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 (31.67 KiB) Viewed 34 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 CAV2gh, where c (0<<< 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 6 feet and the circular hole has radius 2 inches. The differential equation governing the height in feet of water leaking from a tank after t seconds is dh dr h(t)= GANE 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 dh of 8A Solve the initial value problem that assumes the tank is initially full -(800/15-22) (5) 20 A h MY NE circular hole If the tank is initially full, how long (in minutes) will it take the tank to empty? (Round your answer to two decimal places.) 1431 minutes 016 h² (b) Suppose the tank has a vertex angle of 60 and the circular hole has radius 4 inches. Determine the differential equation governing the height hy of water Use c- 0.6 and 9-32 ft/s² Solve the initial value problem that assumes the height of the water is initially 11 feet h(t)= If the height of the water is initially 11 feet, how long (in minutes) will it take the tank to empty? (Round your answer to two decimal places) minutes