# Re: [APD] dilution

On Mon, 7 Feb 2005 13:43:00 +0100, Hendra <hendra at henkoza_nl> wrote:

After reading Liz's email: http://fins.actwin.com/aquatic-plants/month.200501/msg00416.html (or see below), I started to wipe off some dust off my calculus book and made some simple plots.

But it seems like I always get convergence for all %'s of water changes (90 % and 10% and even 1%). So maybe somebody can point out if there is anything wrong with the calculations below.

No, that's right. Without only a constant input, and no outputs other than the water changes, there will always be a (mathematical) convergence. As the concentration of the substance increases, the amount you remove with your 1% water change increases until eventually you are removing as much as you add. Just think about the 1% scenario in a 100 litre tank. You add, say, 1g of substance at every water change. So now you have 1g in the tank, or a concentration of 0.01 g/l. Now, the maths tells you you will eventually end up with 100 times this concentration, or 1 g/l. In other words, when you make your 1% water change, you remove 1% of the substance (1g) and then add 1g back afterwards.

Unfortunately, given that a tank has a large amount of chemical changes producing waste producting and using nutrients at potentially high rates, otherwise the time period between water changes wouldn't matter! And I don't think anybody has suggested sensible consumption and production rates, probably due to the large number of variables (e.g. plant/fish mass). So this is not terribly useful for most of the nutrients people might be interested in.

```--
Andrew McLeod
thefish at theabyssalplain_freeserve.co.uk```

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