Withdrawal from a two-layer inviscid fluid in a duct

Abstract

The steady simultaneous withdrawal of two inviscid fluids of different densities in a duct of finite height is considered. The flow is two-dimensional, and the fluids are removed by means of a line sink at some arbitrary position within the duct. It is assumed that the interface between the two fluids is drawn into the sink, and that the flow is uniform far upstream. A numerical method based on an integral equation formulation yields accurate solutions to the problem, and it is shown that under normal operating conditions, there is a solution for each value of the upstream interface height. Numerical solutions suggest that limiting configurations exist, in which the interface is drawn vertically into the sink. The appropriate hydraulic Froude number is derived for this situation, and it is shown that a continuum of solutions exists that are supercritical with respect to this Froude number. An isolated branch of subcritical solutions is also presented.