Chapter 6, Problem 5PS

Torricelli’s Law Torricelli’s Law states that water will flow from an opening at the bottom of a tank with the same speed that it would attain falling from the surface of the water to the opening. One of the forms of Torricelli’s Law is

$A(h)\frac{dh}{dt}=-k\sqrt{2gh}$

where h is the height of the water in the tank, k is the area of the opening at the bottom of the tank, A(h) is the horizontal cross-sectional area at height h, and g is the acceleration due to gravity ( $g\approx 32$ feet per second per second). A hemispherical water tank has a radius of 6 feet. When the tank is full, a circular valve with a radius of 1 inch is opened at the bottom, as shown in the figure. How long will it take for the tank to drain completely?