Commercially available large wind turbines have blade span diameters as large as

Question

Commercially available large wind turbines have blade span diameters as large as 100M and generated over 3 MW of electric power at peak design conditions. Consider a wind turbine with a 90-m blade span subjected to 25-km/h steady wind turbine with a 90 m blade span subjected to 25 km/h steady winds. If the combined turbine-generator efficiency of the wind turbine is 32 percent determine a) the power generated by the turbine and b0 the horizontal force exerted by the wind on the supporting mast of the turbine take the density of air to be 1.25 kg/m^3 and disregard frictional effects

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Explanation / Answer

v = 25 km/h = 25*1000 / (60*60) m/s = 6.94 m/s

Power = Force*velocity

= Pressure*area*velocity

= (1/2*rho*v^2)*(pi*r^2)*v

= (1/2*1.25*6.94^2)*(3.14*90^2)*6.94

= 5323621 Watts

= 5.32 MW

Considering 32 % efficiency, power generated = 0.32*5.32 = 1.7 MW

b)

Force on mast = Power / velocity

= 1.7*10^6 / 6.944

= 245.3 kN

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