Two sites are being considered for wind power generation. In the first site, the wind blows steadily at 7 m/s for 3000 hours per year, where

Question

Two sites are being considered for wind power generation. In the first site, the wind blows steadily at 7 m/s for 3000 hours per year, whereas in the second site the wind blows at 10 m/s for 1500 hours per year. Assuming the wind velocity is negligible at other times for simplicity, determine which is a better site for wind power generation. Hint: Note that the mass flow rate of air is proportional to wind velocity.

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Thu Thảo 2 weeks 2021-08-28T18:19:42+00:00 2 Answers 0 views 0

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    0
    2021-08-28T18:21:27+00:00

    Answer:

    E.year₂ > E.year₁  (Second site is better)

    Explanation:

    Given data

    V_{1}=7 m/s\\Time_{1}=3000 hours/year\\V_{2}=10m/s\\Time_{2}=1500hours/year

    The  power generation is the time rate of kinetic energy which can be calculated as:

    Power=ΔKE=m×V²/2

    Regarding  that m ∝ V.Then

    Power ∝ V³ ⇒ Power=constant×V³

    Since ρa is constant for both sides and Area is the same as same wind turbine is used

    For First site

    Power_{1}=const.V^3\\Power_{1}=const.(7m/s)^3\\Power_{1}=const.343Watt\\

    For second site

    Power_{2}=const.V_{2}^3\\Power_{2}=const.(10m/s)^3\\Power_{2}=const.1000W

    Calculating energy generation per year for each of two sites

    E.year=Power×Operation time per year

    For First site

    E.year₁=Power₁×Operation time₁ per year

    E_{year1}=const.*343W*3000\\E_{year1}=const.1029000(W.hour/year)

    For Second site

    E.year₂=Power₂×Operation time₂ per year

      E_{year2}=const.*1000W*1500\\E_{year2}=const.1500000(W.hour/year)

    So

    E.year₂ > E.year₁  (Second site is better)

    0
    2021-08-28T18:21:41+00:00

    Answer:

    Site 1.

    Explanation:

    Below are attachments containing the solution.

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