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

Answer 2

The approximate maximum power that the turbine can produce is : 223.55 watts

Given data :

Diameter ( D ) = 10 m

Radius ( r ) = D / 2 = 10/2 = 5 m

density of air ( p )  = 1.2 kg/m³

Betz limit ( Cp ) = 0.593

wind speed ( v ) = 2 m/s

Swept area ( S )

Determine the max power that the turbine can produce

applying the formula below

P = Cp * 1/2 * p * S * v³

  = 0.593 * 1/2 * 1.2$\pi$ * 5² * 2³

  = 223.55 watts

Hence we can conclude that the maximum power the turbine can produce is : 223.55 watts

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