In the pressure washing business we use sodium hypochlorite (or SH / bleach) in 10% and 12.5% concentrations. Is there a simple formula to determine amounts of SH to water to reach a desired concentration for a given volume? For example, I am using 12.5% SH and need a 50-gallon batch of solution with a 1% concentration of SH. I also need a 30-gallon batch with a 6% concentration. What formula would I have to use to get this right every time regardless of the volume or desired concentration?
How Much Bleach?
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Dr.Peterson
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Normally, we like to get you to do the work in order to learn to think for yourself, so we ask you to show what you've tried:
But this sounds like real life, so I'll just answer.
Let's take your first example, and then generalize.
You have 12.5% SH, so x gallons contain 0.125x of SH. You want 50 gallons total, of which 1% (.01*50 = 0.5 gal) is SH. So you want 0.125x = 0.5.
Solving, x = 0.5/0.125 = 4 gallons. The remaining 50 - 4 = 46 gallons will be water.
As a formula, we see that 0.5 was the desired gallons (50) times the desired concentration (1%), and the 0.125 was the provided concentration. So the formula you want is
Trying this out on the second example, we get 30*0.06/0.125 = 14.4, so you'd use 14.4 gallons in 30 - 14.4 = 15.6 gallons of water. Checking, you're using 0.125*14.4 = 1.8 gallons of pure SH, and 1.8/30 = 0.06, the correct concentration.
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But this sounds like real life, so I'll just answer.
Let's take your first example, and then generalize.
You have 12.5% SH, so x gallons contain 0.125x of SH. You want 50 gallons total, of which 1% (.01*50 = 0.5 gal) is SH. So you want 0.125x = 0.5.
Solving, x = 0.5/0.125 = 4 gallons. The remaining 50 - 4 = 46 gallons will be water.
As a formula, we see that 0.5 was the desired gallons (50) times the desired concentration (1%), and the 0.125 was the provided concentration. So the formula you want is
Gallons to use = Desired gallons*Desired concentration/Provided concentration.
Trying this out on the second example, we get 30*0.06/0.125 = 14.4, so you'd use 14.4 gallons in 30 - 14.4 = 15.6 gallons of water. Checking, you're using 0.125*14.4 = 1.8 gallons of pure SH, and 1.8/30 = 0.06, the correct concentration.
Wow. Watching you solve/explain this in such an effortless manner is akin to watching a guitarist play Beethoven's 5th symphony on a classical guitar. I apologize for breaching the guidelines. I was indeed looking for a real-world solution and none of the "experts" in this field could ever wield a respectable answer the way you just did. Thank you so much for giving me your time. Much respect to you.
In keeping with the guidelines I'll work one out.
Solving for 35 Gals of 3% (SH)
35*0.03/0.125 = 8.4 gal of (12.5%) SH
35 - 8.4 = 26.6 gals of water
Checking - 0.125*8.4 = 1.05 gallons pure (100%) SH and 1.05/30 = 0.035
Hmmm... I ended up with 0.005 over the 3%. Did I do this right?
In keeping with the guidelines I'll work one out.
Solving for 35 Gals of 3% (SH)
35*0.03/0.125 = 8.4 gal of (12.5%) SH
35 - 8.4 = 26.6 gals of water
Checking - 0.125*8.4 = 1.05 gallons pure (100%) SH and 1.05/30 = 0.035
Hmmm... I ended up with 0.005 over the 3%. Did I do this right?
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Dr.Peterson
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Your only error was in the check! You divided by 30 instead of 35. Your answer was right.
I'll add that I was thinking as I wrote, that my little brother does calculations like this all the time in his work with greenhouses. He used to occasionally complain about all the math he had to do ... when all he wanted was to be among living things. So I empathize.
Ahh... it was staring me in the face the whole time too. Now I just need to create a calculator with this equation for quick reference. But if I can't, I always have a pencil : )
Funny. I have an nephew with the same personality trait who just graduated from Sam Houston State University with a degree in horticulture, so I can relate. Thanks again for your expert assistance. Sad that the encounter has reached its conclusion. I wish you the best.
Funny. I have an nephew with the same personality trait who just graduated from Sam Houston State University with a degree in horticulture, so I can relate. Thanks again for your expert assistance. Sad that the encounter has reached its conclusion. I wish you the best.
Whoops... I have one more variable to consider. I hope you will indulge me.
Oftentimes we must run solution through what's called a downstream injector. This is called "downstreaming". This injector pulls the solution into the water stream at a commonly used ratio of 10:1.
How would I calculate the required starting concentration?
Example:
To get a 1% SH solution at the end of my hose, what would the be the formula used to determine the required concentration of SH in the draw tank?
My work would be:
Umm.... DELETED. I don't even know where to start : (
Oftentimes we must run solution through what's called a downstream injector. This is called "downstreaming". This injector pulls the solution into the water stream at a commonly used ratio of 10:1.
How would I calculate the required starting concentration?
Example:
To get a 1% SH solution at the end of my hose, what would the be the formula used to determine the required concentration of SH in the draw tank?
My work would be:
Umm.... DELETED. I don't even know where to start : (