Dimensional analysis: The ratio of inertia force to elastic (compressibility) force is known as which dimensionless number?

Introduction / Context:
Dimensionless numbers classify flow regimes by comparing dominant forces. Inertia compared to viscous, gravity, surface tension, or elastic forces yields Reynolds, Froude, Weber, and Mach numbers respectively. Recognizing these pairings is core to similarity analysis and model testing.

Given Data / Assumptions:

• Compressible flow context for elastic forces.
• Standard definitions of classical similitude groups.

Concept / Approach:
Mach number M = V / a compares flow speed V to the speed of sound a, which relates to fluid elasticity (bulk modulus). Hence, Mach represents inertia/elastic force. By contrast, Reynolds is inertia/viscous, Froude is inertia/gravity, and Weber is inertia/surface tension.

Step-by-Step Solution:

Verification / Alternative check:
Compressibility effects (shocks, expansions) become important as Mach approaches or exceeds 1, which is tied to elastic propagation speed a, confirming the force pairing.

Why Other Options Are Wrong:

• Reynolds: inertia/viscous.
• Froude: inertia/gravity.
• Weber: inertia/surface tension.

Common Pitfalls:
Memorization mistakes between Mach and Reynolds; forgetting that elastic forces matter only when compressibility is significant.

Final Answer:
Mach number