Question

Given a wind turbine with blades that sweep out a 10 m diameter circle, and a wind speed of 2 m/s, approximately what is the maximum possible power that the turbine can produce (i.e. taking into account the Betz limit)? Assume that the density of air is 1.2 kg/m3. Group of answer choices

Answer 1

Answer:

223.55 W

Explanation:

v = Velocity of wind = 10 m/s

r = Radius of circle = 5 m

S = Swept area

$\rho$ = Density of air = 1.2 kg/m³

$C_p$ = Power coefficient = 0.593

$P=C_p\frac {1}{2}}\rho Sv^{3}\\\Rightarrow P=0.593\times \frac{1}{2}1.2 \pi \times 5^2\times 2^{3}\\\Rightarrow P=223.55\ W$

The maximum possible power that can be produced by the turbine is 223.55 W