A pond drains through a pipe as shown in Figure. Under a number of simplifying assumptions, the following differential equation describes how depth changes with time:

dh/dt = πd²/4A(h) √2g(h + e)

where h = depth (m), t = time (s), d = pipe diameter (m), A(h) = pond surface area as a function of depth (m²), g = gravitational constant (= 9.81 m/s²), and c = depth of pipe outlet below the pond bottom (m). Based on the following area-depth table, solve this differential equation to determine how long it takes for the pond to empty given that h (0) = 6 m, d = 0.25 m, e = 1 m.

Transcribed Image Text:

h, m 5 4 3 1 A(h), 10* m 1.17 0.97 0.67 0.45 0.32 0.18 0