Suppose that r = f(h) defines the shape of a water clock for which the time marks

Question:

Suppose that r = f(h) defines the shape of a water clock for which the time marks are equally spaced. Use the differential equation in Problem 12 to find f(h) and sketch a typical graph of h as a function of r. Assume that the cross-sectional area A_h of the hole is constant.

Data from problem 12

dh/dt = -c A_h/A_w √2gh,