The ratio of inertia forces to viscous forces, used to characterize flow regime (laminar vs turbulent), is known as which dimensionless number?

Introduction / Context:
Dimensionless numbers collapse complexity and guide similarity between model and prototype. The Reynolds number is paramount in internal and external flows for predicting laminar–turbulent transition and friction behavior.

Given Data / Assumptions:

• Characteristic length L, velocity V, density ρ, and dynamic viscosity μ.
• Newtonian fluid.

Concept / Approach:

Reynolds number Re = (inertia forces)/(viscous forces) = ρ V L / μ. Large Re implies inertia dominates and turbulence is likely; small Re implies viscous dominance and laminar flow. Other dimensionless numbers represent different force balances (e.g., Froude: inertia/gravity; Weber: inertia/surface tension; Euler: pressure/inertia).

Step-by-Step Solution:

Verification / Alternative check:

Check units: ρ V L / μ → (M L^-3)(L T^-1)(L)/(M L^-1 T^-1) = dimensionless, as required.

Why Other Options Are Wrong:

Euler number relates pressure to inertia; Froude compares inertia to gravity; Weber compares inertia to surface tension; Mach compares flow speed to speed of sound.

Common Pitfalls:

Misusing hydraulic diameter for non-circular ducts; forgetting temperature dependence of μ and ν.

Final Answer:

Reynolds number