I was surprised that my inline fan manufacturer couldn’t tell me how to estimate the CFM I’m getting once I’ve attached a carbon filter and put the combo in my tent. So I spent a bit of time on a forum for HVAC professionals and have returned with this:
Estimated CFM = (O - I)^0.5 * k * π * r^2 , where
O and I are the measured pressures outside and inside the tent, respectively, expressed in kPA,
r is the radius of the fan’s ports, and
k is a conversion constant = 8.637 if r is expressed in cm and = 55.73 if r is expressed in inches.
So, as an example, given a pressure difference = 2 kPA and a 4" fan:
Estimated CFM = 2^0.5 * 55.73 * π * 2^2 = 990
990 CFM? What is the rated max CFM of your 4" fan?
Easier to make a swing-gauge & flow the fan at 100% power & at 0%, 25%, 50%, & 75% obstruction while marking out where the gauge ends up at those obstructions, then identify losses on the gauge during install, & finally optimize the system on the gauge. Best thing about it is, no math needed.
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“So, as an example…” means that what follows is an example. 
If you and others think your swing gauge procedure is easier than plugging 2 numbers into the equation I’ve provided, that’s fine. But many of us who use a tent have gauges that show the pressure difference and know the diameter of our inline fan. The equation provides a way to estimate CFM from that information alone.
Sorry, I thought you were giving your example with numbers that you had already tested & the result seemed off, but looking at it again & I should have known that 2 kPa of pressure would not be realistic to begin with. Yours is really not bad info, I got thrown off by your example.
Diy swing gauge is probably easier if you don’t have the tools & don’t want to get them, probably not as easy if you already do have them. I think I actually do have them lol.
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No problem. I chose 2 kPa for convenience in the calculation and didn’t consider how ludicrous getting 990 CFM from a 4" fan would be.
One of the many parameters that’s worth paying attention to when growing in a tent is the air-exchange rate. I’ve seen recommendations ranging from once per minute to once every 5 minutes. I know my tent’s volume but have no way to measure CFM directly. The equation gives an estimate from information I have.
So, as an example, 
990 CFM in my 76 cubic-foot tent would change the air (990/76 =) 13 times/minute. I’d have to keep our cat away from the prodigious suction at the intake port, though. 
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It is an interesting question though, which is easier to do, using a pressure gauge or making a swing gauge. I guess it depends. Using the pressure gauge & your calcs, you could plot out a pressure vs. flow map by blocking off percentages of the intake port of the fan, & then from there just look at the gauge & your plot to check for losses as you build out the system, & then finally to dial in the passive intake to keep that flow (pressure) up.
With the swing gauge I’m plotting out percentage loss of pressure, but I’m not calculating the actual cfm. I either have to go to a published flow map for my fan, or find a flow map for a similar fan & just go off of that. If it’s a centrifugal fan & if I know the max CFM & pressure, drawing a diagonal line can be close. But hybrid axial/centrifugal fans don’t plot like that, so then I’m better off looking for a comparable flow map if my actual fan doesn’t have one, & I still want to just make a swing gauge.
Then of course it’s not always easy to do a straightforwards swing gauge depending on the install, & using pressure gauge would make more sense, even if you had to buy one. I guess you could get a combo gauge & also work off of vacuum if that makes more sense at some point.
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Just thinking about it & I guess I could take my swing gauge measurements & plug them into your equation to get CFM estimates. But an actual proper pressure gauge would be more accurate especially if you wanted more resolution. I was measuring at 25% differences in intake blockage, but 10% differences would be better & I bet the swing gauge would be tougher to mark out accurately with those smaller differences.
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