Bathtub vortex effect on Torricelli's law

Abstract

We investigate experimentally the unsteady draining flow from a rotating tank. The fluid in the tank is first set in solid rotation, before the draining hole is opened. We show that the draining may be drastically reduced by the rotation, as the vortex circulation increases together with the surface deformation. We demonstrate that the usual Torricelli's draining law has to be modified with the surface deformation and that the draining time is mainly governed by a nondimensional parameter corresponding to the ratio of the size of the outlet to the thickness of the Ekman boundary layer.