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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?

Update:

Found the data sheet for the fan. Does anything else here (like the static air pressure) help me find force?

http://www.delta.com.tw/product/cp/dcfans/download...

Update 2:

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

Relevance
  • Anonymous
    1 decade ago
    Favorite Answer

    No, the rated cfm takes that into account.

    For a "back of the envelope" calculation, you are doing all right!

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