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Weber Number Calculator

Enter density, velocity, length, and surface tension to get the Weber number.

Result

How it is calculated

The Weber number compares the inertia of a moving fluid with the surface tension holding it together: We = ρ × v² × L ÷ σ. Here ρ is the fluid density in kg/m³, v is the speed relative to the surrounding fluid in m/s, L is the characteristic length in metres (a droplet diameter, for example), and σ is the surface tension in N/m. With these units the result has no unit. Note that the speed is squared, so doubling v quadruples We. The tool labels the result with a simple cut at 1: below 1 it says surface tension dominates, and at 1 or above it says inertia dominates. The surface tension must be above zero. The label is only a rough guide, because the Weber number where a drop actually breaks up depends on the situation.

Worked example

A water droplet 2 mm across (L = 0.002 m) moves at 5 m/s. Take water density 998 kg/m³ and surface tension 0.0728 N/m. Speed squared: 5² = 25. Numerator: 998 × 25 × 0.002 = 49.9. Weber number: 49.9 ÷ 0.0728 = 685.44. That is far above 1, so the tool reports that inertia dominates. Slowing the same drop to 0.1 m/s gives only 0.27, where surface tension dominates, because speed enters as a square.

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Common mistakes

  • Entering the diameter in millimetres. The length must be in metres, so 2 mm is 0.002, not 2.
  • Using surface tension in mN/m or dyn/cm. The field expects N/m, so 72.8 mN/m must be typed as 0.0728.
  • Using the wrong length. The characteristic length is often the droplet diameter, not the radius, and not the nozzle size unless that is what your correlation uses.
  • Using the speed of the liquid instead of its speed relative to the surrounding gas, when the question is about breakup in a gas flow.
  • Reading the 1 threshold as a breakup limit. It only separates the two labels; real breakup depends on the flow and the setup.

About this calculator

The Weber number (We) is a dimensionless quantity that compares a fluid’s inertial force to its surface tension force: We = ρv²L / σ, where ρ is fluid density, v is velocity, L is a characteristic length (such as droplet diameter), and σ is surface tension. A low Weber number means surface tension dominates and holds a droplet together; a high Weber number means inertia wins and the droplet is likely to deform or break apart.

Fluid dynamics engineers rely on the Weber number to predict droplet and bubble breakup, which matters directly for inkjet printing (getting consistent droplet formation), spray atomization in combustion and agricultural sprayers, and coating processes where a liquid film must stay uniform. Density, velocity, a characteristic length and surface tension are combined into the Weber number, the ratio of inertial to surface-tension forces.

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Comments (1)

  • Editorial team

    Because speed is squared, small changes in velocity move the result a lot. A 2 mm water drop at 5 m/s gives 685.44, and at 10 m/s it gives 2,741.76, exactly four times as much. In sprays the speed that counts is the drop's speed relative to the surrounding air, not its speed over the ground. The 1 cut-off is only a label. Which kind of drop or bubble are you studying, and which breakup value does your source quote?

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