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.^[1][2] 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:

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

See also

• Potential flow
• Conformal mapping
• Velocity potential

References

1. ^ Batchelor, George Keith (1967). An Introduction to Fluid Dynamics. Cambridge University Press. p. 422. ISBN 0521663962. http://books.google.co.in/books?id=Rla7OihRvUgC&dq=an+introduction+to+fluid+dynamics&printsec=frontcover&source=bn&hl=en&ei=m8OMTLuiAZm0cNzclcME&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCEQ6AEwAw#v=onepage&q&f=false. 
2. ^ Raisinghania, M.D.. Fluid Dynamics. http://books.google.com.au/books?id=wq3TU5tArTkC&lpg=PA211&ots=yThvgwi8Rv&dq=milne%20thomson%20circle%20theorem&pg=PA211#v=onepage&q=milne%20thomson%20circle%20theorem&f=false. 

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