Weber number

The Weber number is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It can be thought of as a measure of the relative importance of the fluid's inertia compared to its surface tension. The quantity is useful in analyzing thin film flows and the formation of droplets and bubbles.

It is named after Moritz Weber (1871–1951) and may be written as::$mathit\{We\}\; =\; frac\{\; ho\; v^2\; l\}\{sigma\}$

where
* $ho$ is the density of the fluid.
* $v$ is its velocity.
* $l$ is its characteristic length, typically the droplet diameter.
* $sigma$ is the surface tension.

The modified Weber number,

$We^*=frac\{We\}\{48\}$

equals the ratio of the kinetic energy on impact to the surface energy,

:$We^*=frac\{E\_\{kin\{E\_\{surf$,

where

:$E\_\{kin\}=pi\; ho\; l~^3U~^2/24$

and

:$E\_\{surf\}=2pi\; l~^2sigma$.

References

*Weast, R. Lide, D. Astle, M. Beyer, W. (1989-1990). CRC Handbook of Chemistry and Physics. 70th ed. Boca Raton, Florida: CRC Press, Inc.. F-373,376.