In fluid mechanics, the Reynolds number (Re) is defined as the ratio of inertial force to which competing effect?

Introduction / Context:
Reynolds number (Re) is a cornerstone dimensionless parameter in fluid mechanics. It compares the tendency of a flow's inertia to keep it moving in a straight, mixed state versus the tendency of viscous effects to diffuse momentum and smooth out velocity gradients. Recognizing the correct physical ratio behind Re is essential for predicting laminar–turbulent transitions and for similarity analysis in model testing.

Given Data / Assumptions:

• Characteristic length L and characteristic velocity V are representative of the flow.
• Fluid density rho and dynamic viscosity mu are constants (for the considered conditions).
• We are identifying which competing effect appears in the denominator of Re.

Concept / Approach:

Inertial force scale is proportional to rho * V^2 * (area), whereas viscous force scale is proportional to mu * V * (area / length). Taking their ratio eliminates geometric areas and yields Re = (rho * V * L) / mu. Thus, Reynolds number is the ratio of inertial to viscous effects. It is not a ratio involving gravity, surface tension, elasticity, or compressibility—those appear in other dimensionless groups (e.g., Froude, Weber, Mach numbers).

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Dimensional check: (rho * V * L) / mu is dimensionless. Empirically, low Re flows are laminar (viscous dominated), high Re are turbulent (inertial dominated), matching the interpretation.

Why Other Options Are Wrong:

Surface tension relates to Weber number, gravity to Froude number, elasticity/compressibility to Mach or elastic numbers—not to Reynolds number.

Common Pitfalls (misconceptions, mistakes):

Confusing Reynolds number with Froude or Weber numbers, or thinking Re compares pressure to viscosity instead of inertia to viscosity.

Final Answer:

viscosity