Hovering thrust calulation

1. Dec 5, 2012

reebrah

1. The problem statement, all variables and given/known data
basically I am doing work that requires me to calculate power for given thrust of a fan which is hovering.

2. Relevant equations
We are given the diameter: 0.8m, thrust output of fan: 250kg, rho=1.1455 kg/m^3, and eta which is the fan efficiency = 0.8

3. The attempt at a solution

I found this equation in wikipedia:

P^2 = (T^3) / ( (eta^2)(rho)A)

using this equation I got 7322w of power to attain a thrust of 250kg...This seems a little off. What is wrong here? does anyone know if this is even the correct value or even correct equation? thank you and appreciate it!

2. Dec 6, 2012

BruceW

Your equation looks fine (although, It depends on how the fan efficiency is defined).

One thing which is not right is that you've put thrust in units of kg, but thrust is a measure of force, not mass.

3. Dec 6, 2012

reebrah

Theres also another eq. Ive found on wikipedia which replaces the eta^2 with a constant of four. How can i confirm this is correct? Also you are right about the thrust units.

4. Dec 6, 2012

BruceW

The constant of 4 is assuming that no energy is lost as heat when the air is accelerated. You can derive the equation by considering the volume of air which passes through the fan in some time interval. It is the very simplest model you could imagine, since it neglects the effects of viscosity, turbulence, etc

For your homework, are you meant to be explaining why a particular equation is the correct one? Or were you just asking about the equation because you were curious?

5. Dec 6, 2012

reebrah

No i am just trying to find an accurate way to model power consumed given an amount of thrust and radius of fan. Are their any other factors i should be worried about?

6. Dec 6, 2012

BruceW

Your equation is fine. As I said, you just need to be careful what you use as your fan efficiency, since different people might define it differently. For example, you could keep the constant of 4 in the equation, as well as the fan efficiency, in which case, the fan efficiency would be defined differently.