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

  1. Dec 5, 2011 #1
    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. jcsd
  3. Dec 5, 2011 #2
    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.
     
  4. Dec 5, 2011 #3
    so do is the dynamics method here wrong?
     
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