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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 cAV 2gh, 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 cAV 2gh, where c (0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Question
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 < < < 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 5 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. dh dt = - dh == dt 8 ft Aw -0.6. i If the tank is initially full, how long 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 4 inches. Determine the differential equation governing the heighth of water. Use c = 0.6 and g = 32 ft/s². 42 12 20 ft circular hole π 1² 3 -√64h If the height of the water is initially 10 feet, how long will it take the tank to empty? (Round your answer to two decimal places.) X min
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 cA√ 2gh, 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 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 5 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. dh dt = - dh == dt 8 ft Aw -0.6. i If the tank is initially full, how long 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 4 inches. Determine the differential equation governing the heighth of water. Use c = 0.6 and g = 32 ft/s². 42 12 20 ft circular hole π 1² 3 -√64h If the height of the water is initially 10 feet, how long will it take the tank to empty? (Round your answer to two decimal places.) X min
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