# How to calculate the power required to drive a fan

I need to specify a fan motor combination and wondered if there are formulas that can work this out? The fan we are using is a crossflow fan:

So I'm assuming the power required to drive it is derived from the number of blades, dimensions of blades (including angle of attack), dimension of barrel/wheel and the speed in RPM.

Is this possible or does it need to be worked out practically with experimental measurements etc?

Hopefully this is the correct stack for this question, if not then mods please feel free to edit/close.

Treating it as a macroscopic perspective:

Kinetic Energy

$$E_k = \frac{1}{2}mv^2$$

For working energy in a flow, substitute volume with Area*Velocity and mass with density $\rho$

$$E_k = \frac{1}{2}\rho Av^3$$

With that, you should be able to estimate (after efficiency corrections) the power required.

Otherwise, a search for impeller equations might yield something. Most aerospace formulas are directed towards normal propellers with aerofoils.

• This seems like the best approach I think - I have an anemometer on the way that will allow me to get a good idea of the cross sectional area of the flow. Mar 1 '14 at 14:38
• @SimonBarker sorry I can't help you further. The other option would be computational fluid dynamics or getting a HVAC engineer to work it out to a more detailed degree. It's not a particularly simple system you're dealing with either, otherwise I might have been able to suggest some formulas. Mar 1 '14 at 15:27

Because air is a compressible fluid it's a rather complicated issue. This might be better suited to physics.stackexchange.com, but maybe I can point you in the right direction...

You can think of each rotor blade as a wing moving in a circle, and then you can view it in terms of aerodynamics.

Things we need to consider:

1. The speed the blade near the rotor will be greater than that at the end.
2. The angle of attack affects drag and lift, which translate to airflow. This can be maximized in favor of airflow but is interdependent with RPM.
3. Blades are often shaped along their length to take advantage of #1 and #2.
4. Blade count is somehow related to drag and ambient air velocity or temperature or something.
5. The stator and enclosure shape can induce turbulent air currents, which will increase drag.
6. At high speed you need to take into account laminar flow.
7. Thanks to thermodynamics, all the power you put in has to go somewhere. So the total of heat, airflow, acceleration, friction, and static force (every action has an opposite reaction) is going to give you your net power requirement.

It might be best to experiment, since fluid dynamics can be tricky.