# Using a Fan to move an object

#### bigbeezy

I'm trying to see how fast a fan that produces "x" cfm can move an object that weighs 150 lbs with a cof of 0.04. How would I set up an equation to find this?

Thanks

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#### cragar

to over come friction you haft to produce a force=(.04)n times the normal force
so f= 150(32)(.04) = 192ft lbs.

#### bigbeezy

ok thanks.

one more thing, am I right in converting cfm to ft lbs?

28 cfm = 1338.96 Nm/s = 987.5 ft lbs/s

this doesn't seem right to me.

#### Cantab Morgan

I'm sure this is obvious to everybody but me, but... what does "cfm" stand for?

#### cragar

cubic feet per minute , and im not sure how to convert the whole thing
so u want to convert cfm to foot pounds per second.

#### bigbeezy

yes cfm is cubic feet per minute.

I'm trying to figure out what size fan to use for a project of mine, and I am given the number of cfm the fan produces. I'm wanting to use that to figure out how fast it can propell an object. since it will take 192 ft lbs to move the object, I figured I needed to get cfm to ft lbs, but I am not sure if this would be the correct units for this.

#### lalligagger

That doesn't sound like a direct conversion to me. The fan moves a given volume of air per time, but the force actually acting on the object would involve aerodynamics. How about some more details on the project?

#### rcgldr

Homework Helper
150 lbs normal force, .04 cof, so maximum static friction = 150 lb x .04 = 6 lbs.

The cubic feet per minute rating isn't enough to determine the force.

force = mass x acceleration = mass x (velocity change) / (unit time)
force = mass / (unit time) x velocity change

Ignoring compression effect, and assuming dry air at sea level,

1 ft^3 / min ~= 0.075 lbmass / min = .00125 lbmass / sec = .000039 slug / sec

So CFM x .000039 gives you mass flow.
The change in velocity due to the fan times the mass flow will give you the force at the fan.

Assuming no losses, and that the block captures and stops all the air, the initial force on the object (until it starts moving) will be the same as the force at the fan.

6 lbforce = Velocity_from_fan (ft / sec) x CFM x .000039 slug / sec

#### bigbeezy

not sure what you mean by velocity_from_fan

think of the object as a cart and the fan(s) are mounted onboard the cart pushing air backwards, thus propelling the cart forwards. The only information i have about the output of the fan is in cfm.

#### bigbeezy

just wondering... would hp be benificial in this calculation?

#### mgb_phys

Homework Helper
The force on an object from the airflow is
F = 1/2 (density of air) * (speed of air)^2 * (cross section area) * (drag coefficient)

The drag coefficient depends on the shape of the object and varies from around 1 for a flat plate, 0.5 for a sphere and perhaps <0.1 for an aerodynamic shape.
From the CFM rating of the fan and it's area you can calculate the speed of the air flow (just consider a tube of air of that volume/second going through a fan of that area)

Note that you don't care how much of the air from the fan actually hits the object assuming the air speed is constant.

#### bigbeezy

Let me just see if I'm doing this correctly.

Fan specs: 95 cfm with outlet of 2-11/16 x 2-1/16 inches

Cross section area = 0.038493 ft^2

So the speed of the air would be:

95 cfm / 0.38493 ft^2 = 2467.99 ft/min = 41.1332 ft/sec

So assuming standard air density of 0.075 lb/ft^3 and drag coefficient is 1:

F= 1/2(0.075 lb/ft^3)(41.1332 ft/sec)^2(0.038493 ft^2)(1)
F= 2.4423 ft lbs/sec^2

Is this correct?

#### mgb_phys

Homework Helper
0.1N from a typical CPU fan - sounds reasonable.

#### lalligagger

Note that you don't care how much of the air from the fan actually hits the object assuming the air speed is constant.
Why is this? I also don't understand why the cross section area in your equation is for that of the fan and not the object. It seems to me that on a small object, a large fan would exert less force than a small fan displacing the same volume of air (at a faster velocity).

#### mgb_phys

Homework Helper
All you care about is the airspeed so the same CFM from a larger fan is a different air speed.
Think about the wind - in a gale do you realy care if it a local gust or a weather front 100miles long?

#### lalligagger

Ok, so then is the cross section area in the equation of the fan or of the object?

#### mgb_phys

Homework Helper
In the drag equation it is the cross section of the object.
but in order to convert from cfm to ft/min in the fan you need the area of the fan.

#### rcgldr

Homework Helper
Fan specs: 95 cfm with outlet of 2-11/16 x 2-1/16 inches
Cross section area = 0.038493 ft^2
95 cfm / 0.038493 ft^2 = 2467.99 ft/min = 41.1332 ft/sec
95 cfm = 1.5833 ft^3 / sec

1 lb = 1 slug ft / sec^2.
air density = .075 lbmass / ft^3 = .002331 slug / ft^3 (at about 65 degrees Farenheight)

thrust equation: force = mass flow x exit velocity (assuming initial air velocity is zero)
fan force = (.002331 slug / ft^3) (1.5833 ft^3 / sec) (41.1332 ft / sec) = .1518 lb

Compare to 1755 watt (2.35 hp), 90 mm electric ducted fan:

thrust = 6.06 lb
rotor diameter 90 mm = 3.5433 in
rotor swept area = 9.861 in ^2 = .06848 ft^2
volume_flow = velocity (ft / sec) x .06848 (ft^2)

fan force = (.002331 slug / ft^3) (volume_flow (ft^3 / sec)) (velocity (ft/sec)) = 6.06 lb
fan force = (.002331 slug / ft^3) (.06848 velocity (ft^3 / sec)) (velocity (ft / sec) = 6.06 (slug ft / sec^2)

(.002331) (.06848) (velocity^2) (slug / ft^3) (ft^3/sec) (ft / sec) = 6.06 (slug ft / sec^2)
(.002331) (.06848) (velocity^2) = 6.06

velocity^2 = 6.06 / (.002331 x .06848 ) = 37965
velocity (ft/sec) = 194.85 ft / sec
volume_flow (ft^3/sec) = 13.343 ft^3 / sec = 800.6 cfm

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