Question

A wind-powered generator converts wind energy into electric 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

Power = F $\bullet$ v = Fv
F=v \big(\frac{dm}{dt}\big)=v \Bigg \\{ \frac{d(\rho \times \, volume)}{dt}\Bigg \\}
\, =\rho v \Bigg \\{\frac{d(volume)}{dt}\Bigg \\}=\rho v(Av)=\rho Av^2
$\therefore \, \, \, \, Power \, P=\rho Av^3 \, \, \, \, \, or \, \, \, P = v^3$