Onsite Arithmetic: A Cylindrical Tank Problem – Answers

Onsite Arithmetic: A Cylindrical Tank Problem – Answers

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Here are the answers to this month's practice problem

I have a cylindrical (round) tank that has a diameter of 6 feet and is 5.5 feet deep below the invert of the outlet. (Hint: remember )

1. What is the operating volume in gallons?

For the volume of a cylindrical (round) tank, calculate the area of a circle multiplied by the depth.

So,  gives the area of a circle, and then we multiply that by the depth to get the volume in cubic feet. We then multiply that by our magic number of 7.5 gallons per cubic foot to give us the answer. The value for pi is 3.14, and the radius is half the diameter, so it is 3 feet.

Operating volume in gallons: 3.14 x 3 feet x 3 feet x 5.5 feet x 7.5 gallons per cubic feet = 1,166 gallons for the operating volume

2. What are the gallons per inch?

For gallons per inch, take the area of the circle and multiply it by 1 foot per 12 inches and 7.5 gallons per cubic feet.

Area of a circle: 3.14 x 3 feet x 3 feet = 28.26 square feet

Gallons per inch: 28.26 square feet x 1 foot/12 inches = 28.26 cubic feet per 12 inches = 2.35 cubic feet per inch x 7.5 gallons per cubic foot = 17.6 gallons per inch because the cubic feet cancel out

3. If the flow is 600 gallons, is it large enough?

The tank is not large enough to be a septic tank for a flow of 600 gallons per day because there is less than two days of detention time, which is the required detention time for a septic tank. Based on the estimated daily sewage flow, the tank volume required is 1,200 gallons.

4. If sludge plus scum equals 15 inches, does it need to be pumped? 

The tank is 5.5 feet deep, which equals 66 inches.

Current percent of the tank: 15 inches ÷ 66 inches x 100 = 22.7 percent

If it was a septic tank, it would not quite be at the 25 percent to pump; however, since it is close, I would talk to the homeowner about pumping the tank. With a maintenance frequency of every three years, the tank's sludge and scum levels will be well beyond the need for pumping by the next required visit, so I may suggest revisiting in a year as it should need pumping by that time.

Assuming that it has been three years since the last visit, it has gained an average of 5 inches per year. By next year, the combined depth will be 20 inches and the tank will need pumping. 

Percent of the tank by next year: 20 inches ÷ 66 inches x 100 = 30 percent

This article is part of a series of practice problems for installers:


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