Project: A Cylindrical Tank Problem Consider an open cylindrical tank of height h0 mete...

Project: A Cylindrical Tank Problem

Consider an open cylindrical tank of height h0 meters and radius r meters that is filled with water. A circular hole of radius l meters in the bottom of the tank allows the water to flow out under the influence of gravity. According to Torricelli’s law, the water flows out with the same speed that it would acquire in falling freely from the water level in the tank to the hole.

By making an appropriate change of variables in the differential equation (1.12.7), derive a differential equation for the concentration c(t) of chemical in the tank at time t . Solve your differential equation and verify that you get the same expression for c(t) as you do by dividing the expression for A(t) obtained in the previous problem by V (t).