How to 2D plot using the equation of fi and zi?

[Myo Gyi]

https://en.wikipedia.org/wiki/Potential_flow

[Myo Gyi]

Somebody help me please.

[Myo Gyi]

n = 2;
A = 1;
r=linspace(-1,1,21);
theta = 45;
phi = A.*r^n*(cos(n*theta));
psi = A.*r^n*(sin(n*theta));
plot (phi,psi)
grid on

Answer 1

[Bruno Luong]

The wikipedia page plots only the polar sector 2*pi/(2*n) of the stream lines / potential

The second plot is the full picture.

n = 3/2;
A = 1;
x=linspace(-1,1,21);
y=linspace(-1,1,21);
[X,Y]=ndgrid(x,y);
Z=X+1i*Y;
W = A*Z.^n;
phi = real(W);
psi = imag(W);

close all

subplot(2,1,1);
hold on
plot(phi,psi,'b');
plot(phi.',psi.','g');
axis equal

subplot(2,1,2);
hold on
contour(x,y,phi.',20,'b');
contour(x,y,psi.',20,'g');
axis equal

[Myo Gyi]

Thank you very much sir...

If I don`t want to use complex potential, how can I do it sir..

Just only the value of phi and psi

[darova]

Use polar system of coordinates then:

n = -1.5;
A = 1;
r = linspace(0,2,30);
th = linspace(0,2*pi,100);
[R, TH] = meshgrid(r,th);
fi = A*R.^n.*cos(n*TH);
zi = A*R.^n.*sin(n*TH);
[X,Y] = pol2cart(TH,R);
contour(X,Y,fi,'g')
hold on
contour(X,Y,zi,'b')
hold off