A detention pond is required to hold 0.7 ac-ft. The bottom of the pond is a square with dimension of 30' x 30'. If two opposing sides are vertical, and the other two sides are 1:1 (H:V), find the minimum required detention depth. Ignore the freeboard.

minimum required detention depth is 20.233 ft

Explanation:

given data

volume = 0.7 ac-ft = 0.7 * 43560 ft = 30492 ft³

dimension = 30' x 30'

two sides = 1:1 (H:V)

solution

we get here area of square = 30 * 30

area = 900 ft²

we consider height is y

so volume will be triangular volume

v2 = 2 * { 0.5 * y² * 30 }

v2 = 30y²

and volume = area * height

v1 = 900 y

so total volume v1 + v2

total volume = 900 y + 30y²

30492 = 900 y + 30y²

y = 20.233 ft

so minimum required detention depth is 20.233 ft