Answer:
electric power production = 240.52 kW
Explanation:
provided data
steady wind speed = 10 m/s
diameter = 70 m
overall efficiency rate = 30 percent
air density = 1.25 kg/m³
solution
Kinetic energy equals mechanical energy; thus, wind can be fully converted into work.
The potential of wind power comes from this kinetic energy.
mass flow rate =
.................1
e (mechanical ) =
input values here
e (mechanical) =
e (mechanical) = 50 J/kg
and
mass relation shows
mass = ρ V A..............2
where A stands for area =
therefore, the mass equation becomes
mass = ρ V
substituting yields
mass = (1.25 kg/ m³) × ( 10 m/s) × \frac{\pi 70^2}{4}
mass = 48105.63 kg/s
consequently
electric power generation = m × e (mechanical).........3
electric power production = 48105.63 × 0.0050 KJ/kg
electric power production = 240.52 kW