Subtopic: Bio-fuels and their use in farm mechanization
Question Statement:
Sources of Power: Sources of power on the farm — human, animal, mechanical, electrical, wind, solar and biomass; bio-fuels and their use in farm mechanization.
A horizontal axis drag-type wind rotor fitted with 4 thin rectangular blades having drag coefficient 1.29 is used to extract power when average wind velocity in the rotor plane is 10 km/h. The maximum power coefficient is
Options:
(A) 0.148
(B) 0.191
(C) 0.393
(D) 0.593
Official Answer Key:
B
Step-by-Step Solution & Explanation
For a pure drag-type device the extractable power is P = Cd·½ρA(V−u)²·u, where u is the blade (rotor) speed. Maximising P with respect to u gives the optimum blade speed u = V/3 (analogous to the drag-machine optimum), and substituting back gives the maximum power coefficient:
Cp,max = (4/27) × Cd = (4/27) × 1.29 = 0.1911. (Note: this is distinct from the Betz limit of 0.593 (D), which applies to lift-type, not drag-type, rotors — a common distractor.) Answer: (B) 0.191.
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