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Large wind turbines with a power capacity of 8 MW and blade span diameters of over 160 m are available for electric power generation. Consider a wind turbine with a blade span diameter of 100 m installed at a site subjected to steady winds at 8 m/s. Taking the overall efficiency of the wind turbine to be 34 percent and the air density to be 1.25 kg/m3, determine the electric power generated by this wind turbine. Also, assuming steady winds of 8 m/s during a 24 hour period, determine the amount of electric energy and the revenue generated per day for a unit price of $0.09/kWh for electricity.

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Answer:

85413.20177 W

2050.831684248 kWh

184.5748512 dollars

Explanation:

d = Diameter of blade = 100 m

r = Radius = [tex]\dfrac{d}{2}=\dfrac{100}{2}=50\ m[/tex]

[tex]\eta[/tex] = Efficiency = 0.34

[tex]\rho[/tex] = Density of air = 1.25 kg/m³

V = Velocity of wind = 8 m/s

A = Area = [tex]\pi r^2[/tex]

The power of a wind turbine is given by

[tex]P=\dfrac{1}{2}\rho AV^3\eta\\\Rightarrow P=\dfrac{1}{2}\times 1.25\times \pi\times 50^2\times 8^3\times 0.34\\\Rightarrow P=854513.20177\ W[/tex]

The power is 85413.20177 W

Energy is given by

[tex]E=Pt\\\Rightarrow E=854513.20177\times 24\\\Rightarrow E=20508316.84248\ Wh\\\Rightarrow E=2050.831684248\ kWh[/tex]

The energy is 2050.831684248 kWh

The revenue is given by

[tex]0.09\times 2050.831684248=184.5748512\$[/tex]

The revenue generated is 184.5748512 dollars

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