Suppose water is leaking from a tank through a drcular hole of area A, at its bottom. When water leaks through a hole, friction and Ah2gh, where c (0 < c < 1) is an contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA, 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 radlus 8 feet and the circular hole has radius 2 inches. The differential equation governing the heighth in feet of water leaking from a tank after t seconds is dh dt 5 6/3/2 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 h circular hole G Solve the initial value problem that assumes the tank is initially full. h(t)= If the tank is initially full, how long (in minutes) 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 9-32 ft/s². dh
Suppose water is leaking from a tank through a drcular hole of area A, at its bottom. When water leaks through a hole, friction and Ah2gh, where c (0 < c < 1) is an contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA, 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 radlus 8 feet and the circular hole has radius 2 inches. The differential equation governing the heighth in feet of water leaking from a tank after t seconds is dh dt 5 6/3/2 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 h circular hole G Solve the initial value problem that assumes the tank is initially full. h(t)= If the tank is initially full, how long (in minutes) 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 9-32 ft/s². dh
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 drcular 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 CAV2gh, 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 radlus 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
dt
5
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
G
Solve the initial value problem that assumes the tank is initially full.
h(t)=
If the tank is initially full, how long (in minutes) 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
Solve the initial value problem that assumes the height of the water is initially 11 feet.
h(t)-
If the height of the water is initially 11 feet, how long (in minutes) will it take the tank to empty? (Round your answer to two decimal
places.)
minutes
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