You are free to hold any opinion you wish, but what you just said is simply not true. Nobody here is protected from disagreement, me, Randy, the ownership, staff or you. You are free to, and openly encouraged to debate your point as long as you do so within the confines of the TOS.
You pulled "nearly" and "less" out of a sentence that listed rock, varied flow patterns, striations, eddies, and nearly dead zones. The purpose of the whole list was to describe non-uniform flow. You dropped the context, swapped in "zero," to change the meaning.
Fact and the point: Some areas run below the tank average, and that alone breaks the equal probability assumption your n-passes math requires. You used the wrong model to argue. Full stop.
Also: The differential pressure article you quoted and cited is about pressure drop across industrial filter media. Zero crossover to tank mixing and zero relevance to any argument here, and the line you quoted isn't in it. Was that citation AI Search derived?
I very clearly laid out that your model assumes a single dose of something that can be traced as mixed into the water, not that UV is a single dose. I also clearly laid out that the target itself, parasite, bacteria, or anything else living in the water, is not a single dose, but a series of "doses" as the population expands.
UV doses accumulating was never the argument. The argument is that the calculator you used to make your case doesn't model any of this. Clearly laid in my original post and here.
I said flow moved detritus there, so flow exists there. Reduced flow is what a low-flow zone is. You are confirming my point and calling it a rebuttal.
Note: second time you have misstated what was said. I said non-uniform flow, some areas below the tank average. That is what breaks your equal-probability assumption. It does not require zero.
Telling me to fix my low-flow zones doesn't answer the argument or make yours. Every tank with rock in it has flow variance. It's the reason the uniform mixing model doesn't apply, not a defect in plumbing.
Randy already corrected this. Even in an ideal model with no obstacles and perfect decay math, the number does not reach 100%.
You then cited a calculator that proves him right. It returns 99.9%, not 100%. It never gets there. That is the stirred tank problem. You agreed with Randy in theory, posted the tool that confirms him, and then wrote that "there is no doubt 100% of the water molecules circulate through every powerhead and pump". That is contradictory on its face.
And if your position is that 98%, 99.9%, and 100% are close enough for practical purposes, that dismantles the absolute claim you just made. Your arguments are running into each other.
Randy's point stands in the ideal case. In a real tank with rock, the ideal model does not apply at all, so 99.x% goes out the window too.
Second, and much more important. Water molecules aren't the argument anyway. Theronts (the example you used) are not water molecules. They swim, they respond to flow and light, they concentrate in some zones and avoid others. Sessile stages are attached to surfaces and don't move at all. None of that is evenly distributed, and I said so already. No simple mathematical regression or decay model can account for this in an ideal aquarium, let alone a real one with fish, disease, substrate, rock, and everything else in the way.
Not everything in the water goes through the pumps. Period.
My response has nothing to do with UV being effective or not. I am responding to your claims and arguments about flow. That's all.
You brought detritus into this as your own evidence, and I pointed out it works against you.