Answer:
223.55 W
Explanation:
v = Velocity of wind = 10 m/s
r = Radius of circle = 5 m
S = Swept area
[tex]\rho[/tex] = Density of air = 1.2 kg/m³
[tex]C_p[/tex] = Power coefficient = 0.593
[tex]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[/tex]
The maximum possible power that can be produced by the turbine is 223.55 W
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 )
applying the formula below
P = Cp * 1/2 * p * S * v³
= 0.593 * 1/2 * 1.2[tex]\pi[/tex] * 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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