Water in a rotating cylinder

What you can do here
Observe the free surface of the liquid when the cylinder remains immobile. Gradually increase the angular velocity of the container. What can you see?


How it works
The surface of the liquid takes shape similar to a bowl, which is called rotational paraboloid. The free surface is always perpendicular to the resultant force working on the liquid e.g. water surface in a tilted cup always remains horizontal, which is perpendicular to the direction of gravity force. In case of a rotating cylinder, we have to consider two forces – gravity and centrifugal force. The value of gravity force for a given point on the liquid’s surface does not change during the experiment; whereas the value of centrifugal force increases along with an increase in the angular velocity of the cylinder and the distance from the rotation axis. Close to the rotation axis, where the centrifugal force is small, the gravity dominates, so the fluid remains horizontal, close to the bottom of the container. The farther we get from the centre of the cylinder, the more the centrifugal force impacts the resultant force. The gradually decreasing the impact of the gravity we can observe as the fluid lifting up towards the container’s walls. In a close the proximity of the cylinder’s walls, the liquid gets the highest and is almost vertical, perpendicularly to the centrifugal force.


Interesting facts
A mirror shaped as like a rotational paraboloid ideally concentrates a parallel light beam in at one point called a focus or image point.