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 water leaving the tank per second to cA, V 2gh, where c (0

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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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
water leaving the tank per second to cA, V 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 ap
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
seconds is
dh
5
dt
6h 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 be
8 ft
Aw
20 ft
circular hole
Solve the initial value problem that assumes the tank is initially full.
h(t) =
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 water leaving the tank per second to cA, V 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 ap 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 seconds is dh 5 dt 6h 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 be 8 ft Aw 20 ft circular hole Solve the initial value problem that assumes the tank is initially full. h(t) =
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