February 1st, 2016, 04:25 AM  #1 
Newbie Joined: Feb 2016 From: israel Posts: 17 Thanks: 3  circle approximation
Hi guys, I am trying to apply the Mangler's transformation (fluid dynamics) onto a sphere. In order to do so, I need a single variable function r(x) to approximate a circle. Do you know of any simple method? Accuracy is not an issue. Regards, shai Last edited by skipjack; February 1st, 2016 at 04:31 AM. 
February 1st, 2016, 04:34 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,474 Thanks: 2039 
No function has a circle as its graph if Cartesian coordinates are being used. Can you clarify what you mean?

February 1st, 2016, 05:10 AM  #3 
Newbie Joined: Feb 2016 From: israel Posts: 17 Thanks: 3 
The Mangler's transformation is used for boundary layer flow over an axisymmetric bodies of revolution and is used to simplify the NavierStokes equations. Since a sphere is a body of revolution, I want to use this method and the first step is to define how the radius of the body (a cross section of a sphere = circle) changes.. hope that is more clear.
Last edited by skipjack; February 1st, 2016 at 05:45 AM. 
February 1st, 2016, 06:03 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,474 Thanks: 2039 
If the crosssection is perpendicular to the axis of revolution and the sphere has radius r, the crosssection's radius could be √(r²  x²), the graph of which is a semicircle.

February 2nd, 2016, 05:04 AM  #5 
Newbie Joined: Feb 2016 From: israel Posts: 17 Thanks: 3 
Thanks..


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approximation, circle 
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