Free surface of a liquid in a rotating frame with time-depend velocity

TL;DR

This study investigates how a liquid's surface shape in a rotating frame evolves over time, using smartphone video analysis to compare experimental results with theoretical predictions, enhancing understanding in fluid dynamics.

Contribution

It introduces a novel experimental method using smartphone technology to analyze liquid surface shapes in rotating frames, providing empirical validation of theoretical models.

Findings

Surface develops a parabolic shape upon rotation

Experimental measurements match theoretical predictions

Method demonstrates effective use of smartphone sensors in fluid dynamics

Abstract

The shape of liquid surface in a rotating frame depends on the angular velocity. In this experiment, a fluid in a rectangular container with a small width is placed on a rotating table. A smartphone fixed to the rotating frame simultaneously records the fluid surface with the camera and also, thanks to the built-in gyroscope, the angular velocity. When the table starts rotating the surface evolves and develops a parabolic shape. Using video analysis we obtain the surface's shape: concavity of the parabole and height of the vertex. Experimental results are compared with theoretical predictions. This problem contributes to improve the understanding of relevant concepts in fluid dynamics.