This is technically an engineering question rather than woodworking, but I guess chances are good that someone on here has experience with this, has already tried what works well, and thus can give a better practical answer.
I'm planning to upgrade my shop vac (Festool CTL26) with a small 6'' cyclone (ClearVue CV06, if that matters) and I'm inconclusive about what's best for the "piping". Space and mobility is, unluckily, somewhat of a factor here, so my solution needs to be something that can be tucked onto a systainer sitting on a shop vac rather than a collector with 150mm pipes, a 5HP blower and a 2.5 meter tall cyclone.
The idea behind the cyclone is of course to take away 90% of the dust before it even reaches the vac, which is supposed to both save money on filters and increase the vac's total filter efficiency.
In fact, it appears like someone else already had that exact idea and is selling almost exactly the build that I had envisioned (only with a cheaper cyclone). From the photo, they seem to connect with a 50mm or 2'' hose. Seeing how they're selling that, it probably has to "work". Somehow, at least.
Also, I found some guy on Youtube who showed the same cyclone in action, and he just plugged the standard 27mm hose onto it (although he said it was 36mm). That, too, seemed to work, somehow.
Seeing how it makes almost zero difference both in price and handling, I would however like to use a combination that not just "works somehow" because some guy plugged in something that he had lying around in his shop, but something that works well (i.e. as good as you can get it, for the same money and with the same effort).
The vac has a "native" 50mm inlet (= ca. 2''), but comes with a 3.5 meter 27mm suction hose (which is quite long and thin, in my opinion). Optionally, you can buy 36mm and 50mm hoses (and of course, you can get any-diameter hoses and any-to-any adapters from generic manufacturers). My tools (router, plunge saw, etc.) commonly have 36mm suction (with one exception, which has 27mm).
Intuitively, if a vac has a 50mm inlet, I want to plug something that's 50mm in diameter into that, not anything smaller. But that may be a wrong intuition.
A smaller hose means higher airspeed within the hose (assuming the same flow volume), which is a good thing for a cyclone. Higher speed means more centrifugal force. EPA suggests in their particle matter paper that cyclone efficiency increases with smaller inlet duct area (conclusive, this gives a higher inlet duct velocity). They also say that efficiency increases with the ratio of the cyclone body diameter to gas exit diameter (not sure why that should be the case).
The inlet and outlet diameters are given by the cyclone's build (2.25'', ca. 58mm), but I assume the hose that you attach to the outlet counts, too (a 27mm hose connected to a 58mm outlet via an adapter is really just a 27mm outlet if you're honest!).
Despite that, my guts tell me to choose a 50mm hose to connect vac and cyclone (seeing how a thicker hose will let the vac "suck better, and more easily"), and a 36mm one going from the cyclone to the tool because that one has less weight and is slightly less stubborn than the 50mm one, but it loses only 1/5 as much pressure as the 27mm one and is the same diameter as the outlet on the tool.
I also assume there's less opportunity for turbulences or acceleration-deceleration effects if the hose diameter isn't constantly changing (also, it seems nonsensical to plug a 50mm hose into a 36mm hole, or having a 36mm hole when you only plug a 27mm hose into it).
On the other hand, the "rules" given by EPA suggest that using a 27mm hose on both sides would be the "most optimal" thing to do.
Using the vac's technical specifications (3,900l/min; 24,000Pa) and hopefully correct values for air density and viscosity in an online calculator, I get (assuming a straight steel pipe 1 meter long)
27mm : v = 113.5 m/s = 6,811.5 m/min = 22,347 ft/min, Δp = 58.66mbar
36mm : v = 63.8m/s = 3,831.5 m/min = 12,570 ft/min, Δp = 12.61mbar
50mm : v = 33.1m/s = 1,986.2 m/min = 6,516 ft/min, Δp = 2.45mbar
-- all with turbulent flow (not like it matters, but it seems like you need a hose 1.5 meters in diameter to get laminar flow at these speeds?!)
Meanwhile I've verified these numbers forwards and backwards three times with a pocket calculator, they seem indeed correct. Which is surprising, since even with the 50mm hose, I'm still well above the 4,000 ft/min recommended by the WOOD Magazine article mentioned in this somewhat related answer.
Actual pressure loss on a twisting, ripped plastic hose will obviously be larger than on the assumed straight steel pipe.
But, purely from a flow-speed-at-muzzle perspective, there doesn't seem to be any real difference, I could just as well use the thickest hose to minimize pressure loss, and still be above the 4k figure.
Basically, the question that remains to be answered is inhowfar it makes a difference to the cyclone whether a smaller hose is used. I am still inclined to assume that a somewhat smaller hose on the "tool side" might be a benefit since air enters the vortex with higher velocity.
However, according to the law of continuity, once inside the cyclone, flow speed should rapidly decelerate to accomodate for the cyclone's large diameter anyway.
Surely, this is something that someone else has already come across and tried out which one works best?
Images speak more than a thousand words, so here is what the vac looks like "by default":
... and that's what I want to make of it, and what I wonder: