# Milne-Thomson circle theorem

In fluid dynamics the Milne-Thomson circle theorem or the circle theorem is a statement giving a new stream function for a fluid flow when a cylinder is placed into that flow.[1][2] It was named after the English mathematician L. M. Milne-Thomson.

Let ${\displaystyle w=f(z)}$ be the complex stream function for a fluid flow with no rigid boundaries and no singularities within ${\displaystyle |z|=a}$. If a circular cylinder ${\displaystyle |z|=a}$ is placed into that flow, the complex potential for the new flow is given by[3]

${\displaystyle w=f(z)+{\overline {f\left({\frac {a^{2}}{\bar {z}}}\right)}}=f(z)+{\bar {f}}\left({\frac {a^{2}}{z}}\right).}$