# Power of a Fan and WindMill using Energy vs dynamic method)

1. Dec 5, 2011

### unscientific

1. The problem statement, all variables and given/known data
Determine the power of a windmill using constants where appropriate.

2. Relevant equations
P = Fv
K = (1/2)mv2

3. The attempt at a solution

Dynamics Method
P = Fv

In time Δt, Δm amount of wind passes through the windmill, at speed of v.

Δp = vΔm
= v(AρΔx)

Dividing both sides by Δt,

F = Aρv2

P = Fv = Apv3

Energy Method

In time Δt, Δm amount of wind passes through the windmill, with KE of (1/2)(Δm)v2 .

Energy Transferred = (1/2)(Δm)v2
= (1/2)(ρAΔx)v2

Dividing both sides by Δt,

Power = (1/2)ρAv3

I've thought a long time about this; both methods make sense, but why are they different? Appreciate any help guys!

2. Dec 5, 2011

### LawrenceC

If you combine the Bernoulli equation with the momentum equation (force) across the blades by relating to pressure differential, you will see that you get the same result as you get with energy considerations.

3. Dec 5, 2011

### unscientific

so do is the dynamics method here wrong?