# Plot implicit polar equation streamlines

I'm trying to plot streamlines of Stokes solution to an sphere, the expression of streamlines is

I've seen similar questions before and this what I have tried

As you can see, a=1, U=1, but it seems not to work, any help? Thanks

• Never post unsearchable pictures of equations. Instead typeset them, using MathJax or at lest copyable code. – David G. Stork Jun 24 '20 at 20:51

Perhaps ContourPlot is what you are looking for?

Try (Thanks to MarcoB for his answer and definition of simpler)

ContourPlot[simpler, {x, -2, 2}, {y, 0, 2} ,Contours -> Table[-10^-i, {i, 0, 4}],MaxRecursion -> 4]


• That's what I need! Is there any way I can erase the streamlines inside the semicircle? – Juan Garcia Jun 25 '20 at 19:22
• Add a constraint 'x^2+y^2>1 ' inside Contourplot. – Ulrich Neumann Jun 25 '20 at 21:07
• for example ContourPlot[…,RegionFunction->Function[{x,y},x^2+y^2>= 1] – Ulrich Neumann Jun 26 '20 at 8:06
• Oh yeah I was able to do that, I searched for it! Thanks I chose this as the answer, yet MarcoB's answer really did help. – Juan Garcia Jun 26 '20 at 15:01
expr =
With[
{r = Sqrt[x^2 + y^2], theta = ArcTan[x, y]},
-1/4 (Sin[theta]^2) (1/r - 3 r + 2 r^2)
]


simpler = FullSimplify[ExpandAll@expr]


Region[
ImplicitRegion[simpler == 0, {{x, -2, 2}, {y, 0, 2}}],
Axes -> False, Frame -> True,
PlotRange -> {{-2, 2}, {-2, 2}}
]


• It does work, but what when I try a value of psi other than zero it says Region Embedding dimension:2. I'm new to mathematica so I really don't know what it means. – Juan Garcia Jun 24 '20 at 22:20