Aquarium calculus

Jean-Louis

Registered Member
Jan 14, 2007
2
0
0
How to devise a usefull formula for aquarium water changes.

I have a 50g tank (not including substrate and animals). I want to do daily water changes so that at the end of 6 months I will have replaced 95% of the water present at the beginning of the water change regimen. I want to replace the same volume every day.
1. What volume should I replace each day?
2. What is a general formula I could use for larger or smaller tanks? Or for changing the amount of time over which I replace the 95%. (So I could use it if I decide to set up a X
gallon tank and have my water 'turn over' period every Y months.)
3. What is a general formula I could use that contains the variables from (2) but also allows me to change the periodicity (say I get lazy and only want to do weekly water changes.)
 
It is a math problem after all... i need help to figure out the calculus formulae to solve this problem.
 
Part 1:
50 gal tank/183 water changes/95% 'new' water @ end
====> 0.81 gal per day

Problem setup:
Variables:
oldWater - amount of original water before WC
oldPercent - percent of original water before WC
newOldWater - amount of original water after WC
newWater - amount of 'new' water before WC
newPercent - percent of 'new' water before WC
newNewWater - amount of 'new' water after WC
changeWater - amount of water in the change

newOldWater = oldWater - changeWater * oldPercent
newNewWater = newWater - changeWater * newPercent
oldPercent = oldWater / (oldWater - newWater)
newPercent = newWater / (oldWater - newWater)

I used a spreadsheet to iterate out to 183 days. You can use whatever you'd like.

Part 2:
For general formulae, google renewal equations and get a cup of java. Or use java and the equations above.

Part 3:
See Part 2
 
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