Weber Number Calculator

Calculator

The Weber number compares inertial forces to surface tension forces in a moving fluid interface. Choose what you want to solve for, then provide the remaining inputs.

Solve for

Weber number (We)

Dimensionless input used for inverse solving.

Density (ρ)

Liquids are often ~1000 kg/m³.

Velocity (v)

Use relative velocity at the interface.

Characteristic length (L)

Often droplet diameter, jet diameter, or bubble size.

Surface tension (σ)

Water at room temperature is about 0.072 N/m.

Output precision

Controls rounding of the displayed result.

Formula used

The Weber number is defined as:

We = (ρ · v² · L) / σ

ρ is fluid density (kg/m³).
v is characteristic velocity (m/s).
L is characteristic length (m), often a diameter.
σ is surface tension (N/m).

In inverse mode, the calculator algebraically rearranges the same formula to solve for the selected variable.

How to use this calculator

Select what you want to solve for in the Solve for field.
Enter the remaining known quantities and choose their units.
Click Calculate to show results above the form.
Use Download CSV or Download PDF to export the result.
If the value seems off, double-check units and characteristic length choice.

Example data table

Case	ρ (kg/m³)	v (m/s)	L (m)	σ (N/m)	We
Water droplet	998	2.0	0.003	0.072	166.33
Slow microjet	1000	0.5	0.0005	0.050	2.50
Air bubble	1.2	1.0	0.010	0.072	0.17
Fuel spray	750	30	0.0002	0.025	5400.00
Oil film	900	3.0	0.001	0.030	270.00

Values are illustrative. Real systems may vary with temperature and contaminants.

Weber number guide

A practical reference to interpret results from this calculator.

1) What the Weber number represents

The Weber number (We) compares inertia to surface tension: how strongly a moving fluid resists being “held together” by an interface. Higher We means deformation, waves, and breakup are more likely because kinetic forces dominate the restoring capillary force.

2) Interpreting common ranges

As a rule of thumb, We < 1 indicates surface tension strongly stabilizes droplets and jets; 1–10 suggests noticeable deformation; and We > 10 often signals instability or breakup depending on geometry, viscosity, turbulence, and forcing. Use these ranges as guidance, not strict thresholds.

3) Choosing a characteristic length

Length L should match the physics you care about: droplet diameter for drop impact and breakup, jet diameter for nozzle flows, hydraulic diameter for channels, or bubble diameter for gas–liquid systems. A mismatched L can shift We by orders of magnitude, so document your choice.

4) Typical property values

At ~20–25°C, water has density near 998 kg/m³ and surface tension about 0.072 N/m. Many light oils have surface tension around 0.025–0.035 N/m and densities near 800–900 kg/m³. Surfactants can reduce water’s surface tension significantly, raising We for the same speed.

5) Sprays and atomization

Nozzle and spray design often targets sufficiently large We to promote sheet or jet breakup into droplets. Increasing velocity or nozzle diameter raises We, while higher surface tension lowers it. In practical systems, viscosity and air–liquid interaction also matter, so consider Reynolds and Ohnesorge numbers alongside We.

6) Droplet impact and breakup

For droplets hitting a surface, We helps estimate spreading, splashing, and secondary droplet formation. A higher impact speed or larger droplet diameter increases We and tends to amplify rim instabilities. Surface roughness, contact angle, and ambient gas pressure can shift observed behavior.

7) Similarity and scaling

Matching We between a lab experiment and a full-scale device preserves the balance between inertia and capillarity, which is crucial for free-surface similarity. If exact matching is impossible, prioritize the dimensionless groups most relevant to your failure mode: breakup, entrainment, or wave formation.

8) Practical input tips

Use consistent units, keep temperatures noted, and prefer measured surface tension when additives are present. For multiphase flows, decide whether properties should be those of the dispersed phase or the continuous phase based on the interface being deformed. Recheck that velocity is relative to the interface.

FAQs

1) What is the Weber number used for?

It estimates whether inertia can deform or break an interface, such as droplets, jets, films, or bubbles. Engineers use it to compare operating conditions, scale experiments, and predict regimes like stable flow, deformation, or breakup.

2) Why can my Weber number be extremely large?

Large We usually comes from high velocity, large length scale, or low surface tension (for example, surfactants). Verify the characteristic length and units first; then confirm surface tension and whether velocity is relative to the interface.

3) Which length should I enter for L?

Use the size of the feature that is deforming: droplet diameter for drops, nozzle or jet diameter for jets, bubble diameter for bubbles, or hydraulic diameter for channels. Choose one definition and keep it consistent across comparisons.

4) Does viscosity affect Weber number?

Viscosity does not appear in We, but it strongly influences breakup and damping. For a fuller picture, pair We with Reynolds number or Ohnesorge number to capture viscous and inertial effects together.

5) What surface tension value should I use for water?

Pure water near room temperature is about 0.072 N/m. If salts, detergents, alcohols, or temperature changes are present, surface tension can shift substantially, so measured or literature values for your mixture are better.

6) Can Weber number be used for gas–liquid flows?

Yes. Select properties for the phase that forms the interface being deformed and use the relevant relative velocity. In many cases, liquid properties dominate capillary behavior, but high-speed gas streams can drive deformation and breakup.

7) What does We < 1 mean in practice?

Capillary forces dominate. Droplets and interfaces tend to remain coherent, waves are suppressed, and breakup is unlikely unless turbulence or external forcing is strong. It is still possible to see deformation, but it is typically limited.