The average wind speed on the north Texas plains around Amarillo is approximately 6 m/s. An efficient wind turbine can convert 35% 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 m^3/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 $0.06 per kW-hour?
Hint: the amount of air flowing through the turbine is proportional to the circular area swept by the turbine blades. 1 kW-hour is defined as the energy accumulated at a power rate of 1 kW over a time of 1 hour.