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I'm switching my 29g's water from its current water to RO water. I will be changing the water at a rate of 10g per week. How long will it take to convert the tank to 99.99% RO water(technically it will never reach 100%)?

Maybe it's not a calculus question, but I think it can be set up as one. Let me know!!!

:%)]:|:%)

Well, every water change changes 10/29ths of the water, or 34.48%, meaning that 65.52% remains. So we have .6552 ^ n = 0.0001 where n is the number of water changes. This is the same as saying that (n log 0.6552 = log 0.0001) and this solves to n = 21.78. So that would be 22 water changes of ten gallons each, regardless of how often you do them.

Random notes: evaporation is ignored - it would favor the ratio of tap over RO since it would effectively be RO water that is evaporating out. The ^ symbol is often used for exponentiation when there's no typographical way to write it correctly. Lastly because I'm a stickler this is technically an algebra question.

Last edited by Silverlight at 20-Oct-2004 10:00

LOL in that case I was WAY off course

I came up with (which is no doubt wrong):

c(n+1) = 0.6552 c(n)

Where c is the concentration of original water and n is the number of changes...

doing it long hand (with rounding, where I fell over mainly) I got:

100%-->65.52%
65.52%-->42.93%
42.93%-->28.13%
28.13%-->18.43%
18.43%-->12.08%
12.08%-->7.91%
5.18%-->3.39%
3.39%-->2.22%
2.22%-->1.45%
1.45%-->0.95%
0.95%-->0.62%
0.62%-->0.41%
0.41%-->0.27%
0.27%-->0.18%
0.18%-->0.12%
0.12%-->0.08%
0.08%-->0.05%
0.05%-->0.03%
0.03%-->0.02%
0.02%-->0.01% (20 weeks)

I was going to see if I could find a freeware CAS program to run it through, in which case it _may_ have been more precise...

Hey, I failed maths What can I say?

Dex (A former straight F maths student)

Last edited by dextroze at 20-Oct-2004 10:53

Your technique is perfectly good (and is mathematically equivalent to what I did) but you might have had problems with rounding error.

EDIT: ...which of course you mentioned.

Last edited by Silverlight at 20-Oct-2004 11:04

LOL knowing me: I _would_ find a way to stuff it up

I was sooooo hopeless at maths, and it has been 10 years *feels old*

Oh well, a challenge, even one failed, keeps the old mind active

Dex

edit: just stepped it through windows calculator and was indeed 22 events to get past 0.01%... *mental note: rounding is NOT your friend*

Last edited by dextroze at 20-Oct-2004 11:11

Another problem you're going to have with that is that you're constantly adding nutrients to the tank in the form of food and possibly decaying plant material... your substrate and glass will give off trace amounts of minerals... Carbon dioxide in the air will react with the water and make carbonic acid... you will never get it down to 99.99% pure water in there, no matter how hard you try!

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Superlion is right. All non metal oxides from the air will form acids in water, not to mention the waste that your fishes will give off, (and aquarium decor), etc...

Well, it's also reasonable to interpret the question a little differently: "If I start with a tank filled from the tap, and start water-changing with RO water, how long will it take before my tank is filled, as if I'd started with 99.99% RO?" I don't think the original poster was looking for 99.99% pure water in a running tank!

So, 22 weeks huh?

In order to keep in a little simpler, I was ignoring the many, many factors that could also play into the equation (evaporation, liquid ferts, food, water loss while aquascaping, etc.). Thanks for the solution.



Last edited by just_one_more at 21-Oct-2004 12:08

I'm only in algebra II...calculus is out of the question!