This would be on 100 gallon
Regarding whether or not a skimmer and tank water quality can be reduced to equation(s), I would think that clearly our ecosystems are governed by observable processes that can be represented mathematically. A certain skimmer of specific parameters (whatever you think that the relevant parameters are ) should be able to reduce organics by whatever percentage in a given amount water in a given amount of time. This would be the only empirical, objective way to rate skimmer efficiency. Now this rating can be derived two ways - either through experimentation (dump a bunch of junk in the tank and figure out how much the skimmer removes) or by theory, which it seems to me what this thread is.
Now, whether or not we are smart enough (and I mean myself included) to figure out those variables, thats on us, not an inability for what happens in a skimmer to be described mathematically.
Here's where I get hung up on this conversation so far. The idea that a certain size skimmer works better on a certain size tank. In reality, the skimmer has no idea what size tank it is hooked up to. Its output is only driven by the amount of dissolved organics in the water. So take your biggest skimmer, hook it up to a 10 gallon tank, and drop a dead carp into the tank and it will "skim" like crazy.
The "balance" that we are talking about comes into play when you consider that if you hook a superefficient skimmer up to a very large tank, but dont have enough throughput, the water coming out of the skimmer will be super clean, but since it doesnt turn over the tank fast enough, DOCs in the tank water that have not yet been processed are converted to nitrates before they have a chance to hit the skimmer.
On the other hand, push a ton of throughput through an inefficient skimmer, and the wtaer doesnt come out clean.
Is there a way to combine the throughput with efficiency in an elegant (for instance, energy efficient, small footprint) way, without resorting to simply overpowerign the skimmer (i.e, the "6 footer", which I've owned, btw).