Question

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

Answer 1

electric power generation = 240.52 kW

Step-by-step explanation:

given data

wind is blowing steadily = 10 m/s

diameter = 70 m

overall efficiency = 30 percent

air density = 1.25 kg/m³

solution

we know Kinetic energy is the form of mechanical energy

so wind can be convert to work entirely

and power potential of the wind is kinetic energy

mass flow rate =
`(mv^2)/(2)` .................1

e (mechanical ) =
`(v^2)/(2)`

put here value

e (mechanical) =
`(10^2)/(2)`

e (mechanical) = 50 J/kg

and

We know the mass relation

mass m = = ρ V A ..............2

here A is area =
`(\pi D^2)/(4)`

so mass equation will be

mass m = ρ V
`(\pi D^2)/(4)`

put here value we get

mass m = (1.25 kg/ m³) × ( 10 m/s) × \frac{\pi 70^2}{4}

mass m = 48105.63 kg/s

so

electric power generation = m × e (mechanical) .........3

electric power generation = 48105.63 × 0.0050 KJ/kg

electric power generation = 240.52 kW