Weber number

Physical key figure
Surname	Weber number
Formula symbol	${\displaystyle {\mathit {We}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {We}}={\frac {\rho \,v^{2}\,L}{\sigma }}}$
${\displaystyle \rho }$ density ${\displaystyle v}$ Flow velocity ${\displaystyle L}$ characteristic length ${\displaystyle \sigma }$ Surface tension
Named after	Moritz Weber
scope of application	Two-phase flows

Droplets of splash water after a stone hit. The non-spherical drops are characteristic of large Weber numbers.

The Weber number (named after Moritz Weber , symbol :) is a dimensionless number of fluid mechanics . It is in two-phase flows , e.g. B. a drop of water in air, the ratio of inertial force to the stabilizing surface force : ${\displaystyle {\mathit {We}}}$

${\displaystyle {\mathit {We}}={\frac {\rm {Tr{\ddot {a}}gheitskraft}}{\rm {Oberfl{\ddot {a}}chenkraft}}}={\frac {\rho \,v^{2}\,L}{\sigma }}}$

It is

• ${\displaystyle \rho }$the density
• ${\displaystyle v}$the relative flow velocity between the surrounding medium and the drop
• ${\displaystyle L}$the characteristic length , i.e. usually the diameter of the drop
• ${\displaystyle \sigma }$the surface tension .

The Weber number is used as a measure of bubble formation and droplet deformation , in particular to characterize the atomization quality of a spray: the larger the Weber number,

• the greater the deformation effect of the flow on the drop
• the further the drop has moved away from the spherical shape
• the more the jet of liquid breaks up .

Individual evidence

1. ^ Philip Day, Andreas Manz, Yonghao Zhang: Microdroplet Technology: Principles and Emerging Applications in Biology and Chemistry . Springer Science & Business Media, ISBN 978-1-4614-3265-4 , p. 9 ( limited preview in Google Book search).