Re: [APD] dilution

["Liz Wilhite" <liz_wilhite at hotmail_com>]

> I amde no claims it was. It's just to show how dilution works.

If you assume that nothing is consumed, and you dose the same amount each 
week (X), and you change 50% of the water each week...

Week 1 = X
Week 2 = X + X/2
Week 3 = X + X/2 + X/4
Week 4 = X + x/2 + x/4 + x/8

This is a simple series:

   __
   \       -n
   /__  2   where n goes from 0 to infinity

It converges at 2.  To find the maximum concentration multiply X times 2.  
So at a large number of weeks then you can safely say that the concentration 
after 50% water change + X is equal to 2X. Doesn't matter if it's KNO3 or 
fish poop or some allelopathic substance excreted by plants.  If you are 
doing a 50% water change every 4 weeks but are dosing X each week then at 
the end of a sufficient number of months the maximum concentration of X is 
2(4X) or 8X.  You can set up a series for any dosing and dilution scheme.  
Some of them "converge" or have a maximum value.  Some don't.

A 10% water change weekly and dosing X gives:

X
X+.9X
x+.9X+.81X
X+.9X+.81X+ .729X  which builds up concentration pretty fast.

Liz


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