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. It was named after the English mathematician L. M. Milne-Thomson.

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