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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 CA, v Zgh, where c (0

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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