Weber Number Calculator

At a glance:The Weber number (symbol We) is a dimensionless number in fluid mechanics that measures the ratio of inertial forces to surface tension, especially relevant to interfacial flows — droplets, bubbles, liquid films, sprays and two-phase flow. When a liquid mass (e.g. a droplet) moves through a gas or is ejected at high speed, inertia tends to stretch and tear it, while surface tension acts like an elastic film trying to keep it as a minimal-surface sphere. The Weber number is the ratio of these two forces, deciding whether a droplet stays intact or breaks into a fine mist. It is defined as We=ρ·v²·L/σ. Term by term: ρ is fluid density (kg/m³, water ≈998 at 20°C); v is the characteristic velocity (m/s), e.g. the droplet's speed relative to the surrounding gas or the ejection speed; L is the characteristic length (m), typically the droplet diameter in droplet analysis or the nozzle size in spray problems; σ is surface tension (N/m, water ≈0.0728 at 20°C). The numerator ρv²L is proportional to inertial force, the denominator σ to surface tension, giving the dimensionless We. Physical reading: when We is very small (≪1), surface tension dominates, the droplet stays spherical and resists breakup (tiny disturbances are 'smoothed' by surface tension); when We is large (≫1), inertia overwhelms surface tension, the droplet stretches, deforms and finally shatters into smaller droplets. Spray/atomisation research often cites a 'critical Weber number' (around We≈12 for some bag-breakup modes) above which breakup begins. Example: ρ=998 kg/m³, v=1 m/s, L=0.1 m, σ=0.0728 N/m → We=998×1²×0.1/0.0728=99.8/0.0728≈1371. This is far above 1, meaning at this scale and speed inertia vastly exceeds surface tension and the interface deforms and breaks easily. Note L=0.1 m here is a large scale; a small droplet (L=1 mm=0.001 m) gives We≈13.7, near the breakup threshold. Applications: (1) spray and atomisation design — agricultural spraying, fuel injectors and inkjet rely on controlling We to set droplet size and uniformity; (2) two-phase flow and bubble dynamics — whether a bubble breaks up or coalesces; (3) splash-promoting or splash-preventing surface engineering. Notes: (1) v should be the relative velocity (droplet vs surrounding fluid), not absolute ground speed; (2) L's definition depends on the problem (droplet diameter, nozzle bore) and must be consistent when comparing; (3) the density phase (continuous or dispersed) varies slightly by definition — this tool uses the input ρ; (4) use consistent SI units (kg/m³, m/s, m, N/m) to get the dimensionless We.