Accurate numerical solutions to the problem of finding the location of the interface between two unconfined regions of fluid of different density during the withdrawal process are presented. Supercritical flows are considered, in which the interface is drawn directly into the sink. As the flow rate is reduced, the interface enters the sink more steeply, until the solution method breaks down just before the interface enters the sink vertically from above, and becomes flow from the lower layer only. This lower bound on supercritical flow is compared with the upper bound on single-layer (free surface) flow with good agreement.
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