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AlexAlbert;26833 said:It's just a simple log curve.Can you please show an equation used to produce graphs and final values..
AlexAlbert;26833 said:It's just a simple log curve.Can you please show an equation used to produce graphs and final values..
Figuring the cumulative change in aquarium concentration of Fe (or any element) in PPM after long term daily PMDD use with periodic water changes:
The tricky part about this is knowing depletion rates. I can figure out how water changes will deplete an element, but I don't know how much plants will. Well, since my intent is to avoid overdosing Fe, I'll look at the worst case: one where no Fe is used by the plants (sure, a rotten assumption since the whole point is to provide Fe, but it does yield an upper bound or maximum possible concentration).
Turns out concentration buildup given periodic water changes is one of those Geometric Series things.
Say "D" is the total concentration increase after multiple PMDD doses preceding a water change (figured in mG/ltr per part 1). Say "R" is the portion of pre-change concentration that remains after the water change (ie a 25% water change leaves 75% of concentration).
Well, after 6 weeks, you'd have a cumulative concentration of:
(((((D*R)+D)*R+D)*R+D)*R+D)*R+D or
D*R^5+D*R^4+D*R^3+D*R^2+D*R+D or
SUM n=0 to 5 of (R^n+D)
Now, over many many weeks you'd have a cumulative concentration of;
SUM n=0 to infinity of (R^n+D) or
D/(1+R) Simple result, aye?
So, using this secret formula D/(1+R) and putting it in terms of daily doses, days till water change, and % water change (note: % water change = (1+R)):
Long Term Cumulative Increase in Concentration =
(daily increase from dose)*(doses till change)/(% water change)
in mG/ltr or PPM in days in decimal
only valid if water volume
change >> dose volume
Carrying over the example from part 1): 1.66 ml PMDD dose daily, but with 25% weekly water changes;
(0.0144 mG/ltr Fe)*(7)/(0.25) =
_0.4mG/ltr Fe_ final aquarium concentration
Uh-oh, 4 times too high! That's why I ended up leveling off at a lower PMDD dose, about 1/2 ml a day, for my 45 gallon tank.
Again, this all assumes no depletion, a lousy assumption, so I'd measure Fe as you go. As I said, this calculation is only good for an "upper bound".