Abstract
When emptying a water filled container through a bottom hole, a ``bathtub vortex'' may appear and deform the free surface. Torricelli's law, which predicts the flow rate as a function of the water height, has been known for 400 years, but deviations are observed in the presence of such a vortex. This study focuses on the impact of the bathtub vortex on the emptying velocity. Through an experiment on the unsteady draining flow in a rotating tank, we show that Torricelli's law is modified as a function of the surface deformation, and that the draining time is mainly determined by a nondimensional parameter corresponding to the ratio of the outlet size to the Ekman boundary layer thickness.
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