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I've been trying for a while now to derive the following solution, for a circular cylinder under uniform flow:

[tex]φ(r,θ)=U(r+\frac{R^2}{r})cos θ[/tex]

where φ is the flow potential that satisfies Laplace's equation, as defined in this article:

http://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder

I know how to solve laplace's equation in a rectangular domain, using separation of variables, but here I am at a loss. I simply can't figure out how to implement the circular geometry into the rectangular domain.

To make it more clear, I am assuming a rectangular domain with a circle inside. The domain has a Dirichlet condition on two opposite sides (flow velocity), and a Neuman condition on the surface of the sphere and on the other two sides of the rectangle.

Since this solution is on wikipedia, I figured that it would be well documented, but, after scouring the internet and my books for days, I simply can't find how it's derived anywhere. If someone could provide a link or some help in deriving the solution, I would be grateful

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# How to derive the solution for potential flow around a circular cylinder

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