The equation describing the water height h in a spherical
Chapter , Problem 7.61(choose chapter or problem)
The equation describing the water height h in a spherical tank with a drain at the bottom is
\(\pi\left(2 r h-h^{2}\right) \frac{d h}{d t}=-C_{d} A_{o} \sqrt{2 g h}\)
Suppose the tank’s radius is r = 3 m and that the circular drain hole has a radius of 2 cm. Assume that \(C_{d}=0.5\), and that the initial water height is h(0) = 5 m. Use \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\).
a. Use an approximation to estimate how long it takes for the tank to empty.
b. Use MATLAB to solve the nonlinear equation and plot the water height as a function of time until h(t) is not quite zero.
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