The average wind speed on the north Texas plains around Amarillo is approximatel

Question

The average wind speed on the north Texas plains around Amarillo is approximately 6 m/s. An efficient wind turbine can convert 40% of the kinetic energy of the air (wind) into electrical energy at optimum conditions. If a turbine has blades 25 m in length and the specific volume of the air is 0.95 m3/kg determine a) the rate of power generation for average wind speed conditions on the north Texas plains b) the profit generated in 30 days of operation if electricity can be sold to the generating utilities at a return of S0.06 per kW-hour? Hint: the amount of air flowing through the turbine is proportional to the circular area swept by the turbine blades. I kW-hour is defined as the energy accumulated at a power rate of kw over a time of I hour./

Explanation / Answer

Area of air swept by turbine blade = R2 = (252) = 1963.5 m2

Volume flow rate of air (Q) = Velocity of air x Area of air swept by turbine blade = 6 x 1963.5

Q = 11781 m3/s

Mass flow rate (M) = Volume flow rate / specific volume = 11781 / 0.95 = 12401 kg/s

Convert Kinetic energy -> Electrical energy at 40% efficiency

Rate of Kinetic energy flow through turbine = 0.5(M)(v2) = 0.5(12401)(36) = 223219 J/s

Generated power = 0.4(223219) = 89287.6 J/s = 89.29 kW     -> (a)

Profit in 30 days = (89.29kW)x(24hr/day)x(30days)x($0.06/kW-hr) = $3857.2 -> (b)

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