A conical tank of base diameter D and height H is suspended in an inverted position to hold water. A leak at the apex of the cone causes water to leave with a mass flow rate of c*sqrt(h), where c is a constant and h is the height of the water level from the leak at the bottom.
(a) Determine the rate of change of height h.
(b) Express h as a function of time t and other known constants, ρ (constant density of water), D, H, and c if the tank were completely full at t = 0.
(c) If D= 1 m, H=1 m, ρ = 1000 kg/m3, and c = 1 kg/(s.m1/2), how long does it take for the tank to empty?