# Answer: Suppose water is leaking from a tank through a circular hole of area Ah at its

**Chapter 1, Problem 13**

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Suppose water is leaking from a tank through a circular hole of area \(A_{h}) at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of the water leaving the tank per second to \(c A_{h} \sqrt{2 g h}), 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 in FIGURE 1.3.12. The radius of the hole is 2 in and \(g=32 \mathrm{ft} / \mathrm{s}^{2}\).

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