What is the Reynolds number definition?

• A. Re = μ / (ρ v D).
• B. Re = ρ v D / μ.
• C. Re = ρ v / μ.
• D. Re = ρ g D / μ.

Answer: (B)

Reynolds number tells you how strong inertial effects are compared with viscous effects in a flow. It’s defined as Re = ρ v D / μ, where ρ is density, v is a characteristic velocity, D is a characteristic length (such as pipe diameter), and μ is dynamic viscosity. This arrangement comes from comparing the inertial term to the viscous term in the Navier–Stokes equations, and it yields a dimensionless quantity that indicates whether inertia or viscosity dominates.

That makes the chosen form correct: you take the density times velocity times a length scale, divided by viscosity. The alternative with μ in the numerator would just be the reciprocal of Reynolds number, not the standard ratio of inertial to viscous effects. The option lacking the length scale isn’t dimensionless, and the one that includes gravity introduces a factor that isn’t part of Reynolds number.