Theoretical analysis of the onset of liquid entrainment for slots of finite width

The onset of liquid entrainment during discharge from large reservoirs containing a stratified mixture of two immiscible fluids through a side slot of a finite width is considered theoretically. A previously reported analysis in which the slot was approximated as a two-dimensional line sink has been extended to account for the finite width of the slot. The model resulting from the present analysis is expressed in terms of two simple algebraic equations suitable for hand calculations. According to the present results, the ratio of the critical height to the slot width is dependent only on the Froude number. Numerical results show that the present model approaches the correct physical limits at low Froude numbers and it converges to the predictions of the previously reported simple model at high Froude numbers.