A cylindrical tank is 20 feet high with a diameter of 85 feet. With a flow of 6 MGD to the tank, what is the detention time in hours?

To find the detention time of water in a cylindrical tank, you first need to calculate the volume of the tank and then use that to determine how long it takes for a given flow rate to fill the tank.

The volume ( V ) of a cylinder can be calculated using the formula:

[ V = \pi r^2 h ]

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

Given that the diameter is 85 feet, the radius ( r ) is half of that, which is 42.5 feet. The height ( h ) of the tank is 20 feet.

Substituting these values into the volume formula gives:

[

V = \pi (42.5)^2 (20)

]

Calculating ( (42.5)^2 ):

[

(42.5)^2 = 1806.25

]

Now, substituting this into the volume formula:

[

V = \pi \times 1806.25 \times 20 \approx 11342.06 \text{ cubic feet}

]

Next, you need to convert the flow rate from million gallons per day (MGD) to cubic feet per hour