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he right-circular conical tank shown in the figure below loses water out of a circular hole of area Ah at its bottom. dh dt 8 ft 45√h 8 When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA√2gh, where c (0 < c < 1) is an empirical constant. Determine a differential equation for the height of the water h at time t > 0. The radius of the hole is 5 in., g = 32 ft/s2, and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) X 20 ft h circular hole ft/s

he right-circular conical tank shown in the figure below loses water out of a circular hole of area Ah at its bottom. dh dt 8 ft 45√h 8 When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA√2gh, where c (0 < c < 1) is an empirical constant. Determine a differential equation for the height of the water h at time t > 0. The radius of the hole is 5 in., g = 32 ft/s2, and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) X 20 ft h circular hole ft/s

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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The right-circular conical tank shown in the figure below loses water out of a circular hole of area A₁ at its bottom. dh dt 8 ft 45√h 8 Aw When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cAn2gh, where c (0 < c < 1) is an empirical constant. Determine a differential equation for the height of the water h at time t > 0. The radius of the hole is 5 in., g = 32 ft/s², and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) 20 ft circular hole ft/s
Transcribed Image Text:The right-circular conical tank shown in the figure below loses water out of a circular hole of area A₁ at its bottom. dh dt 8 ft 45√h 8 Aw When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cAn2gh, where c (0 < c < 1) is an empirical constant. Determine a differential equation for the height of the water h at time t > 0. The radius of the hole is 5 in., g = 32 ft/s², and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) 20 ft circular hole ft/s
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