Definition of Mach number in fluid mechanics: Mach number (M) is defined as the ratio of inertial forces (or flow speed) to which fundamental resisting effect?

Introduction / Context:
Mach number is central to compressible-flow analysis. It classifies regimes such as subsonic, transonic, supersonic, and hypersonic, determining whether compressibility and shock waves are important in aerodynamic and gas-dynamic problems.

Given Data / Assumptions:

• Mach number M = V / a, where V is flow speed and a is speed of sound.
• Speed of sound encapsulates the medium’s elasticity via a = sqrt(∂p/∂ρ)_s.
• Continuum, single-phase, no phase change in the regime considered.

Concept / Approach:

Dimensionally, M compares inertial effects to elastic (compressibility) effects in the fluid. High M implies inertia dominates and compressibility cannot be ignored, while low M indicates quasi-incompressible behavior. Thus, Mach number represents a ratio of inertia to elasticity effects, not to viscosity, surface tension, or gravity.

Step-by-Step Solution:

Verification / Alternative check:

In Buckingham Pi terms, M arises from balancing inertia with compressibility, distinct from Reynolds (viscosity) and Weber (surface tension) numbers.

Why Other Options Are Wrong:

(a) relates to Reynolds number; (b) to Weber number; (c) to Froude number; (e) is irrelevant in standard fluid dynamics contexts.

Common Pitfalls:

Confusing Mach with Reynolds or Froude; assuming low M always means incompressible regardless of temperature effects—usually acceptable but context dependent.

Final Answer:

elasticity (compressibility)