Never really looked at it that way, but if I were going to attempt an approximation, I'd look at the diameter of the blades (actually area) times the thickness of the fan to get the total volume then subtract the volume of the hub. That would tell me how much air is "in" the fan at a given moment. Now if you assume a single fan blade, and sweep it around 1 revolution, it would evacuate all that air. If you have 2 blades, you'd only have to sweep 180degrees to evacuate the air. Etc. Then factor in the speed of the fan (RPMs) and you could back out a volumetric flow rate. I'm curious how close that approximation is, so here goes.
Looking at a Sunon PSD48HDAZBX-A 170x150x51mm fan. Says it's a 3 blade fan - 417.2cfm at 6200RPM. Blade diameter is about 133mm and hub is about 1/3 of that (44mm). So volume is 51*pi/4*(133^2 - 44^2) = 630,671 cubic mm = .0222 cubit ft. So for a single revolution, it would evacuate .0666 cubic feet of air (3*.0222). Running at 6200RPM results in 412 CFM. Not bad for an approximation.
-tg
(hope I didn't make a stupid mistake and just got lucky)