Answer:
E.year₂ > E.year₁ (Second site is better)
Explanation:
Given data
[tex]V_{1}=7 m/s\\Time_{1}=3000 hours/year\\V_{2}=10m/s\\Time_{2}=1500hours/year[/tex]
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
[tex]Power_{1}=const.V^3\\Power_{1}=const.(7m/s)^3\\Power_{1}=const.343Watt\\[/tex]
For second site
[tex]Power_{2}=const.V_{2}^3\\Power_{2}=const.(10m/s)^3\\Power_{2}=const.1000W[/tex]
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
[tex]E_{year1}=const.*343W*3000\\E_{year1}=const.1029000(W.hour/year)[/tex]
For Second site
E.year₂=Power₂×Operation time₂ per year
[tex]E_{year2}=const.*1000W*1500\\E_{year2}=const.1500000(W.hour/year)[/tex]
So
E.year₂ > E.year₁ (Second site is better)
