Re: More musing on water change.

[Scott Lewis <ScottWmLewis at attbi_com>]

Tyrone Genade wrote:

> On 25 Jul 2002, at 10:08, Wright Huntley wrote:
>
> The biochemist to the rescue... perhaps.

and..... perhaps someone who understands mathematics to set the record
straight.


> > 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.
>
> The fish produce for arguements sake 10 mg/ml of waster per week. X
> 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... eventually you will reach a situation where
> the tank is a puddle of sluge. No. Plants and bacteria will take the
> waste up and turn it into biomass which is siphoned out from the
> gravel or rinsed from the filter medium. But still there is NO
> EQUILIBRIUM this way. So far Charles is right. 10 pts to him, 0 for
> Wright.

When you do a 25% water change, the tank will reach equilibrium when the
wastes level reaches 40mg/ml.  The math expression to describe how much
waste you have in the tank is as follows:

WC = % of water replaced per week
WL = amount of waste in tank (equilibrium)
WM = waste multiplier
P = pollution added per week, can be expressed in ppm

WL = P/WC
WM = 1/WC

Thus, if you do a weekly water change of 33%, your max level of waste will
be the same as if you let the pollution/waste accumulate for 3 weeks.  2
weeks for 50% changes, 4 weeks for 25% changes, 10 weeks for 10% changes.

In the example you used above, assume you have 40ppm waste at the beginning
of the week, add another 10ppm waste, then do a 25% change.  You end up
taking -out- 12.5ppm waste, this is more than you put in during the week.
That should tell you something......namely, you are taking out more wastes
than is being added.  Thus, the trend of the wastes levels is -down-, not up
as you would have us believe.

This example is somewhat oversimplified in that it assumes there is zero
contribution of wastes in the change water.  Even with a fixed level of
waste in the change water, the same principle holds true with a slightly
more complicated formula.


> If you have a 100 l tank and drip 1 ml of water into the tank every
> minute for 100'000 minutes you will only have a 99.999.... % water
> change. You can never flush the tank 100% unless you remove all the
> water and fish and let the tank dry.

True.  I would not suggest a rate this slow.  But, the wastes levels will in
this case reach an equilibrium roughly of a 10 week old tank with no water
changes.

At 10 ml per minute, this tank would reach roughly the same water change of
50% per week.


These are first order calculations.  Add the effects of evaporation and low
levels of certain waste products in the change water and you would have a
bias added to the equilibrium level.  Certainly nothing like a continuous
increase as you suggest.

Do the math.  It works out.


> Strictly speaking there is no equilibrium in the standard fish tank
> and eventually one will have to do a bigger water change or clean the
> tank as waste builds up.

Do the math.  This is an erroneous statement.  The only part of this
statement that is true pertains to solid wastes that does not get removed
with water changes.  Using a gravel vac during water changes takes care of
this issue.

--
Scott

-- Microsoft Outlook, the hacker's path to your hard disk.




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