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A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the heighth of water in the tank in feet after t seconds is described by -Ah-√2gh, dt where A and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition terms of the symbols Aw A and H. Use g = 32 ft/s². h(t) = Osts

A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the heighth of water in the tank in feet after t seconds is described by -Ah-√2gh, dt where A and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition terms of the symbols Aw A and H. Use g = 32 ft/s². h(t) = Osts

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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3.2-3

By hand, sketch the graph of h(t). h H/2) h H h sec H h H/2 (b) Suppose the tank is 12 ft high and has radius 3 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.)
Transcribed Image Text:By hand, sketch the graph of h(t). h H/2) h H h sec H h H/2 (b) Suppose the tank is 12 ft high and has radius 3 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.)
A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the heighth of water in the tank in feet after t seconds is described by dh dt Ap Aw -√2gh, where Aw and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Aw Ar and H. Use g = 32 ft/s². h(t) = ost≤
Transcribed Image Text:A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the heighth of water in the tank in feet after t seconds is described by dh dt Ap Aw -√2gh, where Aw and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Aw Ar and H. Use g = 32 ft/s². h(t) = ost≤
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A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the heighth of water in the tank in feet after t seconds is described by dh dt Ap Aw -√2gh, where Aw and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Aw Ar and H. Use g = 32 ft/s². h(t) = osts
Transcribed Image Text:A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the heighth of water in the tank in feet after t seconds is described by dh dt Ap Aw -√2gh, where Aw and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Aw Ar and H. Use g = 32 ft/s². h(t) = osts
By hand, sketch the graph of h(t). h H/2) h H h sec H h H/2 (b) Suppose the tank is 12 ft high and has radius 3 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.)
Transcribed Image Text:By hand, sketch the graph of h(t). h H/2) h H h sec H h H/2 (b) Suppose the tank is 12 ft high and has radius 3 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.)
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