I have a closed cylinder that has 10% of its volume filled with water. The cylinder can rotate at low and high speeds and I'd like to know how I can go about describing the behaviour of the fluid in the rotating cylinder at those speeds. Any suggestions on boundary conditions and information on velocity distributions would be greatly appreciated.

I think a similar question was asked here sometimes ago. It has very simple analytical solution and was given in a text book. If you search through this forum, you should be able to find the exact answer.