Question

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

• A. v
• B. $v^{2}$
• C. $v^{3}$
• D. $v^{4}$

Answer 1

Answer: (C)

$v^{3}$

Answer 2

Force $= v\frac{dm}{dt} = v\frac{d}{dt}(V \times \rho) = v\rho\frac{d}{dt}\lbrack A \times l\rbrack = v\rho A\frac{dl}{dt} = \rho Av^{2}$

Power = F × v = $\rho Av^{2} \times v = \rho Av^{3}$ ∴ $P \propto v^{3}$.