Consider the draining of a liquid from a tank. The level of the liquid above the bottom of the tank at any instant of time is z. The cross-sectional area of the tank is At. The flow area at the tank exit is Ae. The exit velocity V is given by  V = Cz^1/2, where C is a constant.

A. Derive a differential equation for z(t).

B. Integrate the differential equation to determine the time taken to drain the tank from level z1 to a lower level z₂.