Fluid at equilibrium in a rotating cylinder: does it have internal motion?

[xnd996]

Suppose I have a fluid of uniform density confined to a roating cylinder of radius $$r$$ turning at an angular speed of $$\Omega$$.

Now I am considering the fluid in the rotating frame and I know that the fluid is in equilibrium. What does this imply?

If the fluid is in equilibrium are there any internal motions? Is the velocity 0? Why?

 

[Andy Resnick]

What you describe sounds a lot like "Newton's bucket', which was a conceptual device claimed to have established a preferred frame of reference (the distant stars).

http://www-history.mcs.st-and.ac.uk/HistTopics/Newton_bucket.html