Weber Number Calculator

The Weber number, We, is a dimensionless quantity that compares the inertial force of a moving fluid to the cohesive force of surface tension. It is the key parameter for predicting whether a liquid droplet or jet remains stable or breaks apart into smaller droplets.

We = ρv²L/σ, where ρ is fluid density, v is characteristic velocity, L is a characteristic length (such as droplet diameter), and σ is the fluid's surface tension.

A low Weber number (We≪1) means surface tension dominates, keeping a droplet spherical and cohesive. A high Weber number (We≫1) means inertial forces dominate, deforming and eventually breaking up the droplet or jet into smaller fragments, the basis of spray atomization.

It is central to spray atomization design (fuel injectors in engines, agricultural pesticide sprayers, spray coating), inkjet printer droplet formation, bubble and foam dynamics, and any process where controlling droplet size and breakup matters.

As Weber number increases past certain empirically determined critical values (roughly We≈12 for a single droplet in a gas stream, though exact thresholds depend on the breakup mechanism), aerodynamic forces overcome surface tension and the droplet deforms and fragments into smaller droplets.

Surface tension force scales with length (proportional to L), while inertial force scales with length cubed (proportional to L³ via volume and hence mass), so as objects get smaller, surface tension becomes relatively more important. This is exactly why the Weber number (which captures this length-dependent balance) is most relevant for droplets and thin jets rather than large-scale flows.

A typical raindrop falling at terminal velocity has a Weber number in the range of roughly 1 to 20 depending on size, in the transitional regime where both surface tension and aerodynamic forces are significant, which is why raindrops above a certain size become unstable and break apart during their fall.

They are independent dimensionless numbers measuring different force balances (inertia versus surface tension for Weber, inertia versus viscosity for Reynolds), but both are often relevant simultaneously in droplet and spray problems, and their ratio defines other useful dimensionless groups like the Ohnesorge number.

No, unlike the Froude number, the Weber number formula contains no gravitational acceleration term, it purely compares inertial and surface-tension forces. Gravity's relative importance in a free-surface flow is instead captured separately by the Froude number or the Bond number.

Surface tension σ is measured in newtons per metre (N/m), equivalently joules per square metre. Water's surface tension is about 0.072 N/m at room temperature, one of the highest among common liquids.