# Plotting Streamlines Maple

I wonder if anybody could help with this. I've been asked to plot the streamlines of the complex potential $\Omega(z)=Uz + \frac{m}{2\pi}ln(z)$ to which I get the stream function $\psi(r,\theta)=rUsin\theta + \frac{m}{2\pi}\theta$.

Hopefully that is correct, but I cannot seem to plot it using polar coords in Maple. I would like to plot a series of streamlines of $\psi = constant.$ Any help appreciated, thanks!

• You can treat $\psi$ as a function of two variables. Is it enough plotting $\psi$? – Mikasa Sep 4 '13 at 14:38
• Can't get the command to work - always comes up with an error. I converted back into cartesian coords and tried a contour plot, but doesn't look quite how I expected it would. – Mike Miller Sep 4 '13 at 14:40
• What is the domain of $z$? What will you do with $U$ and $m$? If we don't have them we cannot make any plots. – Mikasa Sep 4 '13 at 14:42
• $U$ & $m$ are some constant, so I just set them to equal 1. $r > 0$ (I tried $0<r<10$), $0<\theta<2\pi$. Am I making a mistake? – Mike Miller Sep 4 '13 at 14:48

 [> with(plots):
conformal(z+ln(z)/(2*Pi), z = -20*I .. 2+20*I);


And for $\psi$, I think you can consider it as a function of two variables and plot it by the following code:

 [> with(plots):
implicitplot(r*sin(t)+t/(2*Pi), r = 0 .. 10, t = 0 .. 2*Pi);


• Thanks - that's exactly the sort of thing I was expecting. I didn't know about this function on Maple; a great help, thanks! – Mike Miller Sep 4 '13 at 14:56
• @BritMiller: I am glad I could help. :) – Mikasa Sep 4 '13 at 14:58
• With the edit you have put, would you know how to sequence some plots so I could plot for example $\psi =0,1,2,3...$? – Mike Miller Sep 4 '13 at 14:59
• @BritMiller: See this one. I could employ seq to find many curves. – Mikasa Sep 4 '13 at 15:02
• @BabakS. Ishalla zoodtar salamatitoon ro be dast biarin. Terme jadid ham ke dare shoroo mishe! Ye darse khoob ke kheili be Abstract Algebra nazdike ro mikham in term bardaram : Coding Theory. Manam khosh halam az didanetoon. – Mahdi Khosravi Sep 4 '13 at 16:11