# A closed vessel full of water [closed]

A closed vessel full of water is rotating with constant angular velocity $\Omega$ about a horizontal axis. Show that the surfaces of equal pressure are circular cylinders whose common axis is at a height $g/{\Omega}^2$ above the axis of rotation.

Any ideas? I do not know how to start.

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## closed as too localized by David Zaslavsky♦Oct 8 '12 at 3:45

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, see the FAQ.

Use the assumption that water rotates at the same angular velocity as the vessel. Consider a small cube in an arbitrary point of the vessel. Consider the forces acting on the cube: the force of gravity and the force caused by pressure. As the cube is small, the force caused by pressure can be expressed via spatial derivatives of the pressure. Together the forces make the cube move with centripetal acceleration, so you can find the spatial derivatives of pressure $\frac{\partial P}{\partial x}$ and $\frac{\partial P}{\partial y}$ from Newton's second law.