How Does Rotation Affect Fluid Pressure and Surface Height in a Spinning Pan?

[moosemagoo]

A circular pan of liquid (density= rho) is centered on a horizontal turntable rotating with angular speed w. Its axis coincides with the rotation axis. Atmospheric pressure is Pa. R=10 cm
Find expressions for (a) the pressure at the bottom of the pan
and (b) the height of the liquid surface as a function of the distance r from the axis, given that the height at the center is h0.

I have been reading and rereading this problem, but am at a complete loss. I would really appreciate any help!

 

[OlderDan]

A circular pan of liquid (density= rho) is centered on a horizontal turntable rotating with angular speed w. Its axis coincides with the rotation axis. Atmospheric pressure is Pa. R=10 cm
Find expressions for (a) the pressure at the bottom of the pan
and (b) the height of the liquid surface as a function of the distance r from the axis, given that the height at the center is h0.

I have been reading and rereading this problem, but am at a complete loss. I would really appreciate any help!

I'm sure the problem is to be solved in the steady state condition where all of the liquid is circulating with the same angular velocity. Consider the liquid near the bottom
of the pan. Each little bit of mass of the liquid is in circular motion, which requires a centripetal force. Where does that force come from? How does that force depend on the distance from the axis of rotation? How can the necessary force be achieved?