Understanding Pressure Distribution in a Rotating Vessel of Water

[glebovg]

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.

 

[TSny]

Choose an arbitrarily located volume element of the water. Think about what forces act on the element. Then think about what law you can use to relate the forces to the motion.

 

[glebovg]

Choose an arbitrarily located volume element of the water. Think about what forces act on the element. Then think about what law you can use to relate the forces to the motion.

You might as well just say: start answering the question. Your answer is the most general answer in fluid dynamics!

 

[TSny]

The trick, of course, is to transform the "general answer" into a specific answer.

Thus, you will need to identify the specific forces acting on a fluid element and relate the direction of one of those forces to the orientation of a surface of constant pressure. You will need to identify the specific magnitude and direction that the net force must have to produce the specific type of motion of the fluid element.

You have not indicated what aspects of the problem you understand and what aspects are giving you trouble, so it's a bit hard to know how to start helping you.

 

[vela]

Per the forum rules, you need to show an effort at solving the problem yourself before you receive help here. "I don't know how to start" doesn't fly here. Please see https://www.physicsforums.com/showpost.php?p=4021232 for more info.