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Pool & Spa
Mathematics Quiz


1. Basic swimming pool mathematics is critical for which of the following processes?
a. chemical dosing
b. pump and filter sizing
c. heater sizing
d. all of the above

The following questions are based on a community pool with the following dimensions:
The rectangular pool is 42’ wide x 75’ long (non-diving pool). The pool shallow depth is 3’ and has a continuous slope to 6’ in the deep end.

2. Calculate the surface area.
a. 3,000 sq. ft.
b. 3,300 sq. ft
c. 3,150 sq. ft.
d. 2,575 sq. ft.
3. Calculate the volume
a. 106,312.5 gallons
b. 90,000 gallons
c. 125,000 gallons
d. not enough information

4. The local codes require a turnover rate of 6 hours. What is the flow rate (answer to the closest whole number)?
a. 250 gpm
b. 1,771 gpm
c. 350 gpm
d. 295 gpm

5. The filtration system is a high-rate sand filter. A local code requires a filter media rate of 15 gallons per minute per sq. ft. What is the minimum required sq. ft. of filter surface area (closest whole number)?
a. 20 sq. ft.
b. 23 sq. ft.
c. 17 sq. ft
d. 25 sq. ft.

6. A pool has a volume of 45,000 gallons with a turnover rate of 5 hours. What is the flow rate?
a. 750 gpm
b. 150 gpm
c. 300 gpm
d. 125 gpm

7. Based on Question 6, what is the required filter media rate if the filter media is diatomaceous earth?
a. 300 sq.ft.
b. 150 sq. ft.
c. 1,500 sq. ft.
d. 75 sq. ft.

8. A public spa has a diameter of 12’ and an average depth of 3’. What is the volume?
a. 1,130 gallons
b. 2,543 gallons
c. 3,391 gallons
d. 847 gallons

9. Bather load for spas is based on 10 sq. ft. per person. What is the maximum number of bathers in the above spa?
a. 25 people
b. 11 people
c. 16 people
d. 8 people

10. Local code mandates a 30-minute turnover for the above spa. What is the flow rate?
a. 38 gpm
b. 113 gpm
c. 85 gpm
d. 33.9 gpm

11. What is the minimum required cartridge filter surface area for the above spa?
a. 142.5 sq. ft.
b. 32 sq. ft.
c. 227 sq. ft.
d. 53.125 sq. ft.

12. A pool contains 100,000 gallons and a local code requires a 6 hour turnover. The flowmeter reads 225 gpm. Is the pool operation meeting minimum requirements?
a. yes
b. no

13. How much does 1 gallon of water weigh?
a. 8.33 lbs.
b. 7.5 lbs.
c. 10 lbs.
d. 9 lbs.

14. One BTU will heat one pound of water one degree. How many BTUs will it take to heat a 1,000-gallon spa 10 degrees?
a. 75,000 BTUs
b. 83,300 BTUs
c. 166,000 BTUs
d. none of the above

15. Convert the answer in Question 14 to Kilowatts.
a. 24.4 kW
b. 283,196 kW
c. 50 kW
d. 22 kW

16. A pool contains 80,000 gallons, and it has been determined that the Total Alkalinity needs to be raised 40 ppm. The chemical dosage rate using Bicarbonate of Soda is 1.4 lbs., which will raise 10,000 gallons 10 ppm. How much Bicarb must be added?
a. 2-50 lb. bags
b. 45 lbs.
c. 11.2 lbs.
d. 60 lbs.

17. A pool is losing 3” of water per day. The pool is 20’ x 40’, 3’ to 5’ deep. How many gallons of water will be lost in one day?
a. 800 gallons
b. 4,500 gallons
c. 3,000 gallons
d. 1,500 gallons

18. After chemical testing, it is determined that the free available chlorine needs to be raised 4 ppm. You are using sodium hypochlorite (liquid bleach) with a dosage as follows: 10.7 fluid oz. raises 10,000 gallons 1 ppm. There are 128 fluid oz. in 1 gallon. How many gallons will be necessary to add to a pool which is 25’ x 50’, 3’ to 5’ deep?
a. 1 yellow jug containing 2.5 gallons
b. 1.25 gallons
c. 4 gallons
d. 3.75 gallons

19. The pool has a vacuum DE filter which contains 8 grids; each grid is rectangular, 3’ x 5’. What is the total filter surface area?
a. 120 sq. ft. of filter surface area
b. 240 sq. ft. of filter surface area
c. 24 sq. ft. of filter surface area
d. 65 sq. ft. of filter surface area

20 Based on 1.25 lbs. of DE powder for every 10 sq. ft., what is the amount of DE powder for the filter in Question 19?
a. 65 lbs.
b. 30 lbs.
c. 24 lbs.
d. more is better, so add a 50-lb. bag

How did you do? Click here for answers to this month’s aquatics test. Stuck on how to get an answer? Click here for the complete solution.