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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 volum water leaving the tank per second to cA, V2gh, 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 volum water leaving the tank per second to cA, V2gh, 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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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/s? dh dt 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
Transcribed Image Text: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/s? dh dt 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
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 water leaving the tank per second to cA, V2gh, 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 seconds is dh = - dt 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. 8ft 20 ft `circular hole Solve the initial value problem that assumes the tank is initially full. h(t) =
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 water leaving the tank per second to cA, V2gh, 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 seconds is dh = - dt 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. 8ft 20 ft `circular hole Solve the initial value problem that assumes the tank is initially full. h(t) =
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