The Weber number is a dimensionless number in fluid mechanics

Fluid mechanics

Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

 that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flow

Multiphase flow

In fluid mechanics, multiphase flow is a generalisation of the modelling used in two-phase flow to cases where the two phases are not chemically related or where more than two phases are present In fluid mechanics, multiphase flow is a generalisation of the modelling used in two-phase flow to...

s with strongly curved surfaces. It can be thought of as a measure of the relative importance of the fluid's inertia

Inertia

Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...

 compared to its surface tension

Surface tension

Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...

. 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:

where

• is the density
  Density
  The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
  
   of the fluid (kg/m³).
• is its velocity
  Velocity
  In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
  
   (m/s).
• is its characteristic length
  Length
  In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...
  
  , typically the droplet diameter (m).
• is the surface tension
  Surface tension
  Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
  
  (N/m).

The modified Weber number,



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

where


and
.

Applications

One application of the Weber number is for 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.