Question 2.72: Large wind turbines with blade span diameters of over 100 m ......

A large wind turbine is installed at a location where the wind is blowing steadily at a certain velocity. The electric power generation, the daily electricity production, and the monetary value of this electricity 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 from

Then the amount of electricity generated per day and its monetary value become
Amount of electricity =( Wind power )( Operating hours )=(804.2 \mathrm{~kW})(24 \mathrm{~h})=\mathbf{1 9 , 3 0 0} \mathbf{~k W h}
Revenues =( Amount of electricity )( Unit price )=(19,300 \mathrm{~kWh})(\$ 0.06 / \mathrm{kWh})=\mathbf{~\$ 1158} (per day)

Discussion Note that a single wind turbine can generate several thousand dollars worth of electricity every day at a reasonable cost, which explains the overwhelming popularity of wind turbines in recent years.