Engine Performance – Definition of Mechanical Efficiency (ηm) In reciprocating internal combustion engines, mechanical efficiency (ηm) is defined to compare the useful shaft output with the power developed inside the cylinder. Which of the following expressions correctly represents ηm for an engine?

Introduction / Context:
Mechanical efficiency connects what the engine develops in the combustion chamber (indicated power) to what finally appears at the crankshaft (brake power). It highlights mechanical and pumping losses in bearings, piston–ring packs, valve trains, and auxiliaries. Knowing ηm is essential for separating combustion improvements from friction reduction efforts.

Given Data / Assumptions:

• I.P. is the gross power calculated from cylinder pressure–volume data.
• B.P. is the net power measured at the shaft via a dynamometer.
• Frictional power F.P. = I.P. − B.P. represents mechanical and pumping losses.

Concept / Approach:

By definition, mechanical efficiency is the fraction of in-cylinder power transmitted to the shaft. Therefore ηm must relate B.P. to I.P. directly. Because losses are always positive in real engines, ηm is less than 1 and improves when friction or accessory loads are reduced.

Step-by-Step Solution:

Verification / Alternative check:

Motoring tests determine F.P. at various speeds. Substituting F.P. into ηm = 1 − (F.P. / I.P.) yields the same ηm as B.P. / I.P., confirming consistency.

Why Other Options Are Wrong:

Option B inverts the ratio (would exceed 1). Option C equals 1 − ηm (the friction ratio), not ηm itself. Option E is dimensionally incorrect (difference, not ratio). ‘‘None of these’’ is unnecessary because a correct expression exists.

Common Pitfalls:

Confusing ηm with overall efficiency (B.P. divided by fuel energy) or indicated thermal efficiency (I.P. divided by fuel energy). Also, assuming ηm is constant across speed—friction rises with RPM, so ηm typically drops at high speed.

Final Answer:

ηm = Brake power (B.P.) / Indicated power (I.P.)