# Weber number

The **Weber number (<math>W</math>)** is a dimensionless quantity that is useful when analyzing fluid flow when the system in question includes an interface between two fluids. In particular, it is the ratio of the fluid's inertia and the surface tension: <math>W = \frac{\rho v^{2} L}{\sigma}</math>. Here, <math>\rho</math> is the density of the moving fluid, <math>v</math> is its velocity, <math>L</math> is a characteristic length scale (this is generally the length the fluid flows through; for example, for a cylindrical flow, it would be the diameter of the cylinder formed by the fluid), and <math>\sigma</math> is the surface tension.

One can imagine that this Weber number is a good indicator of how well the liquid will flow (if these are the two dominant forces in the system); after all, it gives the ratio of the force inhibiting flow to the surface tension that prevents flow.

## References

[1] A.S. Utada, A. Fernandez-Nieves, J.M. Gordillo, and D.A. Weitz, "Absolute Instability of a Liquid Jet in a Coflowing Stream," PRL 100, 014502 (2008)

[2] http://en.wikipedia.org/wiki/Weber_number