Concept explainers
Leaking cylindrical tank—continued When friction and contraction of the water at the hole are taken into account, the model in Problem 11 becomes
where 0 < c < 1. How long will it take the tank in Problem 11(b) to empty if c = 0.6? See Problem 13 in Exercises 1.3.
11. Leaking cylindrical tank A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the height h of water in the tank is described by
where Aw and Ah are the cross-sectional areas of the water and the hole, respectively.
(b) Suppose the tank is 10 feet high and has radius 2 feet and the circular hole has radius
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Chapter 3 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
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