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Answer:
Explanation:
From the information given;
The velocity of the wind blow V = 7 m/s
The diameter of the blades (d) = 80 m
Percentage of the overall efficiency [tex]\eta_{overall} = 30\%[/tex]
The density of air [tex]\rho = 1.25 kg/km^3[/tex]
Then, we can use the concept of the kinetic energy of the wind blowing to estimate the mechanic energy of air per unit mass by using the formula:
[tex]e_{mechanic} = \dfrac{mV^2}{2}[/tex]
here;
m = [tex]\rho AV[/tex]
= [tex]1.25 \times \dfrac{\pi}{4}(80)^2 \times 7[/tex]
= 43982.29 kg/s
∴
[tex]W = e_{mechanic} = \dfrac{mV^2}{2}[/tex]
[tex]= \dfrac{43982.29 \times 7^2}{2}[/tex]
[tex]= 1077566.105 \ W[/tex]
[tex]\mathbf{ =1077.566 \ kW}[/tex]
The actual electric power is:
[tex]W_{electric} = \eta_{overall} \times W[/tex]
[tex]W_{electric} = 0.3 \times 1077.566[/tex]
[tex]\mathbf{W_{electric} =323.26 \ kW}[/tex]