# Shape of surface of fluid in a rotating tank

1. Jun 6, 2010

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1. The problem statement, all variables and given/known data
A concave astronomical telescope mirror may be made by rotating a circular tank of mercury. Find an expression for the shape of the surface in terms of the density of mercury, the radius from the centre, and the rotation rate.

2. Relevant equations
$$v = r \omega$$

3. The attempt at a solution
Blah, no idea where to start. Like the problem says, the surface would be concave. Spinning faster would make it deeper, as would lowering the density of the fluid in the tank. The shape would be either spherical or paraboloid elliptic. My guess would be parabolic. There would be some pressure variation outwards from the centre, maybe? I don't know. If someone could just throw a couple relevant equations my way, that would be helpful.

2. Jun 6, 2010