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, v Zgh, where c (0
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, v Zgh, where c (0
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
Problem 14P
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![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 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 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
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/s?. See the figure below.
ft
20 ft
'circular hole
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8dfc765-3e19-4ece-b7ca-ad160018d416%2Fca78189a-28a8-4238-bc21-35b8237c33f6%2Fbxqhx3h_processed.jpeg&w=3840&q=75)
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 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 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
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/s?. See the figure below.
ft
20 ft
'circular hole
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
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