Compressible fluids – variability of specific weight “The specific weight of compressible fluids does not remain constant.” Is this statement:

Introduction:Unlike liquids (often approximated as incompressible), gases are compressible and their density varies significantly with pressure and temperature. This affects specific weight, which depends directly on density.

Given Data / Assumptions:

• Specific weight γ = ρ * g.
• Compressible fluid: ρ is a function of p and T.
• Gravity g is approximately constant for terrestrial applications.

Concept / Approach:Because γ is proportional to ρ, any change in ρ due to compression/expansion or heating/cooling changes γ. For gases obeying the ideal-gas relation, ρ = p / (R * T), so γ varies with p and T even at modest ranges.

Step-by-Step Solution:1) Write γ = ρ * g.2) For a gas, substitute ρ from its equation of state (e.g., ideal gas).3) Observe that p↑ or T↓ increases ρ and thus γ; p↓ or T↑ decreases γ.4) Therefore γ is not constant for compressible fluids.

Verification / Alternative check:Atmospheric γ decreases with altitude as p and ρ drop; engineering tables list air density and weight density at different T and p.

Why Other Options Are Wrong:

• False statements ignore the p–T dependence of ρ.
• Restricting to “very high pressure” or “cryogenic” is unnecessary; variability exists over wide conditions.
• g alone does not fix γ without ρ.

Common Pitfalls:Applying an incompressible approximation to gases outside narrow ranges.

Final Answer:True