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} ight)-frac{1}{2 pi}

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).