# 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.

## 3 Answers

This is very rough, might or might not help you....

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. – SimonBarker 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. – MikeFoxtrot 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.

See also:

• I toyed between here and the physics stack but decided here would be a good start. Your answer does a great job of showing how complex this issue is and it seems like any reasonable calculation requires simulation and a lot more maths than I am used to (mechanics any way) - links are useful – SimonBarker Mar 1 '14 at 14:40

For calculating the power required by the fan to set it into operation would be calculated using how much power is generated by the motor that is used by the fan. Now, the fan is like a load to the motor. From reading the picture and trying to make sense out of the air-flow arrows, it seems that air-is pulled into the system from the outside which I assume is going to be warm and air-is pushed out of the system because of the motor spinning the fans. The dimensions of the fan will help you calculate the amount of air-intake and output. If at all one parameter that will influence the power requirements will be the fans mass and the amount of drag the fans create as they spin. Since friction due to drag will add to the load that the motor has to drive.

What you can do is calculate the Power generated by the Motor with No-Load. Then calculate the drag generated by fans which you will take as mass and add it to the fans mass. Now you have mass which will be the load that the motor has to drive. Now calculate how much Power does the Motor generate with this mass which most likely will be the answer to your question. :D