Dimensionless numbers in fluid mechanics The ratio of inertia force to viscous force for a flowing fluid defines which standard dimensionless parameter?

Introduction / Context:
Dimensionless numbers characterize competing physical effects in fluid flow. Recognizing which ratio corresponds to which number is foundational for similarity analysis, scaling, and regime identification (laminar vs turbulent).

Given Data / Assumptions:

• Single-phase Newtonian fluid.
• Characteristic length L and velocity V defined for the flow.

Concept / Approach:
Reynolds number Re compares inertia to viscous effects: Re = (ρ V L) / μ. High Re indicates dominance of inertial effects and potential turbulence; low Re indicates viscous-dominated, laminar behavior. Other numbers represent different force ratios: Froude (inertia/gravity), Euler (pressure/inertia), Weber (inertia/surface tension), and Mach (inertia/compressibility via acoustic speed).

Step-by-Step Association:

Verification / Alternative check:
Common thresholds: in internal pipe flow, Re <~ 2100 (laminar), Re >~ 4000 (turbulent), with transition in between—confirming its role in regime prediction.

Why Other Options Are Wrong:
Froude involves gravity head; Euler relates pressure to inertia; Weber involves surface tension; Mach relates flow speed to speed of sound. Only Reynolds captures inertia/viscous competition.

Common Pitfalls:
Mixing Fanning and Darcy friction factors with Re definitions; forgetting to use consistent units for ρ, μ, V, L.

Final Answer:
Reynolds number