Inverted Conical Tank Suppose that the conical tank in Problem 13(a) is inverted, as...

Inverted Conical Tank Suppose that the conical tank in Problem 13(a) is inverted, as shown in Figure 3.2.5, and that water leaks out a circular hole of radius 2 inches in the center of its circular base. Is the time it takes to empty a full tank the same as for the tank with vertex down in Problem 13? Take the friction/contraction coefficient to be c = 0.6 and g = 32 ft/s².

(reference problem 13)

Leaking Conical Tank 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 8 feet 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

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 Figure 1.3.12. 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 = 32 ft/s². If the height of the water is initially 9 feet, how long will it take the tank to empty?