Equation for diluting nutrient to specific PPM target

This excellent post is from Aberration. He posted these great equations that help when you you want to understand how much more water to add to bring your nutrient PPM's to a certain number, for example.

He has the most detailed journal(s) I've ever seen, and grows fantastic plants. Check out his journal here:

Aberration goes Ker Bloom! - Perpetual


Aberration;1445949 said:
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I mixed up a boosted bloom feed, and it came out hotter than I wanted. I needed to dilute it down. Here's my take on dilution.

If you know how much liquid you have (I had 5 gallons) and the current ppm (mine was 1270) you can find out how much water you need to add to reach a specific ppm by dilution, or what ppm you will get if you dilute with a given amount of water. Of course this assumes low ppm water. Mine comes in at 110 out of the tap, so it's close enough to zero.

If I know what ppm I want to end up with, I can use this:

x = (p * v)/y

where:

v = starting volume
p = starting ppm
x = new volume
y = new ppm

If I want to know what the new ppm will be if I add a specific amount of water, I use this instead:

y = (p * v)/x

So I had 5 gallons of mixed food at 1270 ppm and I wanted something closer to 1150 ppm. How much water do I add?

x = (p * v)/y = (1270 * 5)/1150 = 5.52 gallons

Remember that 5.52 gallons is the new volume which includes the starting volume. So that means I have to add 0.52 gallons, or just a hair over 1/2 of a gallon.

If I wanted to know what ppm I would have gotten if I added 1/2 gallon to the original 5 gallons, I could have done this:

y = (p * v)/x = (1270 * 5)/5.5 = 1155 ppm

(remember that y = 5.5 gallons: x = v + added volume)

In fact, after I added 1/2 gallon exactly, I got 1160 ppm. Right on the money, really. The difference was due to the natural ppm of the water I added. I could add that in to the calculation, but then it gets a lot more complicated and it's probably within the range of natural variation in the strength of a batch anyway. It's nearly impossible to get exact measured amounts with measuring spoons/cups anyway. So this works for me. It always puts me in the ballpark.

As for units, use whatever. You don't have to use my ppm scale. You can use whichever, even EC values. You just have to use the same scale for both ppm values. The same for units of volume. You can use gallons, teaspoons, garbage cans, buckets or whatever as long as you use the same units always.


:peace:

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