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Author Topic: Need to figure out where the constants in this formula come from.  (Read 2811 times)

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Burningkrome

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I’m trying to decipher and expand upon a formula in this paper about water and pool chemistry, however the formula apparently assumes information I don’t have. I don’t know if the constants are calculated from something in the paper, general chemistry or are assumptions of industry standards I can’t find. I’m unable to find contact information for the author and the Journal is basically dead.

The paper is:
Swimming Pool and Spa Water Chemical Adjustments; John A. Wojtowicz, Chemcon, Originally appeared in Journal of the Swimming Pool and Spa Industry, Volume 5, Number 1, pages 39–56.
(http://jspsi.poolhelp.com/ARTICLES/JSPSI_V5N1_pp39-56.pdf)

The base formula is:
VMA = a + b(pH) + c(TA) + d(CA)
Where…

VMA = the volume of 31.45% muriatic acid (HCL) in fl oz to add to 10000 gallons of pool water to reduce its pH to 7.2
a = unknown constant
b = unknown constant
pH = Current pH of the 10,000 pool (between 8.2 and 7.8)
c = unknown constant
TA = the total current alkalinity (ppm)
d = unknwn constant (perhaps a derivative of density aka specific gravity)
CA  = cyanuric acid (ppm)

The functional example is:
VMA = –237.34 + 29.894(pH) + 0.244(TA) + 0.1276(CA)

The formula works to observed data. However, I can’t figure out where the constants for a, b, c, and d actually come from either from the paper or by trying to reverse engineer the formula.

A CLUE: in the paper that author makes the statement, “The required quantity of acid [to add] is readily calculable from the decrease is calculated total alkalinity [TA] at the new pH. Each mol of added acid
neutralizes one mol of total alkalinity.”

So, a later formula for calculating the change in TA when adding Muriatic acid is:
(delta)TA = (fl. oz HCL acid added) x 29.57 x d x p x 1000 x 50/ (EW x V x 3.7854)

Where…
29.57 = conversion mL per Ounce (29.57mL = 1oz)
d = density (specific gravity) = 1.16 for Muriatic acid
p = purity or percent solution = 0.3145 for a 31.45% Muriatic acid solution
1000 = presumably conversion to liter
50 = unknown, perhaps existing concentration of Cyanuric acid as ppm in the pool as a stabilizer
EW = equivalent weight of -36.46 for Muriatic acid
V = total volume of pool = 10,000 gallons
3.7854 = conversion of gallons to liter (1Gal = 3.7854 L)

Any help greatly appreciated!!
 
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Borek

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Re: Need to figure out where the constants in this formula come from.
« Reply #1 on: March 24, 2014, 02:10:55 AM »

Paper clearly states constants come from experimental data fitting.
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Burningkrome

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Re: Need to figure out where the constants in this formula come from.
« Reply #2 on: March 24, 2014, 03:16:55 AM »

Hi Borek.

Yes it does. And then provides a bunch of data with no discussion of what method he used for the data-fitting. I'm wondering if it's possible to figure that out from the information available? Perhaps its a common method I don't know. Or is it mentioned (or implied) elsewhere in the paper.

The reason being, he also mentioned, "These Tables are useful for determining the quantity of muriatic acid required to reduce pH from the 7.8 to 8.2 range to intermediate values in the 7.3 to 7.7 range. For example, to calculate the quantity of muriatic acid required to reduce pH from 8.2 to7.5 one would subtract the quantity of acid to reduce pH from 7.5 to 7.2 from that required to reduce pH from 8.2 to 7.2."

Presumably this can also be done WITH THE FORMULA as opposed to the tables which the formula is intended to replace.

Presumably, one of the parameters (perhaps -237.34) is related to the the initial pH. I'm curious if it's possible to find out which one.

Do you have any suggestions?

Thanks!
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Borek

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Re: Need to figure out where the constants in this formula come from.
« Reply #3 on: March 24, 2014, 03:51:29 AM »

Quote
Multiple linear regression analysis of all of the data in Tables 3A to 6A was performed using the following equation form involving one dependent variable (VMA) and three independent variables (pH, TA, and CA):

http://en.wikipedia.org/wiki/Linear_regression is a variant of a http://en.wikipedia.org/wiki/Least_squares method.
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Babcock_Hall

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Re: Need to figure out where the constants in this formula come from.
« Reply #4 on: March 24, 2014, 03:57:32 AM »

I am not especially knowledgable in this area, but I would say that the author probably used a program capable of doing linear regression, apparently a program that can handle multiple independent variables.  ProStat is one such program (I am sure that there are a number of other ones), but I have not used this particular feature.
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Burningkrome

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Re: Need to figure out where the constants in this formula come from.
« Reply #5 on: March 24, 2014, 06:38:17 AM »

Awesome! Thanks for the info. Perhaps I can recreate it.
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lerouxj

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Re: Need to figure out where the constants in this formula come from.
« Reply #6 on: December 05, 2018, 03:24:15 AM »

Hi Burningkrome,
               Recently, I found the publication you are talking about and, curiously, I have the same question as you. However, I still can not solve the equation. On your side, did you succeed? http://www.chemicalforums.com/Smileys/classic/huh.gif

thanks
Julie
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