Experimental analysis of the free surface of a liquid in a rotating frame

Abstract

The shape of a liquid surface in a rotating frame depends on the angular velocity. In this experiment, a fluid in a narrow rectangular container is placed on a rotating table. A smartphone fixed to the rotating frame records the fluid surface with its camera and, with a built-in gyroscope, the angular velocity. As the table rotates the surface evolves and develops a parabolic shape. Using video analysis we obtain the concavity of the parabola and the height of the vertex. Experimental results are compared with theoretical predictions. This problem contributes to improving the understanding of relevant concepts in fluid dynamics.