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Answer:
0.233
Explanation:
Given that
Diameter of rotor, d = 40 m
Power of rotor, P = 90 kW
Speed of the wind, v = 8 m/s
Density of air, p = 1.2 kg/m³
It is a known fact that
KE = ½mv², where mass flow rate, m
m = p.A.v, where Area, A
A = πd²/4
A = (3.142 * 40²)/4
A = 3.142 * 1600/4
A = 3.142 * 400
A = 1256.8 m², substitute for A in the mass flow rate equation
m = p.A.v
m = 1.2 * 1256.8 * 8
m = 12065.28, substitute for m in the KE equation
KE = ½mv²
KE = ½ * 12065.28 * 8²
KE = 12065.28 * 32
KE = 386088.96 W or
KE = 386.1 kW
Fraction of kinetic energy converted to electric energy is
Fraction = Electric Power / Total KE
Fraction = 90 / 386.1
Fraction = 0.233
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