GATE AG 2015 • Q61 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: I.C. engine systems – fuel, cooling, lubrication, ignition, electrical, intake and exhaust

Question Statement:

A propeller type wind turbine of 8 m diameter generates 4 kW electrical power. If the overall efficiency of power generation system is 32% and the density of air is 1.2 kg m⁻³, the average wind speed in m s⁻¹ is _____.

Official Answer Key:

7.4 to 7.5

Step-by-Step Solution & Explanation

Available wind power = P_elec/η = 4000/0.32 = 12500 W. Wind power formula: P = ½ρAV³, where A = (π/4)D² = (π/4)(8)² = 50.27 m². V³ = P/(½ρA) = 12500/(0.5×1.2×50.27) = 12500/30.16 = 414.5 ⇒ V = 414.5^(1/3) = 7.45 m/s. This lies within the accepted range 7.4–7.5.

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