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, v Zgh, where c (0

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Chapter6: Topics In Analytic Geometry
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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, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cAV2gh, 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
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/s?. See the figure below.
ft
20 ft
'circular hole
Solve the initial value problem that assumes the tank is initially full.
h(t) =
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
Transcribed Image Text: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 <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 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/s?. See the figure below. ft 20 ft 'circular hole Solve the initial value problem that assumes the tank is initially full. h(t) = 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
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