Weber number (We): identify the force ratio it represents In dimensionless analysis of fluid flows with free surfaces, the Weber number expresses the ratio of which two effects?

Introduction / Context:
Dimensionless numbers classify flow regimes and similarity. The Weber number is critical in atomization, droplet breakup, wave formation, and jet impingement where surface tension competes with inertia.

Given Data / Assumptions:

• Characteristic length L, velocity V, density ρ, and surface tension σ.

Concept / Approach:
Weber number is defined as We = ρ * V^2 * L / σ. It therefore measures the relative importance of inertial forces to surface-tension forces. Large We implies inertia dominates and interfaces deform or break; small We means surface tension stabilizes the interface.

Step-by-Step Solution:

Verification / Alternative check:
Related groups: Capillary number Ca = μ V / σ (viscous vs surface). Froude number Fr = V / √(gL) (inertia vs gravity). Reynolds number Re = ρ V L / μ (inertia vs viscosity).

Why Other Options Are Wrong:
They correspond to Fr (gravity), Re (viscosity), or compressibility effects (elastic), not to Weber.

Common Pitfalls:
Confusing We with Fr or Ca; forgetting that σ appears in the denominator.

Final Answer:
inertia force to surface-tension force