Engine Efficiencies — Mechanical Efficiency of an I.C. Engine Given indicated power (I.P.), brake power (B.P.) and frictional power (F.P.), which expression defines mechanical efficiency ηm?

Introduction / Context:
Mechanical efficiency expresses how effectively an engine converts indicated (in-cylinder) power to useful crankshaft power. It quantifies the fraction of power that survives mechanical and pumping losses.

Given Data / Assumptions:

• B.P. is measured at the dynamometer shaft.
• I.P. is deduced from indicator diagrams or cylinder pressure analysis.
• F.P. represents all internal mechanical losses.

Concept / Approach:
The power balance is I.P. = B.P. + F.P. Mechanical efficiency is defined as useful output (B.P.) divided by the power developed inside the cylinder (I.P.). Hence, eta_m = B.P. / I.P. This ratio is always less than 1 and typically ranges from about 0.75 to 0.9 for many automotive engines depending on speed, load, and design.

Step-by-Step Solution:
Start with I.P. = B.P. + F.P.Define eta_m = B.P. / I.P.Therefore, select B.P/I.P. as the correct expression.

Verification / Alternative check:
Check dimensional consistency: both numerator and denominator are powers → dimensionless ratio 0–1, as expected.

Why Other Options Are Wrong:
I.P./B.P. is the inverse; it would exceed 1.B.P./F.P. or F.P./B.P. do not define efficiency; they are loss ratios.I.P./(B.P.+F.P.) reduces to 1, which is meaningless.

Common Pitfalls:
Confusing mechanical efficiency with overall efficiency, which also includes thermal efficiency and fuel energy content.

Final Answer:
B.P/I.P.