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Marat540
2 months ago
11

1 At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass and the power

generation potential of a wind turbine with 70-m-diameter blades at that location. Also determine the actual electric power generation assuming an overall efficiency of 30 percent. Take the air density to be 1.25 kg/m3
Engineering
1 answer:
alex41 [359]2 months ago
8 0

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 = \frac{mv^2}{2}.................1

e (mechanical ) = \frac{v^2}{2}    

input values here

e (mechanical) = \frac{10^2}{2}  

e (mechanical) = 50 J/kg

and

mass relation shows

mass = ρ V A..............2

where A stands for area = \frac{\pi D^2}{4}  

therefore, the mass equation becomes

mass = ρ V \frac{\pi D^2}{4}

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

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