I'll look over my post to make sure I didn't somehow misword something.

Gear backlash is pretty easy to model since it is not really force or time dependent, just position dependent. You can compensate for it well in the retract settings.

Don't get me wrong, I use 1.75mm exclusively - I just don't think there's much in the way of benefits in one over the other.

If the flow is laminar/incompressible/inviscid, then flowrate scales with the square of diameter, assuming all other variables are constant.

But they aren't. The pressure generated by the feedscrew is a function of several variables, including flowrate. Therefore, I simplified to "doesn't quite work like that". In practice, 3mm is 20-50% faster than 1.75mm from a volumetric perspective.

Why is 3mm harder to extrude through the printer? [CITATION NEEDED] Sure you need more force, but you also need less speed. That's why things like gears exist.

Hi Elmoret!

Thanks for the response! That's awesome.

Now, if the flowrate is actually scaling with the square of the diameter, I really don't see why the 3mm would be inferior to the 1.75mm.   Because like you said- gears, and the fact the area crosssection is the same for 3*1.75mm as 1x3mm. In fact,1.75mm would be inferior simply because it's less than 5ish times as strong in bending, because that I more confidentially remember is governed by I^3. But a well supported tube should eliminate the problem for 1.75mm and 3mm. 

So I tried to google up what I was remembering from reprap forum trawling. I'm finding people say that it's just about the volume flowrate going through the nozzle, which this time suggests 1.75mm vs 3mm doesn't matter. 

So while I made an unsupported claim earlier, the only nagging idea is this recollection that say for AC ducting the input diameter and the output diameter matter to determine pressure developed for a given flow, but in this plastic case we're saying only the output diameter matters.  So I guess that memory about AC ducting is either wrong or not applicable? It could very well simply be because with faster moving air and AC ducts you're looking at turbulence related to the constriction

Cons to 1.75mm:
Bigger surfaceArea/volume ratio - problem for storage.
worse for very not-stiff filaments; kinks easily.
more expensive in some locations
worse grip on the filament (though you need less grip.)

Pros to 1.75mm:
less melting stuff in the barrel, more effective retract.
better thermal connection to the heated nozzle.
doesn't require gears that potentially have backlash.
for very stiff or brittle blends (exotic pla blends maybe, acrylic, etc) easier wrap around the spool.

I'm sure I forgot some stuff. I just took the moment to try to summarize a few things since you made me realize I wasn't questioning my previous assumptions.

But they aren't. The pressure generated by the feedscrew is a function of several variables, including flowrate. Therefore, I simplified to "doesn't quite work like that". In practice, 3mm is 20-50% faster than 1.75mm from a volumetric perspective.

Why is 3mm harder to extrude through the printer? [CITATION NEEDED] Sure you need more force, but you also need less speed. That's why things like gears exist.

Not 2x faster, flow through an orifice doesn't work quote like that. You're also limited by pellet conveyor rate (in other words, eventually you just aren't supplying pellets to the melt zone fast enough).

Hi Elmoret, do you think it should be more than 2X faster? I don't quite know how flow through an orifice works, but the pressure caused by flow through an orifice 1/2 the diameter I thought would be either 4 or 8 times greater (it is my vague recollection that the diameter/pressure correlation is ^2 or ^3). But I am sure it depends on various assumptions (since this stuff is slow-moving and not-exactly-fluid I don't really know what governs it.)

To OP: For what it's worth, just because its some bit faster now, doesn't mean you're better off. The problem is 3mm is a lot harder to extrude through the printer than 1.75mm, and originally was used simply because it was available from plastic welding supply stores. The somewhat more common modern convention is 1.75mm for fairly decent reasons.

Since the nozzle is larger, doesn't that mean more material can pass through quicker?

Yes.

More heat (energy): Yes.
More temperature: No.

In other words you set the controller to the same temperature, but it will stay on a greater percentage of the time.