homework problem

Question

The power available from a wind turbine is calculate by the following equation: P=1/2Apv^3

where P= powerI(watts), A= sweep area(circular) of the blades (square meters), p= air density (kg per cubic meter), and v = velocity (meter per second). The world's largest sweep area wind turbine generator in Spain has a blade diameter of 420 feet. The specific gravity of air is 0.00123. Assuming a velocity of 30 miles per hour and the power produced is 5 megawatts, determine the efficiency of this turbine?

Answer 1

 

 Area = pi * 210^2 = 22/7 * 210 * 210 = 22 * 30 * 210 = 660*210 = 138600 square feet

 

P = 5 million watts

 

v = 30 mph

 

  P = (1/2)(138600)(5 000 000) (30)(30)(30) = 9.3555x 10^15