Theoretical analysis of the onset of liquid entrainment for orifices of finite diameter

Abstract

The onset of liquid entrainment during discharge from large reservoirs containing a stratified mixture of two immiscible fluids through a side orifice of finite diameter is considered theoretically. A previously reported analysis by Craya, in which the orifice was simulated by a point sink, has been extended to account for the finite size of the orifice. The model resulting from the present analysis is expressed in terms of two simple equations suitable for hand calculations. The ratio of the critical height to the orifice diameter is found to be dependent only on Froude number (Fr). The present model approaches the correct physical limits at low Fr and it converges to Craya's predictions at high Fr. Some experimental verification of the present theoretical trends is also provided.