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Re: More musing on water change.

>Tyrone Genade wrote:
>>On 25 Jul 2002, at 10:08, Wright Huntley wrote:
>>The biochemist to the rescue... perhaps.
>>>Charles n Sue Harrison wrote:
>>>>There is no equilibrium. and that is a common thought, that there
>>>>must be.
>>No. And I will show why this is wrong but only after I give Wright 
>>a good flaming... (how rare)
>>>OK, Charles. Can you show me the arithmetic that demonstrates that?
>>>If the added poop/concentration each week is *less* than that
>>>contained in 25% of the total volume, you removed more than was added,
>>>with a 25% change. How does that eventually reach a solid sludge
>>>stage? Sounds like a classic partial dilution to me.

Your correct, mathematically, and it depends upon how much one 
changes as to how deep one gets into natural non-equilibrium problems.

>>The fish produce for arguements sake 10 mg/ml of waster per week.
>I suspect you may have meant a total of 10mg/L per week? Lets assume 
>it is more like 1 gram in a 100L tank. Doesn't change the principle, 
>does a 25% water change. Now there is 7.5 mg/ml waster left. One 
>week later and now there is 17.5 mg/ml waste. 25 (%) water change 
>and then there is 13.125 mg/ml...

and then the system adds 10 mg to bring it to 23.125
  another 25% change leaves 75% of the solids or 17.34
then the system adds 10 mg to 27.34, change - 75% left to 20.505,
adding the next week's 10 get us to 30.5 - 75% left to 22.875 mg,
adding another 10 to 32.874, 75% change -> 24.656mg,
adding another 10 to 34.7mg , 75% to 26 mg
adding another 10 to 36 mg and a 25% drops the solids to 27,
adding another 10 -> 37
we have gone 6 weeks and tripled the original solids.

The math is correct, there is an asymptote to the effect of changing 
water, and the final product remains at this concentration of waste 
until something dies or the tank is over fed and the major of change 
of tank water is necessary. The fish keeper is faced with the 
non-equilibrium situation of nature. As Barry pointed out 50% changes 
only double the amount of waste in the asymptote, 75% changes only 
raises it by 25%

If the tank gets major changes weekly the question of equilibrium vs 
non-equilibrium need not be raised.
We may argue equilibrium from the mathematical view and 
non-equilibrium from reality. The larger the environment the smaller 
the effects of our changes. Our fish rooms and our 5, 10, & 20 gallon 
tanks are just too small to be classified as environments in 
equilibrium. It's reality.

I will give the next 10 to my breeders and newly hatched fry.

Charles H.

>You might read what I actually wrote, instead of making assumptions. 
>Note that 13.125 is way less than twice the 7.5 of the previous week 
>and it will continue to asymptotically approach a situation where 
>the removal is 10 (whatevers) per week, and the contaminants are 
>oscillating between 30 and 40  each week. If you remove exactly as 
>much as is added, I fail to see how you can increase the 
>concentration any more.
>Minus 10 for Tyrone. :-) Engineering still works.


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