If I have a single 120mm PC case fan which pushes X cubic feet per minute, will stacking several together proportionally multiply the CFM, velocity, and/or the pressure? If I put them in parallel, i.e. side by side, it seems to me that would proportionally multiply the cross-sectional area, and therefore, volume, of air I can move.
If I treat the fans as weak pumps, then using this article about pumps in series, it would seem the pressure would increase.
It seems like you are drawing an analogy between fans and batteries.
The that analogy (with air pressure and volume flow rate) and batteries (with voltage and current) should be pretty close at low flow rates. In this analogy, any volume that the air travels through will be analogous to a resistor.
I'm not sure if the analogy breaks down when the flow rate causes turbulent air flow.
Sound waves, in this analogy would be like alternating currents. There is even some work on what an acoustic diode would be like.
Fans can be back-pressure sources (this is the case of squirrel-cage blowers, like used in vacuum cleaners), or they can be volume-of-flow sources, or anything inbetween. Probably the familiar radial-blade air mover is most near a volume source (unless airflow is constricted somehow), so a second similar fan in series might rotate like a pinwheel, neither adding to the air velocity nor retarding the airflow (and not taking much power).
The tuyeres of a forge may act as a significant backpressure, and the classic bellows that a forge uses, is a fixed volume source with nearly unlimited forward pressure (because the apprentice works hard!). A vacuum-cleaner style air source could be run with a speed control to drive tuyeres. A single PC cooling fan might not push hard enough, but several in series will to some extent share the backpressure load. Adding fans in series won't add to the volume per minute of the single fan in free air, but might counter backpressure.
