Here are the answers to today’s practice problem.    

1. If a pump tank has the following dimensions — 42 inches by 60 inches by 58 inches deep — what are the gallons per inch? What is the volume of the tank?
For gallons per inch, we need to determine the volume in cubic feet of a 1-foot depth in the tank. Divide by 12 to get the volume for an inch of depth, and then multiply by 7.5 gallons per cubic foot to come up with the gallons per inch.

Remember: You first have to convert the measurements in inches to feet.

So: 42 inches ÷ 12 inches per foot = 3.5 feet; 60 ÷ 12 = 5.0 feet; and 58 ÷ 12 = 4.8 feet

We then calculate the volume: 3.5 feet x 5.0 feet x 1.0 feet/12 inches = 17.5 cubic feet/12 inches. Then we multiply by 7.5 gallons per cubic foot.

17.5 cubic feet ÷ 12 = 1.4 cubic feet/inch x 7.5 gallons/cubic foot = 10.9 gallons per inch since the cubic feet cancel and we are left with gallons per inch.

Volume of the tank is 3.5 feet x 5.0 feet x 4.8 feet = 84 cubic feet x 7.5 gallon per cubic foot = 630 gallons

2. If an off float is set 52 inches from a surface reference point and the on float is activated at a depth of 46 inches, what is the dose volume?
If the floats are 6 inches apart, then the dose volume is 6 inches x 10.9 gallons per inch. The inches cancel and we are left with 65.4 gallons for the dose volume.

3. From the reference point, where should the high-water alarm float be set?
This depends on the swing of the float on the float tree, but at a minimum, it is 3 inches. So from the reference point at the surface, it would be 43 inches from the surface.

4. If there is 6 inches of sludge in the tank, what does this tell us?
If there is sludge in the tank, solids are getting through and the septic tank should be pumped more often. If there is scum in the pump tank, it means there is something wrong with the outlet baffle of the septic tank.

5. If we factor in an 18-inch depth to cover the pump, is the tank still large enough?
To determine if the tank is large enough, we need to add the inches required to keep the pump covered (18 inches) plus the 6 inches for the required dose plus the 3 inches for the alarm float. This equals a total of 27 inches in the 48-inch depth tank, so it is large enough to accommodate the required volume. It would require different depths from the reference point to the where the floats are set.

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

• Onsite Arithmetic: A Basic Tank Problem
• Onsite Arithmetic: A Cylindrical Tank Problem
• Onsite Arithmetic: Pump Tank Math
• Onsite Arithmetic: Setting Alarm Floats
• Onsite Arithmetic: O&M Problem