Chapter 5, Problem 28P

A flow field is characterized by the stream function

$\psi =\frac{1}{2\pi }\left({\tan }^{-1}\frac{y-a}{x}-{\tan }^{-1}\frac{y+a}{x}\right)-\frac{1}{2\pi }\ln \sqrt{x^2+y^2}$

Locate the stagnation points and sketch the flow field. Derive an expression for the velocity at (a, 0).