Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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A tank in the form of a right-circular cylinder standing on end is leaking water through a hole in its bottom. When friction is ignored, the rate of change of the height of the water in the tank is given by this equation: h'(t) = -r²V64.3h where h is the height of the water in feet, t is the time in seconds, and r is the ratio of the hole diameter to the tank diameter. Part A: Solve the Initial Value Problem when r = 0.1 and h(0) = 6. Part B: Given the IVP in Part A, how long will it take the tank to drain completely?
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Transcribed Image Text:A tank in the form of a right-circular cylinder standing on end is leaking water through a hole in its bottom. When friction is ignored, the rate of change of the height of the water in the tank is given by this equation: h'(t) = -r²V64.3h where h is the height of the water in feet, t is the time in seconds, and r is the ratio of the hole diameter to the tank diameter. Part A: Solve the Initial Value Problem when r = 0.1 and h(0) = 6. Part B: Given the IVP in Part A, how long will it take the tank to drain completely?
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