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 (32.28 KiB) Viewed 41 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 heighth in feet of water leaking from a tank after t seconds is dh dt 5 63/2 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/s? See the figure below. h(t)- 8 ft 20 ft h circular hole Solve the initial value problem that assumes the tank is initially full. If the tank is initially full, how long (in minutes) will it take the tank to empty? (Round your answer to two decimal places.) 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 8 feet. F(x)= If the height of the water is initially 8 feet, how long (in minutes) will it take the tank to empty? (Round your answer to two decimal places.) minutes