The equation describing the water height h in a spherical tank with a drain at the bottom
Question:
π(2rh - h2) dh/dt = -CdAo√(2gh)
Suppose the tank's radius is r = 3 m and that the circular drain hole has a radius of 2 cm. Assume that Cd = 0.5, and that the initial water height is h(0) = 5 m. Use g = 9.81 m/s2.
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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For the given values C d A 052 10 2 2 2 10 4 and the differential equation is 6h h 2 dhdt 2 10 4 196...View the full answer
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