When friction and contraction of the water at the hole are taken into account, the model in
Question:
dh/dt = -c Ah/Aw 2gh,
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.
Data from problem 13 (Exercise 1.3)
Suppose water is leaking from a tank through a circular hole of area Ah 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 secondto cAh2gh, where c (0 < c < 1) is an empirical constant. Determine a differential equation for the height h of water at time t for the cubical tank shown in the following figure. The radius of the hole is 2 in., and g = 32 ft/s2.
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Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
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