During the course of an experimental research, a tall cylindrical tank which was initially empty has to be filled with liquid at a constant inflow of m lit/sec. Unfortunately, the flat tank bottom has been corroded and has a small hole of area A0, and therefore sustains a leak (at a rate, r0 lit/sec) as filling continued. If the cross-sectional area of the tank is A and the time-varying height is h(t), then:
A.Obtain the dynamic relationship describing the tank height if the leak rate obeys Torricelli's law, r0=A0√{2gh(t)},where g is acceleration due to gravity. Hint: This is easily done by considering the unsteady-state mass balance on the tank.
B.This research is being done by a smart student who knows that even in the presence of such a 'real life' problem, it is still possible to obtain a final steady-state liquid height in the tank. Suppose you were this smart student, determine the expression to predict the final steady-state liquid height, hss.