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Is this force calculation valid?
I have a ducted fan with a 140mm diameter blade, and a 60mm central motor size. So the cross section of the fan, that is, the area that air can flow through, is
(70mm)^2 *pi - (30mm)^2 * pi = 12566mm^2 = .01256637m^2
The fan is rated at 365cfm, which is 0.1723m^3/s (cubic meters per second)
Now here's were I'm a little uncertain:
Dividing the air flow rate by the cross sectional area, canceling out appropriate units yields 13.7112 m/s, a unit of velocity.
Assuming the density of air is 1.275kg/m^3, multiplying the density of air by the air flow rate yields .21968 kg/s, a mass flow rate.
Multiplying the mass flow rate by the speed yields a 3.0128 kg*m/s^2, which is the Newton, the unit of force.
So according to this logic, the (air flow rate)^2 * (density of air) / (cross sectional area of the fan) = Force exerted by the fan.
Considering this is an 80 watt fan (which is a hell of alot for a little 5 1/2 inch fan), does this seem reasonable, because this doesn't seem like very much force. I haven't bought the fan yet, but is there any way I can very roughly estimate the force this fan exerts given some data?
Found the data sheet for the fan. Does anything else here (like the static air pressure) help me find force?
Hey, using the maximum listed static pressure of the fan yields similar results
409.43 Pa * .01256637m^2 = 5.145 N
3N and 5N are in the same ballpark, which makes me feel more confident.
1 Answer
- Anonymous1 decade agoFavorite Answer
No, the rated cfm takes that into account.
For a "back of the envelope" calculation, you are doing all right!