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Integration - Riemann Sums

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data

    The following table shows the power produced by a 600kW wind turbine at the given wind speed and the number of hours the wind blows at that speed.
    a) Plot the power characteristic as a function of wind speed.
    b) Plot the wind duration curve as a function of wind speed.
    c) Use a Riemann sum to verify that all 8760 hours in a year are accounted for.
    d) Use a Riemann sum to calculate the total yearly energy capture for this wind location (remember energy = power x time).
    e) If the power curve is p(t) and the wind duration curve is w(t), write the energy as an integral.

    Wind Speed Wind duration Turbine output
    m/s hours/year kW
    0 0 0
    2.5 1880 0
    5 2580 10
    7.5 2000 80
    10 1300 220
    12.5 650 400
    15 290 550
    17.5 60 600

    2. Relevant equations



    3. The attempt at a solution

    I have already graphed a&b, How would you use riemann sums to show that all the hours are accounted for? Wouldn't you just add up the number of hours?

    d & e are going over my head, but they don't seem to be hard
     
  2. jcsd
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