Weber number (We) is defined as the ratio of inertia force to surface-tension force. Is this statement correct?

Introduction:Dimensionless numbers help compare competing physical effects in fluid flows. The Weber number measures the relative importance of inertia compared to surface tension, crucial in jet breakup, droplet formation, and atomization.

Given Data / Assumptions:

• Flow with characteristic velocity V and length L.
• Fluid density rho and surface tension sigma.

Concept / Approach:The Weber number is We = inertia force / surface-tension force. In formula form, We = (rho * V^2 * L) / sigma. A large We implies inertia dominates and interfaces deform or break; a small We implies surface tension resists deformation.

Step-by-Step Solution:1) Identify competing effects: inertia vs surface tension.2) Write We = (rho * V^2 * L) / sigma.3) The verbal statement matches the ratio definition; hence it is correct.

Verification / Alternative check:In spray nozzles, increasing V or L increases We, promoting ligament breakup; increasing sigma lowers We, stabilizing the interface. Observations align with the definition.

Why Other Options Are Wrong:

• Incorrect: Conflicts with standard definition in fluid mechanics.
• Only valid for water: The definition is general for any fluid, though sigma and rho differ.
• Valid only for capillary tubes: Weber number applies broadly to free-surface and multiphase flows, not just capillaries.

Common Pitfalls:

• Confusing We with Reynolds number (inertia/viscous) or Capillary number (viscous/surface tension).
• Omitting the characteristic length L in calculations.

Final Answer:Correct