Shape of surface of fluid in a rotating tank

AI Thread Summary
The discussion focuses on determining the shape of the surface of mercury in a rotating tank, specifically in relation to its use in creating a concave astronomical telescope mirror. It highlights that the surface shape is influenced by the rotation rate, density of the fluid, and suggests that the resulting shape could be either spherical or parabolic, with a preference for parabolic. The user expresses uncertainty about how to begin solving the problem and requests relevant equations to aid in their understanding. The relationship between rotation speed and surface depth is emphasized, indicating that faster rotation or lower fluid density increases the depth of the surface. Overall, the conversation seeks clarity on the mathematical modeling of the fluid's surface shape under rotation.
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Homework Statement


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.


Homework Equations


v = r \omega


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.
 
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