Here are the answers to today's practice problem. 

1. If the pump tank is 50-by-60-by-72 inches deep, calculate the gallons per inch.

Convert length and width to feet.

(50 inches ÷ 12 inches per foot) = 4.2 feet
(60 inches ÷ 12 inches per foot) = 5 feet
(72 inches ÷ 12 inches per foot) = 6 feet

Calculate volume (cubic feet) in 1 foot of depth.

4.2 feet x 5 feet x 1.0 foot = 21 cubic feet

Convert to volume in gallons.

21 cubic feet x 7.5 gallons per cubic foot = 157.5 gallons per foot

Calculate gallons per inch.

157.5 gallons per foot ÷ 12 inches per foot = 13.1 gallons per inch

Volume of the tank is 4.2 feet x 5 feet x 6 feet = 126 cubic feet x 7.5 gallons per cubic foot = 945 gallons

Or take 13.1 gallons per inch x 72 inches = 943.2 gallons (The same answer considering rounding during calculation.)

2. The off float is at 54 inches and the on float activation is at 47 inches, measured from a reference point at the surface. What is the dose volume?

Subtract off minus on.

54 inches – 47 inches = 7 inches

Multiply total inches by gallons per inch: 7 inches x 13.1 gallons per inch = 91.7 (or 92 gallons)

3. If the supply line is 100 feet of 2-inch Schedule 40 PVC, what is the drainback volume in gallons?

Calculating drainback requires knowledge of the gallons per foot in a 2-inch PVC pipe. This can be obtained from tables available through pipe supply companies or calculating the volume of a cylinder by taking the area of a circle times the length of the pipe — much easier to look it up on a table. In the table, we found that the gallons per foot of 2-inch PVC pipe is 0.17 gallons per foot.

0.17 gallons per foot x 100 feet = 17 gallons

4. If the cycle counter on the pump reads 46,490 today and read 45,900 on the last visit 120 days ago, what is the number of cycles recorded?

PCR – LCR = number of cycles

46,490 – 45,900 = 590 cycles 

5. What is the total flow and average flow for the 120 days?

Calculate total flow: 590 cycles x 92 gallons per cycle = 54,280 gallons

Calculate average daily flow: 54,280 gallons ÷ 120 days = 452 gallons per day 

6. If the design flow was 300 gallons per day for the system, what does this tell you?

The system is exceeding design flow by 152 gpd. Over the entire 120 days, the total average is 120 days x 41 gallons per day = 4,920 gallons of additional flow; the system will eventually break if this continues.

First check for leaks and extra water sources such as runoff, inflow, etc., and if there are no plumbing leaks, look at flow reduction options or enlarging the system.

Additional Problems:

1. What is wrong with how I calculated the average daily flow?

2. Would that change what you think about how this system is operating?

Answers:

1. What is wrong with how I calculated the average daily flow?

I did not consider the drainback each time the pump ran. It is approximately 17 gallons each time, so:

92 gallons – drainback of 17 gallons = 75 gallons actually delivered to the system

Total flow then becomes 590 cycles x 75 gallons per cycle = 44,250 gallons delivered

Average daily flow becomes 44,250 gallons ÷ 120 days = 369 gallons per day

2. Would that change what you think about how this system is operating?

The average flow still exceeds design flow by 69 gallons per day, so it would not change the thinking that the system is headed for failure and steps need to be taken to reduce the flow rate or enlarge the capacity of the system to accommodate the flow.

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