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bottom. If friction is considered, the height h of the water in the tank as a function of time is given by Ah 2gh dh dt ´Au where Aw and Ap are the cross-sectional areas of the water in the tank and of the hole, respectively, g is the gravitational coefficient, 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 definition in terms of the given initial constants.

bottom. If friction is considered, the height h of the water in the tank as a function of time is given by Ah 2gh dh dt ´Au where Aw and Ap are the cross-sectional areas of the water in the tank and of the hole, respectively, g is the gravitational coefficient, 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 definition in terms of the given initial constants.

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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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 dh An 2gh Aw where Au and An are the cross-sectional areas of the water in the tank and of the hole, respectively, g is the gravitational coefficient, 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 dt definition in terms of the given initial constants.
Transcribed Image Text: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 dh An 2gh Aw where Au and An are the cross-sectional areas of the water in the tank and of the hole, respectively, g is the gravitational coefficient, 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 dt definition in terms of the given initial constants.
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