# Weber Number

on . Posted in Dimensionless Numbers

Weber number, abbreviated as We, a dimensionless number, is used in fluid mechanics, often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces.  It is a measure of the relative importance of the fluid's inertia compared the its surrface tension.  The reason this number is important is it can be used to help analyze thin film flows and how droplets and bubbles are formed.  The Weber number indicates how likely a fluid flow is to overcome surface tension forces.  The magnitude of the Weber number provides insights into the behavior of the fluid in various situations.

### Weber number Interpretation

• We < 1  -  Surface tension forces dominate over inertial forces.  This typically results in a more spherical and compact shape for liquid droplets or jets.
• We ≈ 1  -  Inertial and surface tension forces are roughly balanced.  This can lead to interesting transitional behavior in fluid breakup processes.
• We > 1  -  Inertial forces dominate over surface tension forces.  This often leads to the disintegration of the fluid into smaller droplets or the creation of splashes and sprays.

The Weber number is essential in various fields, including fluid dynamics, engineering, and materials science, where understanding the interaction between fluid flow and surface tension is crucial.  It helps predict and explain phenomena such as droplet formation in inkjet printing, spray painting, and the behavior of liquid fuel sprays in combustion processes.

### Weber number formula

$$We \;=\; \rho \; v^2 \; l_c \;/\; \sigma$$     (Weber Number)

$$\rho \;=\; We \; \sigma \;/\; v^2 \; l_c$$

$$v \;=\; \sqrt{ We \; \sigma \;/\; \rho \; l_c }$$

$$l_c \;=\; We \; \sigma \;/\; \rho \; v^2$$

$$\sigma \;=\; \rho \; v^2 \; l_c \;/\; We$$

Symbol English Metric
$$We$$ = Weber number $$dimensionless$$ $$dimensionless$$
$$\rho$$  (Greek symbol rho) = fluid density $$lbm\;/\;ft^3$$ $$kg\;/\;m^3$$
$$v$$ = fluid velocity  $$ft\;/\;sec$$ $$m\;/\;s$$
$$l_c$$ = characteristic length $$ft$$ $$m$$
$$\sigma$$  (Greek symbol sigma) = surface tension $$lbf\;/\;ft$$   $$N\;/\;m$$

Tags: Flow Fluid