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Pet Forum / Aquaria / Marine Reef / January 2007Calculating final nitrate level after water change
Hello, I realize this is probably a fairly simple equation, but I'm really struggling with it. I'm trying to create a formula (perhaps to eventually work into a classroom lesson) to predict the nitrate concentration in the aquarium AFTER a partial water change. This is complicated by the fact that I use natural ocean water, which, at least in this area, is NOT nitrate free (low, but not free). I realize I could just ignore this semi-insignificant factor, but the point of this is to include all inputs. Any ideas? Thanks Ryan Lenz > I realize this is probably a fairly simple equation, but I'm really > struggling with it. I'm trying to create a formula (perhaps to > eventually work into a classroom lesson) to predict the nitrate > concentration in the aquarium AFTER a partial water change. Yeah, it's pretty simple. Let's take the example of a 125 gallon tank with a nitrate level of 50 ppm. We'll change 25 gallons of the water with water that has no measurable nitrates. Twenty-five gallons is 20% of the water, so we will be removing 1/5 of the nitrates. Put another way, 80% of the nitrates will remain in the tank. Given N is the nitrate level, TS is the tank size, GC is gallons changed, and RN is remaining nitrates. RN = N * (1 - (GC / TS)). Plug in the numbers. RN = 50 * (1 - (25 / 125)) => RN = 50 * .8 => RN = 40. If the water you use for a change has, say, a nitrate concentration of 10 ppm, then just add that back in. Call the concentration N2. The equation would be RN = RN + (N2 * GC / TS). Plug in the numbers. RN = 40 + (10 * 25 / 125) => RN = 44. If you want the entire thing as a single equation, RN = (N * (1 - (GC / TS))) + (N2 * GC / TS). George Patterson No one ever says "It's only a game." when his team is winning. > If you want the entire thing as a single equation, > RN = (N * (1 - (GC / TS))) + (N2 * GC / TS). By the way, "TS" in there is the actual amount of water in the tank, which is usually less than the tank size because of the rock, substrate, etc. in the tank. For example, my 125 gallon tank probably only has about 90 gallons of water in it. Running this exercise with my tank, TS would be 90. George Patterson No one ever says "It's only a game." when his team is winning. > Yeah, it's pretty simple. You are correct! It was pretty simple... and you did a good job with it :-) Let me challenge you with a different mathematical problem: Let's find out how many (x)% water changes we will need to bring (Y) ppm nitrates down to (Z) ppm level :-) Let's simplify the problem (for now) by assuming the tank DOES NOT produce additional nitrates between water changes and the water we use for partial changes is pure: (0) ppm NO3. For example: Jaime has now 100 ppm of nitrates in his tank. How many 10% water changes does he need to do next weekend to bring nitrates down to - let's say 5-10 ppm. Of course it will be easy to plug the numbers into your previous equation for couple of times, and than again and again to get the final number, but what I am asking for is a generic solution :-) Can you assemble an equation to solve this problem ? :-) > Can you assemble an equation to solve this problem ? :-) Us a variation of compound interest calculations. Let n be the number of water changes, N1 be the initial nitrate level, N2 be the desired nitrate level, and P be the percentage of water changed. Then n = log(N2 / N1) / log(1 - P) Solving for N1 = 100, N2 = 10, and P = .1, get get 21.85434512 changes. Solving for N2 = 20, we get 15.2755317. George Patterson No one ever says "It's only a game." when his team is winning. >> Can you assemble an equation to solve this problem ? :-) > [quoted text clipped - 6 lines] > Solving for N1 = 100, N2 = 10, and P = .1, get get 21.85434512 changes. > Solving for N2 = 20, we get 15.2755317. Very good! We should name you a Group Math Wizard :) lol I was beginning to think I was back in high school algebra > >> Can you assemble an equation to solve this problem ? :-) > > [quoted text clipped - 8 lines] > > Very good! We should name you a Group Math Wizard :) > Very good! We should name you a Group Math Wizard :) I don't think so. I'm pretty good at Algebra, but Trig is a lot of work, and I was glad to see the last of Calculus. George Patterson No one ever says "It's only a game." when his team is winning. |
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