Determining the Power Density and the Available Power of a Wind Farm

The elevation of a wind farm is 320 m. There are three rotating blades of the wind turbine and each blade is 12 m in length with a sweep diameter of 24 m. If the air temperature is 30°C and the speed of the wind is 10 m/s, calculate (a) the air density δ, (b) the power density ρ, and (c) the available power from the wind.

Question

Determining the Power Density and the Available Power of a Wind Farm

The elevation of a wind farm is 320 m. There are three rotating blades of the wind turbine and each blade is 12 m in length with a sweep diameter of 24 m. If the air temperature is 30°C and the speed of the wind is 10 m/s, calculate (a) the air density δ, (b) the power density ρ, and (c) the available power from the wind.

Accepted Answer

[latex]T = 30°, h = 320 m, v = 10 m/s, r = 12 m, d = 24 m, g = 9.8 m/s^2[/latex]

a. Equation (16.42)

[latex]\delta =\frac{353}{T+273}e^{\frac{-h}{29.3 imes (T+273)} }[/latex] (16.42)

gives the air density of the wind

[latex]\delta =\frac{353}{30+273}e^{\frac{-320}{29.3 imes (30+273)} }=1.124kg/m^3 [/latex]

b. Equation (16.37)

[latex]P_{in}=\frac{1}{2}A_sρv_a^3[/latex] (16.37)

gives the wind density

[latex]ρ= P_{in}/A_s = 0.5 × 1.124 × 103 = 561.89 W/m^3[/latex]

c. Equation (16.8) gives the sweep area of a blade

[latex]A_s = \pi r^2 = 3.14 imes 122 = 452.389 m^2[/latex]

Equation (16.37) gives the wind power

[latex]P_{wind} = A_s ρ= 452.389 × 561.89 = 254.2 kW[/latex]

Question 16.5: Determining the Power Density and the Available Power of a W...

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