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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 f {\displaystyle f} be the complex potential for a fluid flow, where all singularities of f {\displaystyle f} lie in | z | > a {\displaystyle |z|>a}. If a circle | z | = a {\displaystyle |z|=a} is placed into that flow, the complex potential for the new flow is given by
with same singularities as f {\displaystyle f} in | z | > a {\displaystyle |z|>a} and | z | = a {\displaystyle |z|=a} is a streamline. On the circle | z | = a {\displaystyle |z|=a} , z z ¯ = a 2 {\displaystyle z{\bar {z}}=a^{2}} , therefore