Subtopic: Sources of power on the farm – human, animal, mechanical, electrical, wind, solar and biomass
Question Statement:
A water pumping system is being driven by a propeller type wind turbine having the power coefficient of 0.4. The total pumping head and rate of discharge are 20 m and 7.0 L s⁻¹, respectively. Mean wind velocity is 18 km h⁻¹ and the density of air is 1.2 kg m⁻³. The required diameter of the propeller in m is ______
Official Answer Key:
7.5 to 7.8
Step-by-Step Solution & Explanation
Hydraulic (pumping) power required = ρ_w×g×Q×H = 1000×9.81×0.007×20 = 1373.4 W. Wind velocity V = 18 km/h = 5.0 m/s. Available wind power = Cp×½×ρ_air×A×V³, so the swept area A = P/(Cp×½×ρ_air×V³) = 1373.4/(0.4×0.5×1.2×125) = 1373.4/30 = 45.78 m². Propeller diameter D = √(4A/π) = √(58.32) = 7.63 m, within the accepted band 7.5–7.8.
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