Subtopic: Calculation of power, torque, fuel consumption, heat load and power losses
Question Statement:
A 3-cylinder 4-stroke diesel engine with a bore 73 mm and stroke 78 mm is tested at 2200 rpm. When a braking torque 55 N·m is applied, the indicated mean effective pressure is found to be 1050 kPa. The mechanical efficiency of the engine, in %, is __________. (Rounded off to 2 decimal places)
Options:
(A) 57.21
(B) 61.45
(C) 67.21
(D) 71.25
Official Answer Key:
C
Step-by-Step Solution & Explanation
Step 1 — brake power from the braking torque:
BP = 2πNT/60 = (2π × 2200 × 55)/60 = 12,671 W ≈ 12.67 kW
Step 2 — swept volume per cylinder:
Vₛ = (π/4)D²L = (π/4)(0.073)²(0.078) = 3.2646 × 10⁻⁴ m³
Step 3 — indicated power. For a 4-stroke engine there is one power stroke every two revolutions, so the number of cycles per second is N/(2 × 60):
IP = IMEP × Vₛ × (N/120) × number of cylinders
= 1050 × 10³ × 3.2646 × 10⁻⁴ × (2200/120) × 3
= 342.8 × 18.333 × 3 = 18,853 W ≈ 18.85 kW
Step 4 — mechanical efficiency:
η_mech = BP/IP = 12,671/18,853 = 0.6721 = 67.21 %
Trap: using N/60 instead of N/120 (i.e. treating it as a 2-stroke) halves the IP and gives an impossible efficiency above 100 %.
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