Engine Power Balance – Frictional Power Expression Select the correct relationship for frictional power (F.P.) in terms of indicated power (I.P.) and brake power (B.P.) for a reciprocating engine.

Introduction / Context:
Separating indicated, brake, and frictional power helps quantify where losses occur in an engine. This is central to design optimization and to interpreting dynamometer and indicator measurements.

Given Data / Assumptions:

• I.P. is gross in-cylinder power calculated from pressure–volume data.
• B.P. is net shaft output measured externally.
• F.P. represents mechanical and pumping losses between cylinder and shaft.

Concept / Approach:

The power balance is I.P. = B.P. + F.P. This states that the power developed in the cylinder must either appear at the shaft or be dissipated in friction and pumping. Rearranging gives F.P. = I.P. − B.P., a straightforward expression used in motoring tests and Willans line analysis.

Step-by-Step Solution:

Verification / Alternative check:

Motoring test yields F.P. directly (B.P. = 0 while turning the engine), then I.P. under firing conditions is inferred to verify the balance.

Why Other Options Are Wrong:

'B.P. − I.P.' would make F.P. negative. Ratios do not represent power differences; 'sum' violates conservation since it would exceed I.P.

Common Pitfalls:

Mistaking frictional mean effective pressure (FMEP) trends and assuming F.P. is constant across speeds—it typically rises with RPM.

Final Answer:

F.P. = I.P. - B.P.