Subtopic: Bio-fuels and their use in farm mechanization
Question Statement:
A piston pump is driven by a 5 m diameter horizontal axis wind turbine for supplying water from a borehole with a total pump head of 10 m. The mean velocity of air is 18 km h⁻¹ and the density of air is 1.29 kg m⁻³. The actual power coefficient of the wind turbine is 0.30 and the overall pump efficiency is 60%. Neglecting the transmission losses, the expected pump discharge in L s⁻¹ will be
Options:
(A) 2.90
(B) 5.80
(C) 28.50
(D) 32.27
Official Answer Key:
A
Step-by-Step Solution & Explanation
Wind speed V = 18 km/h = 5 m/s. Rotor swept area, A = (π/4)(5)² = 19.635 m².
Wind power extracted, P_wind = 0.5×ρ_air×A×V³×C_p = 0.5×1.29×19.635×5³×0.30 = 474.9 W.
Hydraulic power delivered to pumping = P_wind × η_pump = 474.9×0.60 = 284.95 W.
Discharge, Q = P_hyd/(ρ_water×g×H) = 284.95/(1000×9.81×10) = 2.905×10⁻³ m³/s = 2.90 L/s. Answer: (A).
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