Polytropic efficiency in multistage compressors: is it constant across stages? Assess the statement: “For a well-designed multistage compressor operating at similar conditions in each stage, the polytropic efficiency can be taken as the same for all stages.”

Introduction / Context:Polytropic efficiency is a differential (small-step) measure that characterizes how closely a real compression process follows an isentropic path. In multistage machines designed with similar geometry, Reynolds/Mach numbers, and cooling arrangements, it is common engineering practice to assume the same polytropic efficiency in each stage for preliminary design and performance prediction.

Given Data / Assumptions:

• Stages have comparable tip speeds, clearances, valve behavior (reciprocating) or blade aerodynamics (dynamic).
• Intercooling restores similar inlet temperatures for each stage (nearly perfect intercooling).
• Pressure ratios per stage are chosen to be approximately equal.

Concept / Approach:Because polytropic efficiency is relatively insensitive to the absolute pressure level when flow regime and geometry are similar, designers often assign a single value across stages. Detailed tests may reveal small differences, but the equal-efficiency assumption is accurate enough for sizing and for estimating overall work and discharge temperatures.

Step-by-Step Solution:

Verification / Alternative check:Factory test results frequently report stage efficiencies within a narrow band; averaging to a single representative polytropic efficiency yields accurate overall predictions.

Why Other Options Are Wrong:

Limiting the statement to single-acting machines or zero clearance is unnecessary; the assumption pertains to similarity, not acting mode.Declaring it false ignores widespread design practice and the basis of stage-stacking methods.

Common Pitfalls:Confusing polytropic efficiency (a differential metric) with isentropic efficiency for the whole machine; the latter can vary more with pressure ratio distribution.

Final Answer:

True