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.

Answer 1

Answer:

Site 1.

Explanation:

Below are attachments containing the solution.

Answer 2

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)