Simple Septic Math

Brush up on your math skills with some basic septic practice problems
Simple Septic Math

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There are a couple basic tank characteristics that are necessary to know when maintaining septic and pump tanks. To determine them in the field requires the use of some basic math to determine areas and volumes. Below is an example of those basic calculations and what can be determined once those values are known.

Let’s say I wanted to know the approximate volume of a rectangular septic tank. With my tape measure I find the tank is 62 inches wide, 90 inches long and 70 inches deep below the outlet baffle. How do I calculate the tank volume? The general formula to determine the volume of a rectangular tank is length x width x depth x 7.5 gallons per cubic foot. Since I measured below the outlet invert at the outlet baffle this is the operating volume of the tank.

There is more than one way to calculate the volume but here is the way I do it:

First the inches must be converted to feet; this is done by dividing the inches by 12 inches per foot to give us the answer in feet.

So, 62 inches divided by 12 inches equals 5.16 feet; 90 inches divided by 12 inches equals 7.5 feet; and 70 inches divided by 12 inches equals 5.83 feet.

To get the volume one multiplies 5.16 feet x 7.5 feet x 5.83 feet  = 225.62 cubic feet.

So the volume of the tank is 225 cubic feet. How many of us measure volumes in terms of cubic feet? The answer is only an engineer. So we need to convert cubic feet to gallons.

For wastewater there is a very important conversion factor that we always should remember: there are 7.48 gallons in a cubic foot. (This is usually rounded to 7.5 to give us an estimate.)

To determine the volume in gallons we multiply 225 cubic feet by 7.5 gallons per cubic foot to give us a tank operating volume of 1,687 gallons. Hopefully your tanks have more even dimensions than this example!

Another important calculation is how many gallons are in an inch of the tank. This is a similar calculation where we need to find the volume of 1 inch of depth in the tank. So, we convert our numbers to feet as above except now instead of 70 inches of depth we are only interested in 1 inch of depth. The formula is length (feet) x width (feet) x 1 foot x 7.5 gallons, which is the volume for 1-foot depth. To find the volume for 1 inch I divide the volume by 12 to give me gallons per inch. For our example this is 5.16 feet x 7.5 feet x 1.0 foot x 7.5 gallons per cubic foot = 290.2 gallons. When I divide by 12 inches the result is 24.18 gallons per inch.

These numbers can help us make some other determinations in the field.

For instance, if I am checking for detention time in the tank and I know from my code we want two days and I know that the flow is 400 gallons per day then it is easy to check; in this case I divide my tank operating volume of 1,687 gallons by 400 gallons per day to get my answer in days of detention time. In this case when I do the division I get 4.2 days, well over my necessary detention time according to the code.

Just based on the depth of sludge and scum I can determine if the tank should be pumped. The general criteria is if the tank has a combined sludge and scum depth more than 25 percent of the tank operating depth, it should be pumped. So if I measured 6 inches of scum and 16 inches of sludge the total would be 22 inches. To determine the percentage I divide 22 inches by 70 inches x 100, which equals 31.4 percent; so this tank should be pumped because it is more than 25 percent.

About the Author
Jim Anderson is connected with the University of Minnesota onsite wastewater treatment education program, is an emeritus professor in the university’s Department of Soil Water and Climate, and education coordinator for the National Association of Wastewater Technicians. Send him questions about septic system maintenance and operation by email to kim.peterson@colepublishing.com.

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



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