Dimensional analysis – definition of Weber number (We) Select the correct definition of the Weber number used in free-surface and multiphase flows.

Introduction / Context:Nondimensional numbers organize complex fluid phenomena. The Weber number is particularly important when surface tension competes with inertia, such as in droplet formation, jets, splashing, and wave breaking.

Given Data / Assumptions:

• Characteristic velocity V, length L, density ρ, and surface tension σ.
• Definition pertains to flows where interfaces and capillarity matter.

Concept / Approach:Weber number compares inertia to surface tension effects: We = (ρ V^2 L) / σ. Large We implies inertia dominates and interfaces deform or break; small We indicates surface tension resists deformation and stabilizes the interface.

Step-by-Step Solution:

Verification / Alternative check:Related groups: Reynolds number Re = inertia/viscous, Froude number Fr = inertia/gravity. By analogy, Weber links inertia and surface tension, matching option D.

Why Other Options Are Wrong:

• Elastic, gravity, or pressure-force ratios correspond to other dimensionless groups, not the Weber number.

Common Pitfalls:Confusing We with Re or Fr; remembering the numerator ρ V^2 L (inertia) divided by σ (surface tension) helps avoid errors.

Final Answer:Ratio of inertia force to surface tension force