Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water leaks through a hole,

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Suppose Water Is Leaking From A Tank Through A Circular Hole Of Area A At Its Bottom When Water Leaks Through A Hole 1 (64.11 KiB) Viewed 26 times

Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA,√2gh, where c (0 < c < 1) is an empirical constant. 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. (Assume the removed apex of the cone is of negligible height and volume.) (a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. The differential equation governing the height h in feet of water leaking from a tank after t seconds is dh 5 == dt 6h3/2 In this model, friction and contraction of the water at the hole are taken into account with c = 0.6, and g is taken to be 32 ft/s². See the figure below. 8 ft 20 ft h circular hole Solve the initial value problem that assumes the tank is initially full. h(t) = 25t) (3) 800√5 - 12 If the tank is initially full, how long (in minutes) will it take the tank to empty? (Round your answer to two decimal places.) 14.31 minutes (b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 3 inches. Determine the differential equation governing the heighth of water. Use c = 0.6 and g = 32 ft/s². dh dt Solve the initial value problem that assumes the height of the water is initially 10 feet. h(t) = If the height of the water is initially 10 feet, how long (in minutes) will it take the tank to empty? (Round your answer to two decimal places.) minutes Aw