Water in a rotating cylinder

HOW

1. Look at the free surface of the liquid when the cylinder is stationary.
2. Gradually increase the speed of the vessel.

WHY

When the vessel is stationary, only the force of gravity acts on the liquid. Its surface is then flat.

When the liquid rotates, there is additionally a centrifugal force. It pushes the liquid towards the side walls of the vessel. The simultaneous action of these two forces creates the shape you observe when you rotate the vessel. It is similar to a bowl, and is called a paraboloid of revolution.