot(20*y-520*y/(2*pi*(x2+y2)=0) hold on ezplot(20

3、*y-520*y/(2*pi*(x2+y2)=40) hold on ezplot(20*y-520*y/(2*pi*(x2+y2)=-40) hold on3. V=30，M=540, C=30,-30,0,60,-60 ezplot(30*y-540*y/(2*pi*(x2+y2)=30) hold on ezplot(30*y-540*y/(2*pi*(x2+y2)=-30) hold on ezplot(30*y-540*y/(2*pi*(x2+y2)=0) hold on ezplot(30*y-540*y/(2*pi*(x2+y2)=60) hold on ezplot(30*y-

4、540*y/(2*pi*(x2+y2)=-60) hold on4. V=100，M=1000, C=30,-30,0,60,-60 ezplot(100*y-1000*y/(2*pi*(x2+y2)=30) hold on ezplot(100*y-1000*y/(2*pi*(x2+y2)=-30) hold on ezplot(100*y-1000*y/(2*pi*(x2+y2)=0) hold on ezplot(100*y-1000*y/(2*pi*(x2+y2)=60) hold on ezplot(100*y-1000*y/(2*pi*(x2+y2)=-60) hold on5.

5、V=10，M=100, C=30,-30,0,60,-60ezplot(10*y-100*y/(2*pi*(x2+y2)=30) hold on ezplot(10*y-100*y/(2*pi*(x2+y2)=-30) hold on ezplot(10*y-100*y/(2*pi*(x2+y2)=0) hold on ezplot(10*y-100*y/(2*pi*(x2+y2)=60) hold on ezplot(10*y-100*y/(2*pi*(x2+y2)=-60) hold on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：=V（r-R2r）si

6、n()+2 ln(r)相应流动的流线方程为：V（r-R2r）sin()+2 ln(r)=C（常量）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 (x2+y2-R2x2+y2) +2 lnx2+y2 =C（常量）1.V=10, R=3, =0.1, C=0,10,20,30,40ezplot(10*y*(1-9/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=0) hold on ezplot(10*y*(1-9/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=10) hold on ezplot(10*y*(1-9/(x2+y2)+

7、0.1*exp(sqrt(x2+y2)/(2*pi)=20) hold onezplot(10*y*(1-9/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=30) hold onezplot(10*y*(1-9/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=40) hold on2.V=20, R=2, =0.1, C=0,20,-20,40,-40ezplot(20*y*(1-4/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=0) hold on ezplot(20*y*(1-4/(x2+y2)+0.1*exp(sqrt

8、(x2+y2)/(2*pi)=20) hold on ezplot(20*y*(1-4/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=-20) hold onezplot(20*y*(1-4/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=40) hold onezplot(20*y*(1-4/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=-40) hold on3.V=50, R=4, =0.1, C=0,10,-10,20,-20ezplot(50*y*(1-16/(x2+y2)+0.1*exp(sqrt(x2+y2)/

9、(2*pi)=0) hold on ezplot(50*y*(1-16/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=10) hold on ezplot(50*y*(1-16/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=-10) hold onezplot(50*y*(1-16/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=20) hold onezplot(50*y*(1-16/(x2+y2)+0.1*exp(sqrt(x2+y2)/(2*pi)=-20) hold on4.V=50, R=3, =-0.3, C=0

10、,20,-20ezplot(50*y*(1-9/(x2+y2)-0.3*exp(sqrt(x2+y2)/(2*pi)=0,-6 6,-5 5) hold on ezplot(50*y*(1-9/(x2+y2)-0.3*exp(sqrt(x2+y2)/(2*pi)=-20,-6 6,-5 5) hold on ezplot(50*y*(1-9/(x2+y2)-0.3*exp(sqrt(x2+y2)/(2*pi)=20,-6 6,-5 5) hold on5.V=1000, R=5, =-1, C=0,20,-20,40，-40ezplot(1000*y*(1-25/(x2+y2)-1*exp(sqrt(x2+y2)/(2*pi)=0,-6 6,-5 5) hold on ezplot(1000*y*(1-25/(x2+y2)-1*exp(sqrt(x2+y2)/(2*pi)=-20,-6 6,-5 5) hold on ezplot(1000*y*(1-25/(x2+y2)-1*exp(sqrt(x2+y2)/(2*pi)=20,-6