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 formula_1 be the complex potential for a fluid flow, where all singularities of formula_1 lie in formula_3. If a circle formula_4 is placed into that flow, the complex potential for the new flow is given by
 formula_5
with same singularities as formula_1 in formula_3 and formula_4 is a streamline. On the circle formula_4, formula_10, therefore
formula_11
Example.
Consider a uniform irrotational flow formula_12 with velocity formula_13 flowing in the positive formula_14 direction and place an infinitely long cylinder of radius formula_15 in the flow with the center of the cylinder at the origin. Then formula_16, hence using circle theorem,
formula_17
represents the complex potential of uniform flow over a cylinder.
References.
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