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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.<ref>{{cite book|last=Batchelor|first=George Keith|authorlink=George Batchelor|title=An Introduction to Fluid Dynamics|url=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|year=1967|publisher=[[Cambridge University Press]]|isbn=0-521-66396-2|page=422}}</ref><ref>{{cite book|last=Raisinghania|first=M.D.|title=Fluid Dynamics|url=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}}</ref> It was named after the [[United Kingdom|English]] mathematician [[L. M. Milne-Thomson]].
 
Let <math>w = f(z)</math> be the complex [[stream function]] for a fluid flow with no rigid boundaries and no [[Mathematical singularity|singularities]] within <math>|z| = a</math>. If a circular cylinder <math>|z| = a</math> is placed into that flow, the complex potential for the new flow is given by:
 
: <math>w = f(z) + \bar{f}\left( \frac{a^2}{\bar{z}} \right)</math>
 
== See also ==
* [[Potential flow]]
* [[Conformal mapping]]
* [[Velocity potential]]
 
== References ==
{{Reflist}}
 
==External links==
 
 
[[Category:Fluid mechanics]]
[[Category:Fluid dynamics]]
[[Category:Equations of fluid dynamics]]

Revision as of 11:09, 17 October 2013

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)+f¯(a2z¯)

See also

References

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  2. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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