A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom.

(a) Suppose the tank is 20 feet high and has radius 8feet and the circular hole has radius 2 inches.In Problem 14 in Exercises 1.3 you were asked to show that the differential equation governing the height h of water leaking from a tank is

dh/dt = - 5/6h^3/2.

In this model, friction and contraction of the water at the hole were taken into account with c = 0.6, and g was taken to be 32 ft/s². See the following. If the tank is initially full, how long will it take the tank to empty?

(b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 2 inches. Determine the differential equation governing the height h of water. Use c = 0.6 and g 5 32 ft/s². If the height of the water is initially 9 feet, how long will it take the tank to empty?

Transcribed Image Text:

10 ft circular hole