Water change math

Bill Stock wrote:
I'll be setting up an automatic water changer in a few weeks and I've been
having trouble with the math.
The reading I've done suggests that a 20% daily water change is still going
to leave the fish swimming in 82% crap (r = e ^ -.2) as opposed to 50% to
100% crap with large weekly water changes. BUT, the detailed formula I've
seen shows the crap remaining as r=(1-a/n)^n, where a is the percentage of
water changed and n is the number of changes. Now assuming I change 1 gph
and a drop is 1/3600 gallons, then I'm left with 99.99% crap because the
changes are so small. (One drop at a time) Am I missing something here or do
I need to remove some water first to make this work?

I believe you are using a static equation, as there are so many
variables, such as cross circulation vs vertical circulation. I like to
have both types of circulation in an aquarium, except in some breeding
enviroments.
I have only used this type of product a few times (it has been many
years ago, and they may have improved) and found that did not do a good
job of removing a lot of the organic muck that ended up in the nitrogen
cycle.

Carl
http://aquarium-nitrogen-cycle.blogspot.com/