Weber number

[2] 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.

The Cauchy stress tensor for an incompressible fluid takes the form: Introducing the dynamic pressure

and, assuming high Reynolds number flow, it is possible to nondimensionalize the variables with the scalings: The free surface boundary condition in nondimensionalized variables is then: Where

The influence of the Weber number can then be quantified relative to gravitational and viscous forces.

One application of the Weber number is the study of heat pipes.

When the momentum flux in the vapor core of the heat pipe is high, there is a possibility that the shear stress exerted on the liquid in the wick can be large enough to entrain droplets into the vapor flow.

The Weber number is the dimensionless parameter that determines the onset of this phenomenon called the entrainment limit (Weber number greater than or equal to 1).

In this case the Weber number is defined as the ratio of the momentum in the vapor layer divided by the surface tension force restraining the liquid, where the characteristic length is the surface pore size.

A splash after half a brick hits the water; the image is about half a meter across. Note the freely moving airborne water droplets, a phenomenon typical of high Reynolds number flows; the intricate non-spherical shapes of the droplets show that the Weber number is high. Also note the entrained bubbles in the body of the water, and an expanding ring of disturbance propagating away from the impact site.