Draining of a Manhole

Estimate the time it takes to drain a 4 ft diameter manhole (inside diameter) that is filled with 2 ft of water through a 2 in drain hole at the bottom.

Applying Bernoulli's equation and assuming the velocity at the top of the water (point 1) is close to zero and therefore, negligible:

p₁ and p₂ are both p_atm, so they cancel

h is a variable, Q_out decreases as h decreases

At t = 0 s, h = 2 ft, hence c = 203.0

Solve for t when h = 0

It takes about 203 seconds to drain the manhole.