Doing some math.

[patoloco]

I was thinking a few days ago, how partial water changes would end up polluting a tank in a very long term.

Only considering nitrates, please, read as follows:

"My fishload raise my nitrate reading 10ppm evey week. At the tank's first water change time, it reads NITRATE 10ppm. I do a 50% water change with clean water (0ppm) and now my tank nitrate concentration is reduced to one half (5ppm.)

Next week, tha tank should be 15ppm. I left 5ppm remianing last week and the fish added their share. Now, that tank has NITRATE 15ppm. My 50% water change lowers it at 7.5ppm.

Next, it's at 17.5ppm, and the water change lowers it to a half, 8.75%

After a few weeks, nitrate will reach 20ppm, and your water change lowers it to 10ppm. Then, fish will raise it to 20, and so on."

My fisrt impression was pollution would keep raising, but after a little help from my excel spreadsheet, to my surprise, it stabilizes.

Now I know that regular water changes are good. I know this post is now irrelevant, but decided to share it. I think it's a good prove how regular water changes are good for your tank.

 

[LunchBox]

so out of curiosity how did it end up stabilizing? Not that I'm disputing anything, but I was just curious.

EDIT:: oh nevermind... I was being math-lazy for a minute there but now that I've thought about it I figured it out

 

[Roan Art]

Pat,

It's a hoot doing that kinda stuff, eh? I love taking some of the numbers I get and looking for patterns in the inkspot. Sometimes you never know what you find and what you do, you end up learning something new.

It's cool.

Oh, now try the same thing on a planted tank and see if there's a difference. At least, I hope that wasn't a planted tank. Either way, try it on the opposite and see if there are changes in the pattern or if it stabilizes faster.

Roan

 

[patoloco]

I found a pattern and no matter what conditions you have, the tank will stabilize on time as long as everything (tap water nitrate, fish nitrate production, plants nitrate consuption, water change schedule, etc...) remains the same.

Example, in my first post I stated an unplanted tank, with a nitrate production of 10ppm per week, and a 50% water change schedule with tap water that would contain no nitrate. According to my calculation, the tank would become stable in 11 weeks.

If we add plants that are able to "eat" 5 ppm of nitrate per week, then it would be stable also at week 10.

If we raise the nitrate production at 30ppm per week: stable at week 13.

However, this will change dramatically if the tap water contains nitrate or if the water changes are reduced. Going back to the first post, the same tank with a production of 10ppm of nitrate weekly, but with a 25% water change will take about 30 weeks to estabilize. If the tap water has a 5 ppm of nitrate, it will take also 30 weeks.

I know all these calculation are hypothetical (¿sp?). I calculated it using 1/100 ppm, which is not really useful in the fishkeeping hobby, since nitrate concentrations are normally measured in 10ppm increments.

 

[patoloco]

Also, I forgot to state that the larger your water changes are, the tank will stabilize at a lower "normal" nitrate concentration.

When you do 50% partials, you nitrate reading will almost be always the sum of the fish production + nitrate in tap water.

If you use to do 25% partials, it will be higher. If you plan doing 75%, it will be lower than that.

Well... I spent almost 2 hour gettin that conclusion.

 

[joephys]

Incase anyone wants to know how this works mathmatically, its a differential equation.

dN/dt = -.5N+10

For those that don't know math, dN/dt is the rate of change of nitrate per week, N is the amount of nitrate. The -.5N means, half of the nitrate is removed in a week, and the +10 means ten nitrates are added every week.

A property of differential equations is that solutions don't cross, and solutions either go towards or away from an equilibrium solution. An equilibrim solutionis when dN/dt = 0, so

-.5N + 10 =0
-.5N= -10
-2(.5N) = -2(-10)
N=20 nitrates at equilibrium

 

[patoloco]

I think you got the best avatar-personality combination of the entire internet.

 

[hurricanejedi]

The same sort of thing happens with bengal cats. The first 3 generations you are reducing the wild gene by breeding them with a domestic. By the 4th generation and onward it is stabalized at about 7% wild and dosne't reduce any further. Therefore at the 4th generation they are considered domestic cats. Its hard to explain this to people but I guess its just another application of the same concept .