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Take a deep breath, man.:frusty:E and g cancel each other out and the average is F
How about not enough information given? Depends on what nitrates were at the start of the year. Could have been 2 billion zasillion ppm and has only gone down to a few million ppm. :wink:Reef Chemistry Question of the Day #68
There are many decisions that go into designing a reef tank. One is whether to have a sump, and if so, how large.
This question bears on just one aspect of sump size: how it impacts the accumulation of unwanted ions in relation to water changes.
Assume that you have a system with a total water volume of 100 gallons and perform a daily water change of 1 gallon.
Also assume that it has a net accumulation (before the daily water change) of 0.25 ppm of nitrate each day and that this net accumulation does not change over time, except when a water change lowers is.
After 1 year, nitrate has accumulated to a certain level. Which value is closest to that level?
A. 0.4 ppm
B. 2 ppm
C. 24 ppm
D. 180 ppm
Now assume everything else is unchanged, but you increase the sump size so that the total water volume is now 200 gallons (twice as large).
How is the nitrate level after 1 year with the larger sump compared to with the smaller sump? Assume no impacts on nitrate except as directly relate to the increased water volume via the same total amount of nitrate added each day as with the smaller sump, and the same 1 gallon water changes daily.
E. It is higher because the 1 gallon water changes are less efficient with a larger total water volume
F. It is the same because only the total production of nitrate matters
G. It is smaller because the nitrate is diluted more with a larger total water volume
Feel free to only answer the second part if you want, as that is the main point of the question.
Good luck!
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true but then we wouldn't care about water changes and how effective they are. Which means we'll miss this entire discussion.7,000 would buy a lot of chaeto and cfl bulbs. Clear that nitrate issue right up
Can I exhale now?Take a deep breath, man.:frusty:
The real question is if you can write an excel formula so that you can get that answer without having to drag it out 365 rows...
Also, Randy, there's very little that excel can't do when it comes to algebraic operations and the like. If there's something you'd like to make as far as an excel sheet goes - complete with graphs, pivot tables, macros, etc - let me know. I'm a total excel nerd and love tooling around with stuff like this.
Also, Randy, there's very little that excel can't do when it comes to algebraic operations and the like. If there's something you'd like to make as far as an excel sheet goes - complete with graphs, pivot tables, macros, etc - let me know. I'm a total excel nerd and love tooling around with stuff like this.
And the answer is...C. 24 ppm and G. It is smaller because the nitrate is diluted more with a larger total water volume
This question did generate a lot of interesting discussion. Perfect!
Like gtbarsi, I used a spread sheet to determine the answer. I didn't know the answer in advance D). More on that later.
beaslbob was the first to point out that one could look at the input vs the output. If the input is 0.25 ppm per day, when the system eventually reaches an equilibrium, the amount removed will have to be the same. So 0.25 ppm in 100 gallons is balanced by something out in 1 gallon. That would have to be 25 ppm in that one gallon to have the same total amount of nitrate as the daily addition.
BUT, there is no reason to assume that you reach equilibrium in a year. In fact, you do not.
So, to the spread sheet method.
In excel you can set up a few column and 365 rows, one for each day. On each day you take the nitrate input (0.25 ppm) and add it to the total from the previous day (the previous row), then multiply the product by 0.99 to account for the water change to get the value for that day.
Run that down 365 rows and you get 24.36 ppm, which rounds to 24 ppm.
If you run that longer and longer, it gets closer and closer to 25 ppm, which is the equilibrium mentioned above.
Now, let's look at a larger sump that doubles the total water volume.
Don't forget that the total nitrate input is the same, so we have only 0.125 ppm per day since the water volume doubled. The multiplying factor in the spread sheet is now 0.995 because you are only changing 0.5%, not 1% of the water volume each day. Eventually this tank must also reach 25 ppm, but it takes a lot longer to get there. At one year you are at 20.97 ppm. Two years you are at 24.33, same as the smaller sump at 1 year.
This question shows two interesting things (at least to me):
1. Larger sumps delay the accumulation of impurities, even with the same water change routine.
2. Excel spreadsheets are a great way to solve problems like these.
Happy Reefing!