A flow field is characterized by the stream function [psi=2 y+frac{1}{2 pi}left(tan ^{-1} frac{y-a}{x}-tan ^{-1} frac{y+a}{x} ight)]

A flow field is characterized by the stream function

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

Derive an expression for the location of the stagnation points. Sketch the flow field.