Willans’ law applicability — throttle- vs cut-off-governed engines: State whether the empirical Willans’ law holds for throttle-governed engines but not for cut-off governed engines.

Introduction:
Willans’ law provides a near-linear relation between hourly steam (or fuel) consumption and indicated power for reciprocating engines over normal operating ranges. Its applicability depends on the governing method used to control the engine’s output.

Given Data / Assumptions:

• Throttle governing: inlet pressure reduced by throttling, cut-off largely constant.
• Cut-off governing: inlet pressure near boiler pressure, cut-off varied with load.
• Steady speed operation, typical engine efficiencies.

Concept / Approach:
Under throttle governing, as the engine load changes, inlet pressure and mass flow vary roughly in proportion, producing a near-linear Willans’ line m = a + b*IP where a is no-load consumption and b is the slope. In cut-off governing, indicated power varies mainly by changing cut-off while pressure remains high; the relation becomes non-linear due to changing expansion ratio and mean effective pressure behavior, so the simple Willans’ law is not reliable.

Step-by-Step Solution:

Verification / Alternative check:
Plotting test data for throttle-governed engines yields straight Willans’ lines; cut-off governed engines show curvature, especially at light loads.

Why Other Options Are Wrong:

• False variants: contradict observed test behavior and standard teaching.
• Requirements for superheat or special timing: not essential to the core applicability difference.

Common Pitfalls:
Assuming Willans’ linearity is universal; mixing up indicated and brake power when plotting the law.

Final Answer: