Question 2.66: At a certain location, wind is blowing steadily at 12 m/s. D......
At a certain location, wind is blowing steadily at 12 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 50- 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
Wind is blowing steadily at a certain velocity. The mechanical energy of air per unit mass, the power generation potential, and the actual electric power generation are to be determined.
Assumptions 1 The wind is blowing steadily at a constant uniform velocity. 2 The efficiency of the wind turbine is independent of the wind speed.
Properties The density of air is given to be \rho=1.25 \mathrm{kg} / \mathrm{m}^3.
Analysis 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 V^2 / 2 per unit mass, and \dot{m} V^2 / 2 for a given mass flow rate:
The actual electric power generation is determined by multiplying the power generation potential by the efficiency,
Therefore, 636 \mathrm{~kW} of actual power can be generated by this wind turbine at the stated conditions.
Discussion The power generation of a wind turbine is proportional to the cube of the wind velocity, and thus the power generation will change strongly with the wind conditions.
