Which non-dimensional number primarily characterizes compressibility effects in fluid flow and is used to judge subsonic, transonic, or supersonic regimes?

Introduction / Context:
Dimensionless numbers classify flow regimes and dominant physics. For compressible flows, identifying the parameter that links local flow speed to acoustic speed is essential for shock prediction, choking, and aerodynamic heating considerations.

Given Data / Assumptions:

• Flow may be subsonic, transonic, or supersonic.
• Local speed of sound a depends on thermodynamic state.
• Flow speed V compared to a informs compressibility significance.

Concept / Approach:

Mach number, M = V/a, is the canonical indicator of compressibility effects. For M ≪ 1, compressibility is negligible; for M ≈ 1, transonic phenomena arise; for M > 1, shocks and expansion waves are prevalent. Other numbers target different physics: Reynolds (inertia/viscous), Weber (inertia/surface tension), Euler (pressure/inertia).

Step-by-Step Solution:

Verification / Alternative check:

Aerodynamics and gas dynamics texts consistently use Mach number as the primary criterion for compressibility-driven behavior and wave phenomena.

Why Other Options Are Wrong:

Weber: Capillarity vs inertia (multiphase). Euler: Pressure vs inertia, not a direct compressibility gauge. Reynolds: Inertia vs viscosity, governs laminar–turbulent transition.

Common Pitfalls:

Assuming high Reynolds automatically implies compressibility; confusing high speed with high Reynolds without considering speed of sound.

Final Answer:

Mach number