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There is a vertical tube, which narrows into smaller tube part of the way down, it is filled with an inviscid, incompressible and irrotational fluid. The bottom/outlet of the tube is at z=0, where the cross-sectional area is represented by A0 and the fluid's speed by q1. The top of the tube is at z=1, the top level of the liquid is at h(t), where t is time, the cross-sectional area of the liquid level is A1 and the speed it is falling at is q0. The pressure is the same at both ends of the tube.

I need to find out how long it takes for the tube to empty under gravity, using Bernoulli's equation, and assuming the flow is approximately steady.

Any help would be appreciated, if any more information is required I will reply asap. Thanks