Milne-Thomson circle theorem

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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.[1][2] It was named after the English mathematician L. M. Milne-Thomson.

Let be the complex potential for a fluid flow, where all singularities of lie in . If a circle is placed into that flow, the complex potential for the new flow is given by[3]

with same singularities as in and is a streamline. On the circle , , therefore


Consider a uniform irrotational flow with velocity flowing in the positive direction and place an infinitely long cylinder of radius in the flow with the center of the cylinder at the origin. Then , hence using circle theorem,

represents the complex potential of uniform flow over a cylinder.

See also[edit]


  1. ^ Batchelor, George Keith (1967). An Introduction to Fluid Dynamics. Cambridge University Press. p. 422. ISBN 0-521-66396-2.
  2. ^ Raisinghania, M.D. (December 2003). Fluid Dynamics. ISBN 9788121908696.
  3. ^ Tulu, Serdar (2011). Vortex dynamics in domains with boundaries (PDF) (Thesis).