Fluid Mechanics — Definition of Reynolds Number In civil and mechanical engineering fluid dynamics, the Reynolds number (Re) is defined as the ratio of the inertia force to which other characteristic force acting within the fluid? Choose the most appropriate classification that appears in the standard definition.

Introduction:
The Reynolds number is a fundamental dimensionless quantity used to predict flow regimes—laminar, transitional, or turbulent—by comparing the dominance of inertia effects to viscous effects in a flowing fluid. It guides pipe design, open-channel hydraulics, and external aerodynamics.

Given Data / Assumptions:

• Steady, incompressible flow is assumed for basic interpretation.
• Characteristic length L and velocity V are identifiable (e.g., pipe diameter and average speed).
• Fluid properties density rho and dynamic viscosity mu are uniform.

Concept / Approach:
By definition, Reynolds number Re compares inertia force to viscous force. In engineering form, Re = (rho * V * L) / mu. High Re means inertia dominates and turbulence is more likely; low Re means viscosity dominates and laminar behavior persists.

Step-by-Step Solution:
Start with dimensional analysis of forces: inertia force ~ rho * V^2 * A, viscous force ~ mu * V * A / L.Form the ratio: (rho * V^2 * A) / (mu * V * A / L) = (rho * V * L) / mu.Thus Re = (rho * V * L) / mu = inertia force / viscous force.

Verification / Alternative check:
In pipe flow, thresholds around Re ≈ 2000 (laminar) and Re > 4000 (turbulent) are widely used. This practical usage aligns with the inertia/viscosity competition that the definition encodes.

Why Other Options Are Wrong:
Surface tension and elastic forces are not in the canonical Re definition for internal flow; gravity enters other nondimensional groups (e.g., Froude number), not Reynolds number.

Common Pitfalls:
Mixing up Re with Froude (inertia/gravity) or Weber (inertia/surface tension); using kinematic viscosity nu incorrectly—remember Re = V * L / nu where nu = mu / rho.

Final Answer:
viscous force