Weber number

Remarks

It is a dimensionless number: surface tension has dimension $\mathsf{M} \mathsf{T}^{-2}$, the same as $\rho U^2 L$. Example: a water drop of diameter $L = 1\ \mathrm{mm}$ moving at $U = 1\ \mathrm{m/s}$, with $\rho = 1000\ \mathrm{kg/m^3}$ and $\sigma \approx 0.072\ \mathrm{N/m}$, has $\mathrm{We} \approx 14$. Non-example: $\rho U L / \sigma$ is not a Weber number; it has dimension $\mathsf{T}/\mathsf{L}$, since one factor of the speed is missing. The Weber number is the ratio of the dynamic pressure $\rho U^2$ to the capillary pressure scale $\sigma / L$.