What is the detention time in minutes for a basin that is 15ft in diameter and 12ft deep treating a flow of 0.532 mgd?

To determine the detention time for a basin, the formula to use is:

[ \text{Detention Time (minutes)} = \frac{\text{Volume of the Basin (gallons)}}{\text{Flow Rate (gallons per minute)}} ]

First, calculate the volume of the basin. The volume of a cylindrical basin can be calculated using the formula:

[ \text{Volume} = \pi \times r^2 \times h ]

where ( r ) is the radius and ( h ) is the height (or depth).

In this case, the diameter is 15 feet, so the radius will be:

[ r = \frac{15 \text{ ft}}{2} = 7.5 \text{ ft} ]

The depth of the basin is:

[ h = 12 \text{ ft} ]

Using these dimensions in the volume formula:

[ \text{Volume} = \pi \times (7.5)^2 \times 12 ]

Calculating the area first:

[ r^2 = 7.5^2 = 56.25 ]

So,

[ \text{Volume} = \pi \times 56.