# Milne-Thomson circle theorem

Let $w = f(z)$ be the complex stream function for a fluid flow with no rigid boundaries and no singularities within $|z| = a$. If a circular cylinder $|z| = a$ is placed into that flow, the complex potential for the new flow is given by:
$w = f(z) + \bar{f}\left( \frac{a^2}{\bar{z}} \right)$