Reference no: EM13519424

A tall, cylindrical tank is being filled, from an initially empty state, by a constant inflow of q liters/sec of liquid. The flat tank bottom has corroded and sustains a leak through a small hole of area A0. If the cross-sectional area of the tank is denoted by A, and time-varying height of liquid is h(t), then: (a) find the dynamic relationship describing tank height, if the volumet- ric leak rate obeys Torricelli's law, q0 = Aoy/2gh(t) (g is gravita- tional acceleration). (b) determine the relationship to predict the final steady-state liquid height in the tank. (c) define x = y/h , separate variables and deduce the implicit solution for h:
(d) sketch the curve for h versus t, and compare with the case for a nonleaking tank.