Non-dimensional number governing jet breakup/spray formation The formation of liquid sprays from an orifice or nozzle is primarily characterized by which dimensionless number?

Introduction / Context:
When a liquid jet emerges from a nozzle, it may remain intact, form ligaments, or break into droplets. Predicting atomization is vital for fuel injectors, sprinklers, and spray dryers. Surface tension competes with inertia to resist breakup, and their ratio is captured by a specific dimensionless group.

Given Data / Assumptions:

• Largely incompressible liquid; ambient gas resistance present.
• Characteristic length typically the jet diameter; characteristic velocity the exit speed.
• Gravity may be secondary compared to capillarity and inertia during initial breakup.

Concept / Approach:

The Weber number We = ρ V^2 L / σ compares inertial forces to surface-tension forces. Higher We means inertia overwhelms surface tension, promoting ligament formation and droplet breakup. Reynolds number governs viscous effects, while Froude assesses gravity influence; Mach concerns compressibility of gases and is irrelevant at typical liquid-jet speeds.

Step-by-Step Solution:

Verification / Alternative check:

Empirical spray maps classify regimes (dripping, jetting, atomization) primarily by We and Re; breakup boundaries shift with nozzle design and ambient gas properties.

Why Other Options Are Wrong:

(a) Gravity is less dominant at nozzle exit for small L, high V. (c) Viscosity influences internal losses and ligament thinning but does not set the primary breakup threshold. (d) Liquids are effectively incompressible; Mach applies to high-speed gases. (e) Euler is not the standard criterion for jet breakup.

Common Pitfalls:

Using Re alone to predict atomization; neglecting σ changes with temperature or surfactants, which alter We and thus breakup behavior.

Final Answer:

Weber number (inertia vs surface tension)