Water enters a vertical cylindrical tank of cross-sectional area 0.01 m2 at a constant mass flow rate of 5 kg/s. It leaves the tank through an exit near the base with a mass flow rate given by the formula 0.2h kg/s, where h is the instantaneous height in m. If the tank is initially empty,
(a) Develop an expression for the liquid height h as a function of time t.
(b) How long does it take for the water to reach a height of 10 m? Assume density of water to remain constant at 1000 kg/m3.