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Fish Math III: The Ultimate Water Change :-)
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Which water change routine will keep his nitrate below 40 ppm?
I have no idea how to solve this
14%
 14%  [ 7 ]
10% every week
2%
 2%  [ 1 ]
20% every week
47%
 47%  [ 23 ]
25% every 2 weeks
16%
 16%  [ 8 ]
30% every 2 weeks
12%
 12%  [ 6 ]
35% every month
2%
 2%  [ 1 ]
40% every month
4%
 4%  [ 2 ]
Total Votes : 48

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Marcos Avila
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Joined: 05 Feb 2003
Location: Santo Andre (Brazil)

PostPosted: 2003.08.16(Sat)16:16    Post subject: Fish Math III: The Ultimate Water Change :-) Reply with quote

OK, this one should be a little less trivial than the previous ones. Tommy finally convinced his landlord to let him have a huge tank in his new apartment, so he set it up with all the goodies, did a perfect fishless cycle for a couple weeks, and then added his wonderful adult Red Devil Cichlid breeding pair. In order to know the tank behavior better and decide what will be his optimal water change routine in this tank, he started measuring the nitrate levels along the following weekends after adding the fish, and got these results (no water changes during this period):

1st weekend: 10 ppm (10 mg/L)
2nd weekend: 15 ppm (15 mg/L)
3rd weekend: 20 ppm (20 mg/L)
4th weekend: 25 ppm (25 mg/L)

Tommy is a busy guy and doesn't want to invest more time and money than necessary in the tank maintenance. Assuming that there won't be any significant change in the tank water's chemical behavior over the next several months, and knowing that keeping the nitrate level below 40 ppm is good enough for a non-planted tank like his, which of the options above will guarantee the minimum effort that still allows him to achieve this goal in the long term?
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Last edited by Marcos Avila on 2003.08.17(Sun)0:13; edited 1 time in total
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Cyradia
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Joined: 06 Feb 2003
Location: Winston-Salem, NC

PostPosted: 2003.08.16(Sat)19:08    Post subject: Reply with quote

Dude, I had to bust out real math for that! That was great!
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Irons
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Joined: 27 Feb 2003
Location: Buffalo, NY

PostPosted: 2003.08.17(Sun)11:39    Post subject: Reply with quote

That took a little time. Fortuanatly, I was able to eliminate a few right off the bat. That was fun anyway. Intersting results. Not the one I thought right off.
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Tommy
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Joined: 06 Feb 2003
Location: Mountain View, CA

PostPosted: 2003.08.17(Sun)14:42    Post subject: Reply with quote

You forgot the part about how badly Tommy sucks at math which is why he needs the help in the first place Wink

:::sadly clicks on "I have no idea..." Confused :::
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anonapersona
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Joined: 06 Feb 2003
Location: Houston, Texas

PostPosted: 2003.08.17(Sun)16:08    Post subject: but, there's still an easier way Reply with quote

True, it cannot be done on the 4th weekend, but at a certain point, Tommy could do even less work.
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Marcos Avila
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Joined: 05 Feb 2003
Location: Santo Andre (Brazil)

PostPosted: 2003.08.17(Sun)22:06    Post subject: Reply with quote

Hmmm...interesting...17 people have replied and only 3 have chosen what I consider the correct answer Shocked Before I show the solution, let me state that I've only recently realized this mathematical approach towards developing a guideline for routine water changes, and I haven't actually applied it to any tank, so feel free to argue with me if you find any hidden variable...

The general approach is surprisingly simple: assuming that your setup builds up X ppm of nitrate during the period T between water changes and you want to make sure the nitrate levels reach no more than Y ppm when the time for a water change comes, then the amount of water you should change every T days is simply X/Y. No matter what the current nitrate level is, if you stick to the routine of changing X/Y amount of water every T days your tank will eventually reach a steady-state regime where the nitrate level doesn't rise over Y because the amount of nitrate you remove in the water change is the exact same as the amount that has built up since the last water change!

Using the example above, Tommy's measurements showed that his tank builds up 5 ppm of nitrate per week. If he wants to do water changes every 2 weeks, the tank will build up 10 ppm of nitrate in between them, so in order to maintain nitrate levels at no more than 40 ppm he has to change 10/40 = 25% every 2 weeks, which is the correct answer!

Of course, he may choose to do water changes only every month, but in this case his tank builds up more than 20 ppm in between water changes (a month has a little more than 4 weeks) so in this case he'll need to do at least 20/40 = 50% water change per month in order to keep nitrate below 40 ppm, so the two 'monthly' options in the problem are wrong because 30% and 40% are not enough, nitrate will keep building beyond 40 ppm.

Or, he may choose to do weekly water changes and in this case the amount is 5/40 = 12.5% per week, so the two 'weekly' options in the problem are wrong because 10% is not enough and 20% is overkill, in the latter case his nitrate levels will remain at a lower level than 40 ppm, resulting in a greater effort than he really needs. Wink

Obviously, this guideline assumes that nitrate is the determining factor in the need for water changes, and that the nitrate buildup will not change over time, which can easily happen if you overpopulate, overfeed or don't do proper maintenance on your filters, fail to remove accumulated organic matter, and so on, so it would be important to check the nitrate buildup occasionally and fine-tune your routine.

Comments? Smile
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Irons
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Joined: 27 Feb 2003
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PostPosted: 2003.08.18(Mon)6:25    Post subject: Reply with quote

I calculated the every week by doing this...
25ppm * .80(20% change) = 20ppm (week1)
20ppm + 5ppm(weekly build up) = 25ppm
25ppm * .80 = 20ppm (week2)
Wash, rinse, repeat.

I did not pick 25% every two weeks because:
25ppm * .75(25% change) = 18.75ppm(Week1)
18.75ppm + 10ppm(two week build-up)= 28.75ppm
28.75ppm * .75= 21.56(Week 3)
21.56ppm + 10ppm= 31.56ppm
This eventually spirals up to over 40ppm.
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anonapersona
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PostPosted: 2003.08.18(Mon)11:06    Post subject: But Tommy is lazy Reply with quote

Tommy won't do any water change until the tank reaches 40 ppm, he will not start on the 4th weekend, he will wait until the 7th weekend.

But, then he will decide to do a 50% water change if he uses a Python, a 25% water change if he uses buckets, its a big tank and who can devote a weekend morning to hauling buckets around?
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ACE125
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Joined: 05 Feb 2003

PostPosted: 2003.08.18(Mon)12:13    Post subject: Reply with quote

Irons wrote:
I calculated the every week by doing this...
25ppm * .80(20% change) = 20ppm (week1)
20ppm + 5ppm(weekly build up) = 25ppm
25ppm * .80 = 20ppm (week2)
Wash, rinse, repeat.

I did not pick 25% every two weeks because:
25ppm * .75(25% change) = 18.75ppm(Week1)
18.75ppm + 10ppm(two week build-up)= 28.75ppm
28.75ppm * .75= 21.56(Week 3)
21.56ppm + 10ppm= 31.56ppm
This eventually spirals up to over 40ppm.


The problem with this is that you
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Marcos Avila
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Joined: 05 Feb 2003
Location: Santo Andre (Brazil)

PostPosted: 2003.08.18(Mon)12:58    Post subject: Reply with quote

Thanks ACE for wording the main idea very clearly...it doesn't matter WHEN you start making the water changes nor what is the CURRENT level of nitrates (high or low), as long as you stick to the routine described above, in the long term your nitrate levels will inevitably CONVERGE to the level you chose in the formula!

Let's change Irons's example a little: notice what would happen if Tommy got very lazy and allowed the nitrates to build up to 60 ppm before doing his first water change:

60ppm * .75(25% change) = 45ppm(Week1)
45ppm + 10ppm(two week build-up)= 55ppm
55ppm * .75= 41.25(Week 3)
41.25ppm + 10ppm= 51.25ppm

So you see that the level is slowly decreasing towards 40 ppm Wink
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Success with a fish/tank is measured in YEARS, not months or weeks...


Last edited by Marcos Avila on 2003.08.18(Mon)14:10; edited 1 time in total
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