Leaking Conical Tank A tank in the form of a rightcircular cone standing on end, vertex

Chapter 3, Problem 13

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Leaking Conical Tank A tank in the form of a rightcircular 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 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?

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