Weber Number⚠ unverified
Physics / Fluids · Compute the Weber number of a flow
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| density | density | kg/m**3 | 1.0 | Fluid density |
| velocity | velocity | m/s | 1.0 | Flow speed |
| length | length | m | 1.0 | Characteristic length scale |
| surface_tension | surfacetension | N/m | 1.0 | Surface tension |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | We | kilogram * meter / newton / second ** 2 | Weber number, dimensionless |
The science & history
Understanding the Parameters
- $\rho$, $v$, $L$ — raise inertial stress $\sim\rho v^{2}$.
- $\sigma$ — surface tension (water ≈ 0.072 N/m at room temperature); higher $\sigma$ lowers We.
- We — low We: surface tension shapes the interface (spherical drops); high We: inertia shatters ligaments and sprays.
Derivation (Approaching a Proof)
Inertial force scale $\sim \rho v^{2} L^{2}$; surface-tension force scale $\sim \sigma L$. Their ratio:
$$\mathrm{We} = \frac{\rho v^{2} L^{2}}{\sigma L} = \frac{\rho v^{2} L}{\sigma}.$$
Dimensionless companion to Reynolds Number (viscosity) and Froude Number (gravity).
History
Named after Moritz Weber; standard in multiphase and atomisation research throughout the 20th century.
Related Concepts: Reynolds Number, Froude Number, Dynamic Pressure, Drag
Notes: Registry calculator weber-number (unverified). Registry unit bug: output labelled
like kilogram * meter / newton / second ** 2 instead of dimensionless (that combination actually
simplifies to 1 if units are consistent — the label is still wrong/confusing).