Question

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 80-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. Assume that the wind is blowing steadily at a constant uniform velocity and that the efficiency of the wind turbine is independent of the wind speed.

Answer 1

We know that:

Kinetic energy is the only form of  mechanical energy the wind possesses, and it can  be converted to work entirely.

Therefore, the  power potential of the wind is its kinetic energy,  which is V²  /2 per unit mass, and mV² / 2 for a  given mass flow rate:

e (mech) = k e =  V²  /2

e (mech) = (10 m/s)² / 2

To convert the units from m/s to kJ/kg,

e (mech)  = 50 m² /s² x ( 1 kJ/kg / 1000 m² /s²)

e (mech)  = 0.050 kJ/kg

Now,

We also know the relation

m = ρVA

Also A = π D²/4, so above equation becomes:

m = ρV (π D²/4)

m = (1.25 kg/ m³) ( 10 m/s) x ( 3.14 x 80 m x 80 m)/ 4

m = 62,800 kg/s

So,

E (mech) = m x e (mech)

E (mech) =  62,800 kg /s x 0.050 kJ/kg

E (mech) = 3,140 kW

Therefore, the 3140 kW of actual power can be generated by this wind turbine at the given conditions.