Chapter 4.3, Problem 154E

Torricelli’s law states that for a water tank with a hole in the bottom that has a cross-section of A and with a height of water ii above the bottom of the tank, the rate of change of volume of water flowing from the tank is proportional to the square root of the height of water, according to

$\frac{dV}{dt}=-A\sqrt{2gh}$, where g is the acceleration due to gravity. Note that $\frac{dV}{dt}=A\frac{dh}{dt}$. Solve the resulting initial-value problem for the height of the water, assuming a tank with a hole of radius 2 ft. The initial height of water is 100 ft.