Compressibility in fluids – blanket statement check “All gases have compressible flow and all liquids have incompressible flow.” Evaluate this statement.

Introduction / Context:
Compressibility refers to density changes in response to pressure variations. Whether a flow should be modeled as compressible or incompressible depends on operating conditions, not just the substance being a gas or a liquid.

Given Data / Assumptions:

• Mach number M = V / a as a compressibility indicator for gases.
• Liquids with small but non-zero bulk compressibility.
• Engineering approximations commonly used in pipelines and hydraulics.

Concept / Approach:
Gases can often be treated as incompressible when M ≲ 0.3 and density variations are negligible. Liquids, although far less compressible than gases, do show density changes under high pressure or rapid transients (water hammer), requiring compressible models. Thus, the blanket statement is not universally correct.

Step-by-Step Reasoning:

Verification / Alternative check:
Classic practice treats air flows in HVAC ducts (low speed) as incompressible, while high-speed gas flows require compressible equations. Conversely, water hammer analysis for liquids uses wave speed and compressibility explicitly.

Why Other Options Are Wrong:

• “Correct” is overly absolute.
• Conditional options provided are incomplete or irrelevant to the general statement.

Common Pitfalls:
Equating “gas” with “compressible” in every case or assuming “liquid” always incompressible, which can mislead design decisions.

Final Answer:
Incorrect