绕圆柱无环量流动和有环量流动流线分布图.docx
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绕圆柱无环量流动和有环量流动流线分布图
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:
¥=8rsin(8)
兀
相应流动的流线方程为:
8rsin(0)-=C(常量)
兀
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:
8y=C(常量)
兀
1.8=10,M=500,C=10,-10,0,20,-20
ezplot('10*y-500*y/(2*pi*(xA2+yA2))=10')
holdon
ezplot('10*y-500*y/(2*pi*(xA2+yA2))=-10')
holdon
ezplot('10*y-500*y/(2*pi*(xA2+yA2))=0')
holdon
ezplot('10*y-500*y/(2*pi*(xA2+yA2))=20')
holdon
ezplot('10*y-500*y/(2*pi*(xA2+yA2))=-20')
holdon
2.8=20,M=520,C=20,-20,0,40,-40
ezplot('20*y-520*y/(2*pi*(xA2+yA2))=20')
holdon
ezplot('20*y-520*y/(2*pi*(xA2+yA2))=-20')
holdon
ezplot('20*y-520*y/(2*pi*(xA2+yA2))=0')
holdon
ezplot('20*y-520*y/(2*pi*(xA2+yA2))=40')
holdon
ezplot('20*y-520*y/(2*pi*(xA2+yA2))=-40')
holdon
20六520y/(2tt(x2+y2))=-40
*ilIhiIi
-S-4-2D246
3.8=30,M=540,C=30,-30,0,60,-60
ezplot('30*y-540*y/(2*pi*(xA2+yA2))=30')
holdon
ezplot('30*y-540*y/(2*pi*(xA2+yA2))=-30')
holdon
ezplot('30*y-540*y/(2*pi*(xA2+yA2))=0')
holdon
ezplot('30*y-540*y/(2*pi*(xA2+yA2))=60')
holdon
ezplot('30*y-540*y/(2*pi*(xA2+yA2))=-60')
holdon
30y-540y/(2打(x2+y2)>-60
-6^4-2D246
4.oo=10O,M=1000,C=30,-30,0,60,-60
ezplot('100*y-1000*y/(2*pi*(xA2+yA2))=30')
holdon
ezplot('100*y-1000*y/(2*pi*(xA2+yA2))=-30')
holdon
ezplot('100*y-1000*y/(2*pi*(xA2+yA2))=0')
holdon
ezplot('100*y-1000*y/(2*pi*(xA2+yA2))=60')
holdon
ezplot('100*y-1000*y/(2*pi*(xA2+yA2))=-60')
holdon
6
100y-1000W(277(k,/))=-60
-G-4*20246
X
5.8=10,M=100,C=30,-30,0,60,-60
ezplot('10*y-100*y/(2*pi*(xA2+yA2))=30')
holdon
ezplot('10*y-100*y/(2*pi*(xA2+yA2))=-30')
holdon
ezplot('10*y-100*y/(2*pi*(xA2+yA2))=0')
holdon
ezplot('10*y-100*y/(2*pi*(xA2+yA2))=60')
holdon
ezplot('10*y-100*y/(2*pi*(xA2+yA2))=-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:
,、•,…r...
w=oo(r——)sin(0)+——ln(r)
兀
相应流动的流线方程为:
F_.、一一.
③(r--)sin(9)+一ln(r)=C(吊重)
兀
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:
r、一一
(-)+一ln=C(吊室)
兀
8=10,R=3,r=0.1,C=0,10,20,30,40
ezplot('10*y*(1-9/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=0')
holdon
ezplot('10*y*(1-9/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=10')
holdon
ezplot('10*y*(1-9/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=20')
holdon
ezplot('10*y*(1-9/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=30')
holdon
ezplot('10*y*(1-9/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=40')
holdon
10y(1-9/(A2+y2))>0.1exp(sqrt(x-2))/(2开)=40
-6-4-20246
8=20,R=2,r=0.1,C=0,20,-20,40,-40
ezplot('20*y*(1-4/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=0')
holdon
ezplot('20*y*(1-4/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=20')
holdon
ezplot('20*y*(1-4/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=-20')
holdon
ezplot('20*y*(1-4/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=40')
holdon
ezplot('20*y*(1-4/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=-40')
holdon
20y(14/(1+/))+。
J€*p佰qrl仪»)=-40
2
.4
-6^^4-20246
8=50,R=4,r=0.1,C=0,10,-10,20,-20
ezplot('50*y*(1-16/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=0')
holdonezplot('50*y*(1-16/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=10')
holdon
ezplot('50*y*(1-16/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=-10')
holdonezplot('50*y*(1-16/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=20')
holdonezplot('50*y*(1-16/(xA2+yA2))+0.1*exp(sqrt(xA2+yA2))/(2*pi)=-20')
holdon
50y(M6/(A2+y2))+0.1exp{sqrt(x^y2))/(2兀)=-20
8=50,R=3,r=-0.3,C=0,20,-20
ezplot('50*y*(1-9/(xA2+yA2))-0.3*exp(sqrt(xA2+yA2))/(2*pi)=0',[-6
6,-55])holdon
ezplot('50*y*(1-9/(xA2+yA2))-0.3*exp(sqrt(xA2+yA2))/(2*pi)=-20',[-6
6,-55])holdonezplot('50*y*(1-9/(xA2+yA2))-0.3*exp(sqrt(xA2+yA2))/(2*pi)=20',[-6
6,-55])holdon
50y(V9/(x2+y3)}-0.3exp(sqrt(x2+/)y(2开户20
8=1000,R=5,r=-1,C=0,20,-20,40,-40
ezplot('1000*y*(1-25/(xA2+yA2))-1*exp(sqrt(xA2+yA2))/(2*pi)=0',[-6
6,-55])
holdon
ezplot('1000*y*(1-25/(xA2+yA2))-1*exp(sqrt(xA2+yA2))/(2*pi)=-20',[-6
6,-55])
holdon
ezplot('1000*y*(1-25/(xA2+yA2))-1*exp(sqrt(xA2+yA2))/(2*pi)=20',[-6
6,-55])
holdon
ezplot('1000*y*(1-25/(xA2+yA2))-1*exp(sqrt(xA2+yA2))/(2*pi)=40',[-6
6,-55])
holdon
ezplot('1000*y*(1-25/(xA2+yA2))-1*exp(sqrt(xA2+yA2))/(2*pi)=-40',[-6
6,-55])
holdon
1000y(1-25/(x2+y2))-1exp(sqrt(x2+y2))/(2tt)=-40
-6
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