Answer:
a) 50 J/kg
b) 721 67 KW
Explanation:
The velocity of the wind v = 10 m/s
diameter of the blades d = 70 m
efficiency of the turbine η = 30%
density of air ρ = 1.25 kg/m^3
The area of the blade A = [tex]\pi d^2/4[/tex]
A = [tex]\frac{3.142 * 70^2}{4}[/tex] = 3848.95 m^2
The mechanical energy air per unit mass is gives as
e = [tex]v^2/2[/tex] = [tex]\frac{10^2}{2}[/tex] = 50 J/kg
Theoretical Power of the turbine P = ρAve
where
ρ is the density of air
A is the area of the blade
v is the velocity of the wind
e is the energy per unit mass
substituting values, we have
P = 1.25 x 3848.95 x 10 x 50 = 2405593.75 W
Actual power = ηP
where η is the efficiency of the turbine
P is the theoretical power of the turbine
Actual power = 0.3 x 2405593.75 = 721678.1 W
==> 721 67 KW
