The motion of a cavity in a vertical rotating tube

Abstract

Experiments are performed to measure the upward velocity U of the cavity resulting from the draining of a vertical liquid-filled tube of radius b, which rotates about its axis at various speeds. With no rotation the cavity moves so that the Froude number U/(gb)½ is constant, where g is the gravitational acceleration. For high angular velocities Ω, however, the cavity appears to adopt a constant value of the Rossby number U/Ωb, implying that gravitational forces are dominaked by centrifugal forces. The cavity velocity finally achieved is found to be the same as the maximum group velocity of infinitesimal waves, so that U/Ωb = 0.52. Approximate theoretical models which satisfactorily describe the development of the motion are constructed.