By Connie Sue Centrella
The service sector of the swimming pool industry has long been challenged with how to effectively manage cleaning routes, provide pool and spa owners with the best water quality and maintain pool equipment at its optimal operational efficiency. The ability to effectively and properly provide these services depends on one key element: understanding swimming pool mathematics.
Gather long-term data
Water quality management, chemical dosing, hydraulics, pump, filter and heater requirements all depend on an understanding of basic arithmetic and geometry. Successful pool service companies calculate water volume and chemical dosing requirements for each pool they maintain. By means of record keeping and analyzing historical data of each pool, the technician can effectively manage chemical costs by neither under- nor over-treating the pool.
Unfortunately, many service technicians guess at how much chemical is necessary. This guesswork may lead to bacterial illnesses, increased chemical costs, damage to swimming pool surfaces, equipment failure and unhappy customers.
Do the math
The study of swimming pool mathematics begins with volume: how much water the pool contains. Chemical manufacturers provide dosage charts which are denoted by so many ounces, gallons or pounds per 10,000 gallons. Without knowing the volume of water in the pool, the service technician cannot provide the proper dosages. In addition, the basis of swimming pool hydraulics depends on total gallons to calculate flow rate (gallons per minute) and filter media rate.
One cubic foot contains 7.48 gallons of water. A swimming pool is a vessel with three dimensions: length, width and depth. Multiplying the length x width x average depth will give the cubic feet in the vessel (pool).
Therefore, the first step is to calculate the flat plane across the top of the pool. From geometry, the area of a rectangle is length x width. This calculation is called the surface area of the pool. Many state codes determine maximum bather load by using surface area as the basis. The universal maximum bather load for spas and hot tubs is one bather for every 10 square feet.
Once the surface area has been determined, then the depth must be considered. Since most swimming pools have varying depths, determine the pool’s average by adding the shallow-end depth to the deep-end depth and divide the sum by two. If there are varying depths, this process can be done by taking three depths dividing by three and so on. This is only an average, as when you review the profile of a swimming pool, there are coves at the corners which actually create less water, but for most chemical and hydraulic calculation purposes, the pool industry assumes the walls are perpendicular to the floor. This calculation is average depth (AD).
Example:
- A 15’ x 30’ pool, three to five feet deep, contains 13,500 gallons.
- 30’ x 15’ x 4’ x 7.5 = 13,500 gallons
After the volume is determined, the technician can chemically treat the water. Suppose you want to raise the chlorine residual three ppm using calcium hypochlorite. As an example, the chemical dosage for calcium hypochlorite is as follows: if two oz. of cal hypo will raise 10,000 gallons one ppm; 8.1 oz. would raise 13,500 gallons three ppm. Figure 1 illustrates a useful form for determining chemical dosages.
It is imperative that the service technician maintains a chemical dosage chart for all the chemicals used on his/her maintenance route and add the proper amount of chemical required. Without strategic calculation of chemical addition, damage to the equipment or pool surface may occur due to an increase in acidity or alkaline property of the pool water.
Hydraulics
One of the key areas of concern is the matter of understanding hydraulics. In order to achieve optimum water clarity, the swimming pool technician must know how to size the pool pump and filter system. Equipment manufacturers provide various hydraulic charts to be used in sizing the pump and filter. In order to read these charts, the technician must understand a few basic calculations.
Turnover rate
The amount of time it takes to theoretically move all the pool water through the filtration system is referred to as the turnover rate. Pump requirements, piping specifications and filter sizing are all determined by the turnover rate. Depending on the building and health codes, turnover rates can vary from 30 minutes in a public spa to eight to 10 hours in a residential pool. Turnover is based on achieving the optimum water clarity with variables such as usage, bather load and swimming environment. Environment means whether the pool is located indoors or outdoors, whether the pool is exposed to high winds, rain or other factors which would allow for high contamination.
Flow rate
After the turnover is assessed, the technician can calculate the flow rate. The hydraulic charts used in swimming pool calculations are based on gallons per minute (gpm). A simple calculation for flow rate is to divide the pool volume (gallons) by number of hours and then divide by 60 (minutes in one hour).
Flow rate = Volume of pool water / Turnover rate x 60 minutes
If the pool contains 30,000 gallons of water and the turnover rate is eight hours, the flow rate would be: 30,000 gallons ÷ 8 hours ÷ 60 min/hr = 62.5 gpm
“Size pump to pool and filter to the pump”
This is the phrase used in the pool industry to assure that the filter system is capable of receiving the gpm necessary to achieve water clarity.
The three basic types of pool filtration are sand, cartridge and diatomaceous earth. Each type of filter is designed to receive a determined amount of gallons per minute per square foot of filter surface area. This is called filter media rate (FMR). In calculating FMR, the technician must first determine the turnover rate, calculate the gallons per minute, then divide the gpm by the FMR. NSF Standard 50 has set the following public pool standards for FMRs for each type of filter:
- High-rate sand: 12-20 gpm/ft2
- Cartridge: 0.375 gpm/ft2
- Diatomaceous earth: 2.0 gpm/ft2
An example is a diatomaceous earth (DE) filter. Most manufacturers design the DE filter based on two gpm per square foot of filter surface area. Based on this FMR, the technician is able to determine the filter size requirement.
On the illustration pool with 30,000 gallons and a turnover rate of eight hours, the flow rate is 62.5 gpm. Using a FMR for DE of two gpm/square foot, the following filter size can be determined:
Filter area = Flow rate / Filter media rate
62.5 gpm / 2 gpm/sq.ft. = 31.15 sq. ft. of filter surface area
DE filter grid surface area is calculated by taking the measurements of one side (L x W). Since a DE filter grid removes particulate matter from both sides, the surface area is multiplied by two. Then multiply the square footage of one grid by the number of grids in the system, to determine the total square footage of filter surface area. The DE grid is coated with a powder, either natural-based diatomaceous earth or man-made fiber at the rate of 1.25 pounds per 10 sq. ft. Without knowing the filter surface area of the system, the technician would not be able to sufficiently coat the DE filter, thus losing the ability to achieve maximum water clarity.
Many pool technicians have experienced a filter system that was designed improperly, thus creating water clarity conditions. A filter designed without enough surface area will not trap the particulate matter in the pool water. This creates an unsafe pool condition. It is imperative that any pool be designed to create good water clarity conditions so that the pool main drain can been seen clearly at all times. 
Hydraulics is basically the study of water flow and movement, which involves circulation, filtration, cleaning, heating and sanitizing. Pumps, filters, cleaning systems, heaters, automatic chlorinators and controllers all depend on proper hydraulic data to operate at full potential.
Heating calculations
An interesting and useful calculation for pool technicians is how to determine the BTUs necessary to raise the pool water temperature. The formula is as follows:
- One BTU will heat one pound of water one degree.
- One gallon of water weighs 8.33 pounds.
- Therefore, 8.33 BTUs are necessary to heat one gallon of water one degree.
If the technician wants to raise the temperature of a 500-gallon spa 10 degrees, a simple calculation will be: 500 gallons x 8.33 BTU x 10 degrees = 41,650 BTUs.
This is providing the pool heater is 100 percent efficient. Most pool heaters are not that efficient; therefore, the technician must consult the heater manufacturer’s specifications to determine efficiency. If the heater is 80 percent efficient, the technician must divide the BTUs by the efficiency rating. In this example, the heater would be sized as follows: 41,650 BTUs ÷ 0.80 efficient = 52,063 BTUs.
Conversion for and electric heater
One kilowatt = 3,412 BTUs. In our example, an electric heater would need to be sized as follows: 41,650 BTUs/ 3,412 BTUs/kw = 12.2 kilowatts.
Water loss
One final useful calculation is how to determine water loss. If a pool is losing water from evaporation, splash out or a pool leakage, the amount of chemical used will increase, creating an increase in maintenance costs. This simple formula will assist the technician in showing the consumer that a repair may be necessary.
One square foot of water surface area one-inch deep contains 0.625 gallons of water. A 20’ x 40’ pool has a surface area of 800 square feet. One inch of water loss (800 sq. ft. x 0.625 gallons/sq. ft.) would equal 500 gallons of water. If the pool loses three inches per day, this is 1,500 gallons per day or 10,500 gallons per week! This could be as much as one-third of the entire pool water replacement each week. By using this calculation, the technician has empirical data to explain to the pool owner that this water replacement (dilution) will create changes in chemical balance which places an additional cost burden, thus that a repair is necessary.
Use mathematics to succeed
In conclusion, it is imperative that all pool service technicians have an understanding of swimming pool and spa mathematics. Without this knowledge, the swimming pool or spa water may reach a hazardous condition which will result in poor water clarity, unbalanced water and poor sanitation. It is the responsibility of all technicians operating and maintaining swimming pool and spa water to make an effort to obtain additional education in swimming pool/spa mathematics provided by the chemical and equipment manufacturers as well as industry education forums.
About the author
Connie Gibson Centrella is Director of Education for Team Horner. In addition, she is Program Director for the online Aquatic Engineering Technology Program at Keiser University eCampus. She was recently honored with the Evelyn C. Keiser Teaching Excellence Award, “Instructor of Distinction”. Centrella is an industry veteran with over 40 years experience in the pool and spa field. She is a former pool builder with extensive knowledge in pool construction and equipment installation as well as manufacturing. She serves on the Education Committee of the National Swimming Pool Foundation and has been a CPO instructor for 25 years.