

Liquid Paraboloid
Name: Nate
Status: educator
Grade: 912
Location: IL
Country: USA
Date: Summer 2013
Question:
We have a thin, wide, tall, parallelepiped that is 1/3 filled with a fluid (colored water). When placed on a rotating platform, it forms a section of a paraboloid. This is a similar to how some telescope mirrors are manufactured. Looking at the centripetal force equation, F=4*pi*pi*r/T*T, the force is proportional to the radius, not the radius squared. So why do we have a paraboloid?
Replies:
Hi Nate,
The behavior you describe is indicative of fluid dynamics. Flow of liquids in a tube is unique and largely dynamic pressure driven. You are probably observing centripetal force, dynamic pressure and adhesion(at the interface).
The mathematics are chaotic(dynamic) rather than straightforward. The reference below is concerning development of an algorithm. In the thought analysis, the author presents(by figure) and gives examples of the very phenomenon you observe. His analysis is the part about midway through using an inverted T tube. His conclusion is that the force is proportional to both, r and v squared.
http://www.fractalforums.com/let'scollaborateonsomething!/developingfractalalgorithmforfluiddynamics/?PHPSESSID=6997a99a02090ebaeea945c88aeaa7cf
Cars at v/t in a radius may be a much easier and more definable lab demonstration of centripetal force.
Hoping this helps! Peter
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