i'll add that fans are not magic. there are actually equations (& many of them) to design & estimate CFM vs RPM for a given fan geometry. i won't put them together for you because i just got done investing years in college learning them & know it would take years to teach them to you. to oversimplify things a bit:
a fan's noise & CFM depend mainly on the aerodynamics of the rotor (yeah, you also have bearing vibration & structural resonance runing around too). regardless, most fans have a distinct "design point", where the rated RPM keeps the blades at the optimal angle of attack, so the energy transfer from the motor to the air is optimized for the required CFM (electrical power/kinetic energy is minimized). of course different fans have different design point RPMs, that's also why thier blade geometry is different, but not by happenstance.
it is mostly large scale turbulence created by flow separation at off design angles of attack that create noise. the below scan from my textbook sort of illustrates blade stall, which very much complicates any prediction of off-design noise & CFM levels:
you can use your intuition to conceptualize how RPMs off the design operating point & back pressure (or foreward pressure) can lead to this separation on rotor blades. back or foreward pressure is another determining factor in noise & CFM calculations for both on & off design. to add these effects, we must consider many more variables that add up to the total Fanno Friction Factor (not worth doing for PC cooling systems, at least yet).
the bottom line, spinning rotors become essentially useless when the blades are in a stalled condition. if you know wings a little, you know you want to avoid stalling the wings of an aircraft. if forward moving wings (like spinning rotor blades) are beyond the stall angle of attack, the "lifting circulation" surrounding the wing stops & lift drops drastically, sending the aircraft barreling into the ground if there is not enough pilot skill, speed, & altitude to recover (unless you're like Patty Wagstaff, cheers Patty;-).
BTW, that image of rotor stall & the velocity vectors might give you a clue as to how us aeros would go about our "magic"
. i reality none of it is majic. if you are curious enough, i have a bunch of those equations posted on my website (some with & some without context). look at the bottom "A Taste of..." section; "Propulsion" & "Aerodynamic Equations" are the files that have it all:
nemaste's Aero Page