Finding stream functions for a cylinder [fluid mechanics]

[Niles]

Homework Statement

Hi

The stream function for a cylinder with radius $a$ in a uniform crosswind is given by (https://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder#Stream_function)
$$\psi = Ur \sin(1-a^2/r^2)$$
How does one show this formally?

 

[Chestermiller]

The stream function satisfies Laplace's equation also. All you need to do is figure out what the boundary conditions are.

Chet