A town plans to use windmills to meet the power demand at peak periods. The number of windmills needs to be determined.

Assumptions:

Air is at 1 atm and 25^oC with a density of 1.18 kg/m³.

Windmill Capturing the
Kinetic Energy in the WInd

The exergy of the blowing air is the kinetic energy the air possesses. When the windmills work at their perfect condition, they will capture the exergy in the air totally and transfer it completely to electric power. Therefore, the maximum power available from a windmill is the kinetic energy of the the blowing air.

For per unit mass of air, the kinetic energy of air is,

      x = ke = v²/2 = 15²/2 = 112.5 J/kg

The amount of air passing through the rotor of the windmill per unit time is

The maximum power available to one windmill is the multiplication of the exergy of air per unit mass, and the amount of air passing through the rotor of the windmill per unit time. That is,

To meet the 1,000 kW power gap, the number of windmills needed is

      n = 1,000/156.3 = 8