Concept explainers
Efficiency of wind turbines A wind Turbine converts wind energy into electrical power. Let v1 equal the upstream velocity of the wind before it encounters the wind turbine, and let v2 equal the downstream velocity of the wind after it passes through the area swept out by the turbine blades.
a. Assuming that v1 > 0, give a physical explanation to show that
b. The amount of power extracted from the wind depends on the ratio
Calculate R(1) and explain how you could have arrived at this value without using the formula for R. Give a physical explanation of why it is unlikely or impossible for it to be the case that r = 1.
c. Calculate R(0) and give a physical explanation of why it is unlikely or impossible for it to be the case that r = 0.
d. The maximum value of R is called the Betz limit. It represents the theoretical maximum amount of power that can be extracted from the wind. Find this value and explain its physical meaning.
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Calculus: Early Transcendentals (3rd Edition)
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