A horizontal-axis multibladed wind turbine of Cp0.4 pumps15 L/s through20 m head. Wind speed8 m/s; pump and transmission efficiencies70% and90%; air and water densities1.2 and1000 kg/m³. Find rotor diameter in m (two decimals).
Hydraulic power isρgQH=1000(9.81)(0.015)(20)=2943 W. Turbine shaft output must be2943/(0.7×0.9)=4671.43 W. Set this equal to Cp(ρair/2)AV³, giving A≈38.016 m². Diameter √(4A/π)=6.96 m.
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