I remember sitting in high school math class and griping along with the other students: why do I need to learn this stuff? When will I ever use this in real life? I also remember intentionally selecting English as my college major so I could avoid further math. To top that off, I ended up permanently in the pool industry!Then I found out that to determine the volume of a square, rectangular, oval or kidney pool a service tech needs to apply one of several geometric formulas. Fortunately, they are not too complicated…The funny part comes when you need to find the volume of a freeform pool. The instructions essentially say “divide the pool into rough geometric shapes, solve for those shapes, add the numbers together, and you will be somewhere in the ballpark.” Not only can this be difficult on some pools, but determining the average depth for these kinds of pools is an added challenge. Obviously a better way needed to be found.Much to my surprise, as we at onBalance were working on correcting industry alkalinity dosage charts, and debunking the “Acid Column Myth,” one of my old math lessons jumped back at me: if A x B = C, then C ÷ A = B! Or in other words, in terms of water chemistry, since a specific amount of acid or base added to a specific volume of water results in a given, specific alkalinity shift, then we can rearrange those variables and say that the amount of a chemical added, divided by the change in alkalinity, equals the water volume!The one tricky part about doing this at poolside is that to get an accurate answer you need to be able to test alkalinity to within one part per million, rather than the common 10 ppm precision of most poolside test kits. So get a glass, and add precisely 10 times as much pool water as is normally used for an alkalinity test sample. Then add enough color indicator to see it well. (Using more or less color indicator will not change the results of the test – it just helps you see the endpoint, or color transition better.) Then start adding the drops of titrant – but now each drop is 1 ppm instead of 10! This will obviously use up more titrant, but you only do this once per pool, and we promise you the test kit supplier won’t mind if you buy refills of their solutions ;0)Here is the simple field method we use:• Take a water sample of 10 times the normal amount from the pool for testing.• Add acid, soda ash, or another chemical which alters total alkalinity to the pool. Add enough to make a noticeable shift in total alkalinity – at least 10 to 20 ppm.• Write down exactly how much you used.• Wait for the chemical to completely blend throughout the water. (This time will vary from 45 minutes to several hours depending on the method of addition, the circulation, etc.)• Take a second 10X water sample from the pool.• Test the total alkalinity of the two samples (using the dilution method, or another comparable means of getting withing 1 to 2 ppm of the answer).• Find the formula number for the chemical you used from the list below.• Apply the following formula (using the appropriate formula number depending on which chemical was used):(formula number)(amount of chemical used in quarts or pounds)—————————————————————————— = Pool Volume(Number in ppm that the TA changed)Here are a couple of examples. First, if you add 5 pounds of sodium bicarbonate to a pool, and the starting TA was100 ppm and the ending TA was 116 ppm, then:(71,400 for baking soda)(5 pounds)—————————————— = a 22,000 gallon pool(116 – 100, or 16 ppm)Or if you add two quarts of acid to a pool and the alkalinity drops 12 ppm:(125,000 for muriatic acid)(2 quarts)——————————————— = a 21,000 gallon pool(120 – 108, or 12 ppm)Actually, the volumes in the examples came out to be 22,312.5 and 20833.33, but of course that is too precise – round off to the nearest 1000 gallons. The margin of error should be around 5%)Formula NumbersSodium Bicarbonate (baking soda) - 71,400Sodium Carbonate (soda ash) - 113,200Sodium Sesquicarbonate (sesqui) - 80,000Muriatic Acid - 125,000Sulfuric Acid - 126,700Sodium Bisulfate - 47,000
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  • Oops,
    I meant, perimeter squared divided by 18 x 7.5
  • Hi Que,

    Thought you might find another formula for calculating volumn of freakyfreeform pools interesting. This formula was to me by a CPO instructor about 15 yrs. ago. It will give you a starting point so that you can then "back into" the actual volumn. It works reasonably well, and again, is only a starting point.

    Perimeter squared divided by 18.

    For the most part, if you can get within 2,000 or even 5,000 gals. with the initial calculation, then it becomes simple to "back into" the volumn.

    If 1.5 lbs. of bicarb raises TA at the rate of 10ppm. per 10,000 gal. then to raise a 22,000 gal. pool by 40ppm. could be expressed as: 1.5 x 4 x 2.2 = 13.2 lbs. bicarb required.

    To "back into" the volumn, retest TA after 24 hrs. and simply reverse the formula

    13.2 divided by (1.5 x 4) = 2.2 or 22,000 gal.

    While not as accurate as your method, it is simple, teachable, and close enough for field work..
  • Que

    Thanks for your insightful post. I am encouraged by the face that the average PGN subscriber WANTS to learn more. Our debates are lively and respectful and that always means we have a great opportunity for knowledge to transfer from mind to mind. There have been a small, but growing, vocal minority that have been challenging the "democratically" decided rules of health and building departments. Science and engineering by democracy just does not work. We use the scientific method: Characterization, hypothesis, predictions, and experiments. In this way, we can either confirm or deny the hypothesis.

    The endless "opinion debates" are coming to an end. It appears that through historical study, we are about to narrow in on the window (1950-1970) where we left science and started down the path of folklore and rule by committee.

    Fortunately the basic principles of science only get better by the day and by today;s standards, keeping a pool clean is rather low-tech.'
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