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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:Ψ=V∞rsin(θ)-Msin(θ)2πr相应流动的流线方程为:V∞rsin(θ)-Msin(θ)2πr=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-M2πryx2+y2=C(常量)1.V∞=10,M=500,C=10,-10,0,20,-20ezplot('10*y-500*y/(2*pi*(x^2+y^2))=10')holdonezplot('10*y-500*y/(2*pi*(x^2+y^2))=-10')h
2、oldonezplot('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')holdon2.V∞=20,M=520,C=20,-20,0,40,-40ezplot('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*
3、(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')holdon3.V∞=30,M=540,C=30,-30,0,60,-60ezplot('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
4、*y-540*y/(2*pi*(x^2+y^2))=60')holdonezplot('30*y-540*y/(2*pi*(x^2+y^2))=-60')holdon4.V∞=100,M=1000,C=30,-30,0,60,-60ezplot('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+
5、y^2))=60')holdonezplot('100*y-1000*y/(2*pi*(x^2+y^2))=-60')holdon5.V∞=10,M=100,C=30,-30,0,60,-60ezplot('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
6、-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:Ψ=V∞(r-R2r)sin(θ)+Γ2πln(r)相应流动的流线方程为:V∞(r-R2r)sin(θ)+Γ2πln(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)+Γ2πlnx2+y2=C(常量)1.V∞=10,R=3,Γ=0.1,C=0,10,20,30,40ezplot('10*y*(1-9/(x^2+y^2))+0.1*exp(sqrt(x^2+y^2))
7、/(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