How many minutes of detention time will a flow of 8,328 gpm through a cylindrical tank 20 feet high with a diameter of 80 feet allow?

To determine the detention time in a cylindrical tank, we need to calculate the tank's volume and then divide that volume by the flow rate.

Firstly, we start by calculating the volume of the cylindrical tank. The formula for the volume ( V ) of a cylinder is given by:

[

V = \pi r^2 h

]

Where:

• ( r ) is the radius of the cylinder, which can be calculated from the diameter. In this case, the diameter is 80 feet, so the radius ( r ) is 40 feet.

• ( h ) is the height of the cylinder, given as 20 feet.

Now, plugging in the values:

[

V = \pi (40)^2 (20)

]

[

V = \pi (1600) (20)

]

[

V = 32000\pi \text{ cubic feet}

]

Using the approximation ( \pi \approx 3.14 ), we can further refine the volume:

[

V \approx 32000 \times 3.14 \approx 100480 \text{ cubic feet}

]

Next, we need to convert the flow rate from gallons per minute (