Centrifugal compressor pressure ratio: Increasing impeller tip speed and lowering inlet temperature generally increase achievable pressure ratio (within Mach and stress limits).

Introduction / Context:
In centrifugal compressors, pressure rise is closely tied to blade tip speed and inlet density. Designers balance mechanical limits, surge margin, and choking constraints to reach a target pressure ratio efficiently.

Given Data / Assumptions:

• Idealized compressor behavior with reasonable efficiency.
• Tip speed U2 increases with rotational speed and radius.
• Inlet total temperature affects inlet density and relative Mach numbers.

Concept / Approach:
The ideal specific head of a centrifugal compressor scales approximately with U2^2. Therefore, higher tip speed increases head and potential pressure ratio for a given efficiency. Lower inlet temperature increases density, reduces inlet Mach number for the same volumetric flow, and can allow higher pressure ratio before choking or stall occur.

Step-by-Step Solution:

Verification / Alternative check:
Compressor performance maps show higher pressure ratios at higher corrected speeds and at lower corrected inlet temperatures (after accounting for scaling), consistent with the statement.

Why Other Options Are Wrong:

• Incorrect: Ignores fundamental speed–head relation.
• Correct only if speed is reduced: Contradictory.
• Geometry only: Geometry matters, but operating speed and inlet conditions significantly shift performance.

Common Pitfalls:
Overlooking limits such as tip Mach number, blade stress, and surge/choke boundaries when attempting to raise pressure ratio by speed alone.

Final Answer:
Correct