big fan connected to small tube
 

Hi,

I have a question regarding fans and connecting them to a tube that is of a smaller diameter than the fan, a good example would be a vacuum, where you get big airflow through a very small tube.

How much airflow is lost when you connect a bigger fan to a smaller tube ? For example 12x12cm fan connected to a 10x10 or 8x8 tube. I am guessing it depends on the power of the fan, for instance vacuum "fan" being 2000W and computer fan being 1 or 2W. Is there a formula to calculate how much is lost ?

Had to dig up some of that old aerodynamics theory, but I think you could try with:

Delta P = f * Rho * (L / D) * (v^2 / 2); f=64/Re

Delta P = Pressure loss
Rho = Density air
L = Length pipe
D = Diameter pipe
v = velocity air
Re = Reynolds number

The flow Q1 = Q2; v1 * A1 = v2 * A2

Which means that the flow speed will increase in the smaller tube and thus increase the drag

Disclaimer: All in metric, laminar, isotropic flow!

It's not possible to do it without knowing some basic data about the fan, but as you can see from the equations the higher the flow speed the higher the losses.

If you must move the air through a smaller diameter tube, because of dimensional constraints, then try to keep the tube as short as possible, or at least keep the bottleneck short. For example, if you must move the air a total of 200cm, but the constraint is only 50cm, then use a larger diameter tube of the remaining 150cm.

And keep the tube smooth, without any sharp bends.