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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 $w=f(z)$ be the complex stream function for a fluid flow with no rigid boundaries and no singularities within $\left|z\right|=a$. If a circular cylinder $\left|z\right|=a$ is placed into that flow, the complex potential for the new flow is given by:

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

See also

• Potential flow
• Conformal mapping
• Velocity potential

References

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