Subtopic: Sources of power on the farm – human, animal, mechanical, electrical, wind, solar and biomass
Question Statement:
A horizontal axis lift type wind rotor of diameter 4 m is used to run a pump at a wind velocity of 15 km·h⁻¹ at standard atmospheric pressure and temperature (density of air is 1.23 kg·m⁻³). If velocity of wind leaving the rotor blade is reduced to one-third of the approaching wind velocity, the thrust acting on the blade of the wind rotor in N is ______. [round off to 2 decimal places]
Official Answer Key:
118.90 to 119.60
Step-by-Step Solution & Explanation
By actuator-disc (momentum) theory, the mass flow through the rotor uses the AVERAGE of upstream and downstream velocities: V₁ = 15 km/h = 4.1667 m/s; V₂ = V₁/3 = 1.3889 m/s; V_avg = (4.1667+1.3889)/2 = 2.7778 m/s. Rotor swept area A = πD²/4 = 3.14×16/4 = 12.56 m². Mass flow rate ṁ = ρAV_avg = 1.23×12.56×2.7778 = 42.91 kg/s. Thrust = ṁ(V₁−V₂) = 42.91×(4.1667−1.3889) = 42.91×2.7778 = 119.2 N.
Section 4 — Soil and Water Conservation Engineering
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