Wind Energy A site evaluated for a wind farm is observed to have steady winds at a speed of 8.5 m/s (Fig. 2-12). Determine the wind energy (a) per unit mass, (b) for a mass of 10 kg, and (c) for a flow rate of 1154 kg/s for air.

Question

Wind Energy

A site evaluated for a wind farm is observed to have steady winds at a speed of 8.5 m/s (Fig. 2-12). Determine the wind energy (a) per unit mass, (b) for a mass of 10 kg, and (c) for a flow rate of 1154 kg/s for air.

Accepted Answer

A site with a specified wind speed is considered. Wind energy per unit mass, for a specified mass, and for a given mass flow rate of air are to be determined.

Assumptions Wind flows steadily at the specified speed.

Analysis The only harvestable form of energy of atmospheric air is the kinetic energy, which is captured by a wind turbine.

(a) Wind energy per unit mass of air is

[latex]e=\mathrm{ke}=\frac{V^{2}}{2}=\frac{(8.5 \mathrm{~m} / \mathrm{s})^{2}}{2}\left(\frac{1 \mathrm{~J} / \mathrm{kg}}{1 \mathrm{~m}^{2} / \mathrm{s}^{2}}\right)=36.1 \mathrm{~J} / \mathrm{kg}[/latex]

(b) Wind energy for an air mass of [latex]10 \mathrm{~kg}[/latex] is

[latex]E=m e=(10 \mathrm{~kg})(36.1 \mathrm{~J} / \mathrm{kg})=361 \mathrm{~J}[/latex]

(c) Wind energy for a mass flow rate of [latex]1154 \mathrm{~kg} / \mathrm{s}[/latex] is

[latex]\dot{E}=\dot m e=(1154 \mathrm{~kg} / \mathrm{s})(36.1 \mathrm{~J} / \mathrm{kg})\left(\frac{1 \mathrm{~kW}}{1000 \mathrm{~J} / \mathrm{s}}\right)=41.7 \mathrm{~kW}[/latex]

Discussion It can be shown that the specified mass flow rate corresponds to a 12-m diameter flow section when the air density is [latex]1.2 \mathrm{~kg} / \mathrm{m}^{3}[/latex]. Therefore, a wind turbine with a wind span diameter of [latex]12 \mathrm{~m}[/latex] has a power generation potential of [latex]41.7 \mathrm{~kW}[/latex]. Real wind turbines convert about one-third of this potential to electric power.

Question 2.2: Wind Energy A site evaluated for a wind farm is observed to ...

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