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5. A tank in the shape of a cylinder standing on end leaks water through a circular hole in its bottom. If friction is considered, the hcight h of the water in the tank as a function of time is given by A V2gh ´Aw dh dt where Aw and A, are the cross-scctional arcas of the water in the tank and of the hole, respectively, g is the gravitational cocfficient, and 0

5. A tank in the shape of a cylinder standing on end leaks water through a circular hole in its bottom. If friction is considered, the hcight h of the water in the tank as a function of time is given by A V2gh ´Aw dh dt where Aw and A, are the cross-scctional arcas of the water in the tank and of the hole, respectively, g is the gravitational cocfficient, and 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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5. A tank in the shape of a cylinder standing on end leaks water through a circular hole in its bottom. If friction is considered, the height h of the water in the tank as a function of time is given by A 2gh A where Aw and A are the cross-sectional arcas of the water in the tank and of the hole, respectively, g is the gravitational cocfficient, and 0 < c < 1 is a constant. Solve for h(t), given that the initial height of water is H. Sketch the graph of h(t) and give its interval I of dh dt definition in terms of the given initial constats.
Transcribed Image Text:5. A tank in the shape of a cylinder standing on end leaks water through a circular hole in its bottom. If friction is considered, the height h of the water in the tank as a function of time is given by A 2gh A where Aw and A are the cross-sectional arcas of the water in the tank and of the hole, respectively, g is the gravitational cocfficient, and 0 < c < 1 is a constant. Solve for h(t), given that the initial height of water is H. Sketch the graph of h(t) and give its interval I of dh dt definition in terms of the given initial constats.
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