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Parks & Rec Business
| Swimming Pool and Spa Mathematics The keys to controlling costs and maintaining a healthy and safe aquatic facility are all in the numbers By Connie Sue Centrella No more half a bucket! This is a phrase I use when I begin my educational sessions on swimming pool calculations. One of the most important concerns to any facility manager is the safe use and the cost of chemicals. For the aquatic manager to clearly understand chemical dosing, as well as other operational parameters, we have to go back to the beginning and review swimming pool geometry. Pool Geometry Lets refresh our memory and review the basic formulas from Geometry 101, and begin with understanding surface area and its effect on safe user loads. The surface area is the flat plane across the top of the pool. This area is denoted as square footage of surface area. Many state codes use this surface area to calculate user load, i.e., one user for every 20 sq. ft. of surface area. A large percentage of aquatic facilities are designed with a swimming area, diving area or a combination of the two. Many of these have rectangular shapes. To calculate the surface area of a rectangle or a square, follow this formula: The area of a rectangle is L x W. By measuring the length and multiplying it by the width of a swimming pool, we can find the surface area. In the example above, the surface area will be 50 x 20 or 1,000 sq. ft. If the user load is 20 sq. ft. per person, then the maximum number of users would be 50 people. Finding surface area of circular pools and spas Many wading pools and spas are circular in shape. To find the surface area of a circle, follow this formula: pi (3.14) x radius x radius (πr2 ). This gives the surface area across the top of the circular spa/pool. In the circle to the right, the diameter is 10 across. The radius is ½ the diameter. So the radius would be 5. Using the formula above, 3.14 x 5 x 5 equals 78.5 sq. ft. Calculating the safe user load for a circular spa/pool The universal bather code for spas is 10 sq. ft. per user. In this situation, the maximum number of people who can use the spa is 7 people. Knowing the formula will assist you with calculating the maximum users the spa is designed to hold at any one time. An excessive number of users will encourage the risk of contamination, resulting in an increase in chemical requirements, as well as putting an excessive load on the filtration system. Free form shaped pools and spas There are additional geometric shapes, such as an oval, kidney or freeform shape that the aquatic manager should understand if he or she is to size the pool properly. Understanding Volume Volume is the space inside the pool or spa, and in this case, we want to know the amount of water within the pool or spa. Once the pool volume (# of gallons of water) is calculated, then the pool manager can proceed with the calculations for chemical dosages, turnover times, flow rates and filter area. Follow this formula One cu. ft. of water contains 7.48 gallons. In order to calculate the volume, the depth of the pool must be measured. The simplest way is to measure the depth in two to four places along the length of the pool, starting in the shallow end and ending in the deep end, usually at the main drain. Then take an average depth. As an example, if the depth starts at 3, goes to 5, and ends at 9, the average depth would be 3+5+10 = 18. Divide 18 by the number of measurements you took (3), i.e., 10/3 = 6. So, the average depth (AD) equals 6 ft. The formula for the pool volume (gallons) is the surface area across the top of the pool x average depth x 7.48 gallons. L x W x AD x 7.48. (Some resources use 7.5 gallons/ cu. ft). This calculation is an estimate, as most pools vary with radius corners, coved corners, or step displacements, water in the piping or a surge chamber. But these estimates are sufficient for swimming pool calculations. Some professionals prefer to divide the pool into sections, calculate the gallons in each section, and then add together. Chemical Dosages In order to effectively treat swimming pool water to insure that the users are protected against recreational water illnesses (RWIs) and provide bather comfort against burning eyes and itchy skin, you need to learn how to properly add chemicals and in the correct dosages. Most manufacturers of pool chemicals base their dosage on either 5,000 or 10,000 gallons. As an example, 2 oz. of Calcium Hypochlorite will raise 10,000 gallons of pool water 1 ppm. To calculate the correct dosage for a pool that is 20 x 50 with average depth of 4, follow this formula: L x W x AD x 7.5 (we will round up in our exercises), so 50 x 20 x 4 x 7.5 = 30,000 gallons. We want to raise this pool 3 ppm of free available chlorine. To do so, it will take: 2 oz. x 30,000 gallons x 3 ppm = 2 oz. x 3 x 3 or 18 oz. = 1.125 # 10,000 gallons 1 ppm Thus, you will need to add 1.125 lbs. of Calcium Hypochlorite. Knowing how to calculate the number of gallons assures that you eliminate the error of adding too much chemical or guessing (i.e., half a bucket syndrome!). In the Water Chemistry course, we will study additional dosages. Turnover Rate Turnover rate is the amount of time it takes to theoretically move all the pool water through the filtration system. Pump requirements, piping specifications and filter sizing are determined by the turnover rate. The turnover rate is based on the measurement of particulate matter in the pool/ pollutants. Different usages and bather loads mandate the turnover rate (time). Most health departments have conformed to the following standards. Swimming Pools 6 hours Spas 30 minutes Wading pools 1-2 hours Waterparks/specialty pools 3-4 hours Physical therapy/ health club as low as 3 hours. Flow Rate The rate of flow measures how many gallons of water per minute are moving through the return piping. Now that you have determined the turnover rate, you are ready to calculate the pool piping (hydraulics), pump and filter system sizing. The formula for understanding the rate of flow is: Flow Rate = Pool Volume = Gallons per hour = GPM Turnover Rate 60 minutes If the turnover rate is 6 hours, the flow rate in a pool containing 30,000 gallons would be 30,000 gallons divided by 6 hours divided by 60 minutes equals 83.3 gpm. Once the gpm is determined, the pump and filter can be sized. Using a Flowmeter One of the ways in which the aquatic manager can determine if the pool is operating at health code requirements is to look at the flowmeter. The flowmeter is a device that measures how many gallons of water are flowing through the return piping. If the flowmeter indicates a less than required gpm, there could be a number of reasons. The filter may be dirty, impeding the flow of water through the filter; in addition, there may be a restriction on the suction side of the pump from the skimmer, main drain or hair and lint basket. These are areas of concern that need to be promptly addressed. You cannot troubleshoot the system without knowing the number of gallons and turnover rate. Filter Media Rate Knowing the filter media rate will help you achieve water clarity and optimal operation. As our calculations are flowing, there is one additional formula you need to know. There are basically three types of filtration systems being utilized in aquatic facilities: sand, cartridge and diatomaceous earth (D.E.). When a pool is engineered to achieve water clarity and optimal operation based on usage, the size of the filter is determined by how many gallons will flow through each sq. ft. of surface area every minute. This is known as filter media rate. The NSFI (National Sanitation Foundation International) Standard 50 has set the following public pool standards for filter media rates (FMR) for each type of filter: High-Rate Sand 12 20 gpm/ft2 Cartridge 0.375 gpm/ft2 Diatomaceous Earth 2.0 gpm/ft2 The rule is to size the pump to the pool (gpm) and the filter to the pump. Therefore, the formula for knowing the filter area can be learned by dividing the flow rate by the filter media rate. Flow rate = Filter area Filter media rate An example would be the 30,000-gallon pool with 83.3 gpm. Sand Filter If the sand filter media rate is based on 15 gallons per minute per sq. ft., the formula would be 83.3gpm / 15 gpm/ft2 = 5.53 sq. ft. of filter surface area as the minimum requirement to achieve water clarity. D.E. Filter In the same pool, using D.E. filtration, it would require 83.3 gpm/2 gpm/ft2 = 41.65 sq. ft. of filter grid area, and in the cartridge filter 83.3 gpm/ 0.375 gpm/ft2 = 222.13 sq. ft. of cartridge media. If you are having difficulty achieving water clarity, the required filtration versus the existing filter should be analyzed, and necessary replacement or upgrading may be needed. Hydraulics 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. We will study hydraulics more in depth later in our course. At this time you should know the maximum gallons per minute that should flow through the piping. The piping for the pool will be determined by how many gallons per minute will flow through the piping. There have been incidents where a manager has put a larger pump on a system (more is not always better in swimming pool engineering). By doing so, the pump is trying to pull more gpm through the pipe than the pipe can withstand. (1 1/2 pipe is capable of handling 43 gpm.) This can cause major stress on the piping and pump system, resulting in friction issues and leakages as well as pump cavitations. There are additional calculations necessary in the engineering phase or renovation phase of swimming pool construction. Heating Issues have been raised in which a pool/spa heater was purchased without a true understanding if that heater would be capable of achieving the proper increase in water temperature. The formula for calculating the required BTUs is BTUs= Gallons x 8.33 x οF temp. rise One BTU will heat one lb. of water 1 degree. One gallon of water weighs 8.33 pounds. Therefore, 8.33 BTUs are necessary to heat one gallon of water 1 degree. Example: A spa contains 1,000 gallons and the desired temperature rise is 5 degrees. The formula is; 1,000 gallons x 8.33 pounds/gallons x 5 degree temperature rise = 41,650 BTUs to heat the spa 5 degrees (provided the heater is 100% efficient). Water Loss If a pool or spa is losing water, you need to be able to determine if the water loss is through evaporation, bather splash out or plumbing leakage. To understand the cause of the loss, you will need to know the following: One sq. ft. of surface area 1 deep contains 0.625 gallons of water. Therefore, the formula for calculating 1 water loss in a 20 x 50 pool is L x W x 0.625 gallons or 1,000 x 0.625 or 625 gallons in 1. If the pool loses 3 of water per day, that calculates out to 1,875 gallons of water. In theory, if you do not refill, it will take 16 days for the pool to empty. You should be reminded that refilling (dilution) changes the chemical balance and creates an additional burden on chemical costs if the water loss is not identified and repaired quickly. In the end, mathematics is essential for all successful swimming pool and spa operation. Water-quality management, chemical dosing, hydraulics, pump, filter and heater requirements all depend on your understanding of basic arithmetic and geometry. The inability to understand and calculate these basic formulas will result in hazardous conditions and possibly threaten the health and safety of the facility. Connie Gibson Centrella is Program Director for the online Aquatic Engineering Program at Keiser University eCampus. She was recently honored with the Evelyn C. Keiser Teaching Excellence Award Instructor of Distinction. Ms. Centrella is an industry veteran with over 40 years experience in the pool and spa industry. She is a former pool builder with extensive knowledge in pool construction and equipment installation as well as manufacturing. You can reach her via e-mail at ccentrella@keiseruniversity.edu Sidebar #1 For those looking to achieve a college degree program in the aquatics field, the Keiser University Associate of Science Aquatic Engineering Degree offers a two-year degree consisting of 60 semester hours that are achieved exclusively online. Each student is required to complete 36 credit hours of major courses and 24 credit hours of general education courses. The degree program encourages students to broaden their knowledge in all aspects of swimming pool and spa management and operation. The online feature makes the degree program available to the national and international community of pool and spa professionals, and those seeing employment in the field. The online format enables schedule flexibility and increased access to those currently employed. For more information about the Aquatic Engineering degree at Keiser University, visit www.keiseruniversity.edu and click on Online Education, call 866-535-7371, or e-mail ccentrella@keiseruniversity.edu and request a brochure. Sidebar #2 The Pool Math Workbook from the National Swimming Pool Foundation is a terrific resource and truly makes math easier. This is the first textbook that focuses solely on calculations in swimming pool and spa field. Order online at www.nspf.org or call 719-540-9119. |
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