At a wind farm, one turbine (A) is subjected to average wind speeds of 6.0 m/s. An identical turbine (B) at this site is subject to average wind speeds of 7.2 m/s.Determine the expected % increase in power generated by turbine B with respect to turbine AExpress your answer to 3 significant figures
Question
At a wind farm, one turbine (A) is subjected to average wind speeds of 6.0 m/s. An identical turbine (B) at this site is subject to average wind speeds of 7.2 m/s.Determine the expected % increase in power generated by turbine B with respect to turbine AExpress your answer to 3 significant figures
Solution
The power generated by a wind turbine is proportional to the cube of the wind speed. This is expressed by the formula:
P = 0.5 * p * A * v^3
where: P is the power, p is the air density, A is the area swept by the turbine blades, v is the wind speed.
Given that the turbines are identical and the air density is the same for both, we can ignore p and A in this case. The power ratio of turbine B to turbine A is then:
P_B/P_A = (v_B/v_A)^3
Substituting the given wind speeds:
P_B/P_A = (7.2/6.0)^3 = 1.728
This means that turbine B generates 1.728 times the power of turbine A, or a 72.8% increase in power.
So, the expected increase in power generated by turbine B with respect to turbine A is 72.8%.
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