Compressor behavior — how does volumetric efficiency vary with compression ratio? For a reciprocating air compressor, the volumetric efficiency typically __________ with an increase in overall compression ratio (all else equal).

Introduction / Context:
Volumetric efficiency (eta_v) indicates how effectively the compressor cylinder fills with fresh charge. It is reduced by clearance volume and by backflow of hot residual gas. Understanding how eta_v changes with compression ratio is important for predicting capacity at higher pressures.

Given Data / Assumptions:

• Positive-displacement reciprocating compressor with nonzero clearance.
• Compression and expansion approximately polytropic.
• Comparisons made at similar inlet conditions except for delivery pressure.

Concept / Approach:
A standard expression is eta_v = 1 + C - C * (p2/p1)^(1/n), where C is clearance ratio, p2/p1 is compression ratio, and n is the polytropic index. As p2/p1 increases, the term (p2/p1)^(1/n) increases, reducing eta_v.

Step-by-Step Solution:
Start from eta_v = 1 + C - C * (p2/p1)^(1/n).Differentiate conceptually: increasing p2/p1 increases the subtracted term.Therefore, eta_v decreases as compression ratio rises.

Verification / Alternative check:
Indicator diagrams show increased re-expansion of trapped clearance gas at higher delivery pressures, displacing more of the fresh charge, confirming the decrease.

Why Other Options Are Wrong:
(b) contradicts the formula; (c) ignores clearance effect; (d) typical machines do not show a rise then fall solely from compression ratio; (e) while C matters, the trend with higher p2/p1 is still a decrease for any C > 0.

Common Pitfalls:
Confusing isentropic efficiency (a loss measure) with volumetric efficiency (a capacity measure).

Final Answer:
decreases