Suppose water is leaking from a tank through a circular hole of area A, at its bottom. 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. A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (Assume the removed apex of the cone is of negligible height and volume.) (a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. The differential equation governing the height h in feet of water leaking from a tank after t seconds is dh 5 dt 6h3/2 In this model, friction and contraction of the water at the hole are taken into account with c = 0.6, and g is taken to be 32 ft/s². See the figure below. 8 ft 20 ft circular hole If the tank is initially full, how long will it take the tank to empty? (Round your answer to two decimal places.) minutes (b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 4 inches. Determine the differential equation governing the heighth of water. Use c = 0.6 and g = 32 ft/s². dh dt If the height of the water is initially 10 feet, how long will it take the tank to empty? (Round your answer to two decimal places.) min
Suppose water is leaking from a tank through a circular hole of area A, at its bottom. 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. A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (Assume the removed apex of the cone is of negligible height and volume.) (a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. The differential equation governing the height h in feet of water leaking from a tank after t seconds is dh 5 dt 6h3/2 In this model, friction and contraction of the water at the hole are taken into account with c = 0.6, and g is taken to be 32 ft/s². See the figure below. 8 ft 20 ft circular hole If the tank is initially full, how long will it take the tank to empty? (Round your answer to two decimal places.) minutes (b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 4 inches. Determine the differential equation governing the heighth of water. Use c = 0.6 and g = 32 ft/s². dh dt If the height of the water is initially 10 feet, how long will it take the tank to empty? (Round your answer to two decimal places.) min
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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Transcribed Image Text:Suppose water is leaking from a tank through a circular hole of area A, at its bottom. 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.
A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom.
(Assume the removed apex of the cone is of negligible height and volume.)
(a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. The differential equation
governing the height h in feet of water leaking from a tank after t seconds is
dh
5
dt
6h3/2
In this model, friction and contraction of the water at the hole are taken into account with c = 0.6, and g is taken to be
32 ft/s². See the figure below.
8 ft
20 ft
circular hole
If the tank is initially full, how long will it take the tank to empty? (Round your answer to two decimal places.)
minutes
(b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 4 inches. Determine the differential equation
governing the heighth of water. Use c = 0.6 and g = 32 ft/s².
dh
dt
If the height of the water is initially 10 feet, how long will it take the tank to empty? (Round your answer to two decimal
places.)
min
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