Steam engine geometry: definition of clearance ratio Clearance ratio in a reciprocating steam engine is defined as the ratio of:

Introduction / Context:
Clearance volume is the volume remaining in the cylinder when the piston is at the end of its stroke (dead center). The clearance ratio is a dimensionless parameter that strongly influences volumetric efficiency, compression work, and indicator diagram shape.

Given Data / Assumptions:

• V_c = clearance volume.
• V_s = swept volume (displacement) between dead centers.
• Cut-off is a valve-timing event, not used in the definition.

Concept / Approach:
The standard definition is: Clearance ratio, C = V_c / V_s. This ratio is used in analytical expressions for compression and expansion parts of the cycle and in estimating the mass of residual (cushion) steam present at the beginning of the stroke.

Step-by-Step Solution:
Identify V_c as the volume at dead center when piston travel is zero.Identify V_s as the volume swept by the piston during one stroke.Form the ratio C = V_c / V_s.Therefore, option (a) precisely matches the accepted definition.

Verification / Alternative check:
Textbook formulae for volumetric efficiency include terms in C = V_c / V_s, confirming the definition used industry-wide.

Why Other Options Are Wrong:
Options (b) and (c) incorporate volume at cut-off, which is unrelated to the basic definition. Option (d) is the inverse of the standard ratio; (e) uses total cylinder volume, which is V_c + V_s, not part of the definition.

Common Pitfalls:
Mixing up clearance ratio with compression ratio; in steam engines they are related but distinct concepts.

Final Answer:
clearance volume to the swept volume