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

enter image description here

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

enter image description here

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

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    $\begingroup$ Never post unsearchable pictures of equations. Instead typeset them, using MathJax or at lest copyable code. $\endgroup$ Jun 24, 2020 at 20:51

2 Answers 2

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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]

enter image description here

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  • $\begingroup$ That's what I need! Is there any way I can erase the streamlines inside the semicircle? $\endgroup$ Jun 25, 2020 at 19:22
  • $\begingroup$ Add a constraint 'x^2+y^2>1 ' inside Contourplot. $\endgroup$ Jun 25, 2020 at 21:07
  • $\begingroup$ for example ContourPlot[…,RegionFunction->Function[{x,y},x^2+y^2>= 1] $\endgroup$ Jun 26, 2020 at 8:06
  • $\begingroup$ 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. $\endgroup$ Jun 26, 2020 at 15:01
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expr = 
  With[
    {r = Sqrt[x^2 + y^2], theta = ArcTan[x, y]},
    -1/4 (Sin[theta]^2) (1/r - 3 r + 2 r^2)
  ]

initial expression

simpler = FullSimplify[ExpandAll@expr]

simplified expression

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

region plot

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  • $\begingroup$ 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. $\endgroup$ Jun 24, 2020 at 22:20

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