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Solved: The maximum power that can be extracted by a find
Chapter 20, Problem 58P(choose chapter or problem)
The maximum power that can be extracted by a wind turbine from an air stream is approximately
\(P=k d^{2} v^{3}\)
where d is the blade diameter, v is the wind speed, and the constant \(k=0.5\mathrm{\ W} \cdot \mathrm{s}^3/\mathrm{m}^5\). (a) Explain the dependence of P on d and on v by considering a cylinder of air that passes over the turbine blades in time t (Fig. P20.58). This cylinder has diameter d, length L = vt, and density \(\rho\). (b) The Mod-5B wind turbine at Kahaku on the Hawaiian island of Oahu has a blade diameter of 97 m (slightly longer than a football field) and sits atop a 58-m tower. It can produce 3.2 MW of electric power. Assuming 25% efficiency, what wind speed is required to produce this amount of power? Give your answer in m/s and in km/h. (c) Commercial wind turbines are commonly located in or downwind of mountain passes. Why?
Text Transcription:
P = kd^2v^3
k = 0.5 W cdot s^3/m^5
rho
Questions & Answers
QUESTION:
The maximum power that can be extracted by a wind turbine from an air stream is approximately
\(P=k d^{2} v^{3}\)
where d is the blade diameter, v is the wind speed, and the constant \(k=0.5\mathrm{\ W} \cdot \mathrm{s}^3/\mathrm{m}^5\). (a) Explain the dependence of P on d and on v by considering a cylinder of air that passes over the turbine blades in time t (Fig. P20.58). This cylinder has diameter d, length L = vt, and density \(\rho\). (b) The Mod-5B wind turbine at Kahaku on the Hawaiian island of Oahu has a blade diameter of 97 m (slightly longer than a football field) and sits atop a 58-m tower. It can produce 3.2 MW of electric power. Assuming 25% efficiency, what wind speed is required to produce this amount of power? Give your answer in m/s and in km/h. (c) Commercial wind turbines are commonly located in or downwind of mountain passes. Why?
Text Transcription:
P = kd^2v^3
k = 0.5 W cdot s^3/m^5
rho
ANSWER:Solution 58P
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