Selective Withdrawal from Two-Layer Fluid

The discharge from a stably stratified reservoir is set by a valve, but the quality of the water and the flow pattern near the valve is determined by the interaction of the stratification and the geometry of the reservoir. In a two-layered system this control is at a single section. In previous work in this area the gradually varied flow assumption was made. In this paper it is shown that an alternative assumption, i.e., at the critical section (the virtual control) the velocity field in each layer is radial, with velocities in each layer that are only functions of the radial distance, yields a simple theory. This theory gives, for a particular discharge and given upstream conditions, the ratio of the discharge from each layer. It is applicable to the practical cases where the flow is not gradually varied. Experimental results are presented which support the theory.