Apond drains through a pipe as shown in Fig. P20.21. Under a number of simplifying assumpt...

Apond drains through a pipe as shown in Fig. P20.21. Under a number of simplifying assumptions, the following differential equation describes how depth changes with time:

FIGURE P20.21

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 e = 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 = 1m.