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Bathtub vortex effect on Torricelli's law

A. Caquas1,2, L. R. Pastur1,*, A. Genty2, and P. Gondret3

  • 1Unité de Mécanique, ENSTA Paris, Institut Polytechnique de Paris, Palaiseau, France
  • 2Université Paris-Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, Gif-sur-Yvette F-91191, France
  • 3Université Paris-Saclay, CNRS, Laboratoire FAST, Orsay F-91405, France

  • *Corresponding author: luc.pastur@ensta-paris.fr
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Phys. Rev. Fluids 8, 044702 – Published 25 April, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.044702

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.

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Phys. Rev. Fluids 8, 044702– Published 25 April, 2023
  • Received 27 July 2022
  • Accepted 28 March 2023
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