Lol, i was laying in bed the other night doing maths... How sad haha, thats why I started the thread!-)
Duanes is your 5ppm after water change? Gather if you were to leave it a week it would be alot higher? Thats the beauty of the extra effort of multiple water changes, more constant nitrate levels... Why dont you run a drip system?
I don't think the maths is correct. Excluding the nitrate content of the new water (that is, assuming 0ppm) then:
Before the water change you have 100gal with 20ppm.
After the water drainage you have 50gal with 20ppm nitrate because the nitrate being measured is a mass fraction/mass concentration. You aren't removing 10ppm nitrate, you are halving the amount of water holding 20ppm of nitrates.
After adding 50gal of (pure) water you then have reduced the tank to 10ppm in 100gal.
If the 50gal new water has 10ppm nitrates then you would end up with 100gal with nitrates at 15ppm. If the water had 20ppm nitrates then you would end up with 100gal with 20ppm nitrates.
Think of it this way - you have a 100gal tank filled with salt water and drain half of it. You aren't making the water half as saline. When you add in 50gal of RODI water you are.
Cheers humphrey, so you are saying my initial calculations were right... Think I know what you mean, jk dilution point is not a factor because we are not working in percentages of nitrate.... The more I look at this with a sober head I think my initial math was correct, come back jk, reduce my nitrate with math again lol...By removing 50% at 20ppm then replacing 50% of 0ppm you are halving excisting nitrate.
This site will do the calculations for you. And yes, the math in the OP was correct despite whatever beverages were consumed.
The way I look at it is that regardless of whether one looks at the WC as removing a certain quantity of nitrate (mass) or diluting the ppm of nitrates by adding nitrate-free water, the result ends up at the same place.