Find the Best Fan or Propeller for Efficient Cooling in a 3 1/2" Device

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TL;DR
Required air for cooling
I have space in a device about 3 1/2" across and need to get 12cfm of fresh air from this area via a reducing funnel with a ration of 15:1, into a 3/4" tube requiring cooling air inside it at a velocity of 4000fpm. How do I select a fan or drone propeller combination that will do this?
 
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If you have space for a 3 1/2" x 3 1/2" footprint (as opposed to a circular footprint? wasn't clear there), then you could get a 90mm PC fan and file down the sides until it fit (it's only 1mm oversize). If that's too much flow (if that even matters for your application), you can wire a resistor in series with the fan to reduce the power output.

If you meant 3 1/2" circular footprint, then try a 60mm fan.

The fan specifications usually include a flow rate in cfm.

If it was me, I would just buy an extra powerful fan and throttle it with different resistors until I saw 12cfm on the other side of the reducer. Ignoring turbulence, just basic Bernoulli equation says you'd only have to fight 260Pa of back-pressure which is chump change, so one of these PC fans (espeically a 90mm) should be plenty of oomph. If you reaaaaaally need it to be 12cfm as opposed to "good enough" (which I strongly recommend if possible), you would need a hot-wire anemometer for flow measurement.
 
You will need more than a muffin fan. A velocity of 4000 FPM has a velocity pressure of 1.0 in w.c. (inches of water). If your 3/4" tube is short, the fan needs to be rated for 12 CFM at 1.0 inches of water pressure. A long tube, especially if it has bends, will need more pressure. That will require a centrifugal blower, not a fan.

Here is a possibility: https://orionfans.com/productFiles/datasheet/OAB908AN.pdf. I'm sure that there are other fans available that will meet your needs. This is just the first one that I found on a quick search. Digikey, Newark, and Mouser are the first sources I would look into. There are other sources, these are just the ones off the top of my head.
 
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@jrmichler is right. I had no idea fans were that finnicky to back-pressure, but if it takes this blower 60W to maintain 20 CFM at 260Pa (about one inch H2O) then there's no way a PC fan will do anything close to 12 CFM. My bad.
 
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