In the process of validating the math for my bleach automation system, and I ended up down a rabbit hole learning about various methods of how bleach concentrations are characterized.
Correct me if I'm wrong here, but, I think it's most common for US companies to specify the concentration as the weight percent of NaOCl (i.e. mass of NaOCl / total mass), yes? I don't think "trade percent", nor "active chlorine weight percent" are common based on how this document describes it.
Moving on ...
Arriving at the mass of chlorine needed to achieve a given PPM concentration is relatively straight forward (shown below). But, measuring mass is considerably more troublesome than measuring the volume through a positive displacement pump. So, that lead me to this chart (page 2) that conveniently lists the grams of active chlorine per liter of various concentrations of various bleach solutions. Curious thing about that table: the g/l is nonlinear with the % concentration. Observe that 10% (active CL) concentration has 14.3% more active chlorine per unit volume than the 1% concentration has per unit volume after accounting for 10x factor. I don't understand why that is. (paging chem_geek to the white courtesy phone )
So, if anyone wants to check my work, here's the math I came up with, which gives a slightly different result than the pool calculator.
delta_ppm -- how many PPM we want to raise the FC by
# gallons -- how big the pool is
% chlorine -- bleach strength in weight % NaOCl (per discussion above)
I want to arrive at fluid oz's (volume, not weight) to pump out. For clarity, I'll use "FlOz" for fluid ounces (volume), and "OzW" for ounces of weight. All my calibrations are in US measurements, so, I apologize in advance for having to deal with mixed units.
delta_ppm * gallons * 8.345 lbs/gallon * 16 OzW/lbs * 1E-6/ppm = Pure Cl2 in OzW (weight ounces)
Now use %chlorine strength as a lookup to get the g/l value from chart mentioned above. Since 958.6 g/l = 1 ozW/FlOz, we can arrive at the volume:
Pure Cl2 OzW * 1/(table lookup g/L) * 958.6(g*FlOz)/(l*ozW) = Fluid Oz bleach (volume) to pump
An example 100K gallons, +1PPM, 5.25% bleach: 1 * 100000 * 8.345 * 16 * 1E-6 * 1/53.7 * 958.6 = 238.3 Fl Oz, where the Pool calculator gets 237
Now do same but with 10.5% bleach: 1 * 100000 * 8.345 * 16 * 1E-6 * 1/115.9 * 958.6 = 110.4 Fl Oz, where the Pool calculator gets 119
I'd call that good enough for this pool boy
Note that all of this is subject to a density/temperature relationship that will change the result a few (unaccounted for) percentage points.
So, yeah, I'm that kinda nerd to do all this, but, at least it's documented where I hope someone else might get some use out of it. Please do comment if you have a better data source or find an error!