67 Large wind turbines with blade span diameters of over 100

-67 Large wind turbines with blade span diameters of over 100 m are available for electric power generation. Con- sider a wind turbine with a blade span diameter of 100 m installed at a site subjected to steady winds at 8 m/s. Taking overall efficiency of the wind turbine to be 32 percent and

Solution

The overall efficiency of any machine is = (Final Output Energy) / (Net Input Energy)

In case of wind turbine: net input energy = kinetic energy of air mass entering into the circular space spanned by turbine blades.

D = diameter of the wind turbine blade, rho = density of air, V = velocity of air

E1 = ½*((pi/4*D²)*rho *V) *V² = ½*(pi/4 *100[m]*100[m] * 1.25 [kg/m³] * 8 [m/s]) *(8 [m/s])²

Or

E1 = 2,513,274 [kg-m/s²]*m/s = 2,513,274 [W] = 2,513 [kW]

Electric power generated = 0.32 * 2,513,274 = 804,248 [W] = 804.25 [kW] – Answer

Amount of electrical energy generated in 24 hour period = 804.25*24 = 19,302 [kWhr] - Answer

Revenue generated = 804.25*24 [kWhr] * $0.09/[kWhr] = 1737.2 $ -- Answer