The Weber number (We) is a

dimensionless number A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...

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

multiphase flow In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve s ...

s with strongly curved surfaces. It is named after Moritz Weber (1871–1951). It can be thought of as a measure of the relative importance of the fluid's

inertia Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...

compared to its

surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...

. The quantity is useful in analyzing thin film flows and the formation of droplets and bubbles.

Mathematical expression

The Weber number may be written as: :

\mathrm = \frac
 = \left( \frac \right) \frac 
 = \frac

where *

C_\mathrm

is the

drag coefficient In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equ ...

of the body cross-section. *

\rho

is the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

of the fluid ( kg/ m³). *

v

is its

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

(m/ s). *

l

is its characteristic

length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...

, typically the droplet diameter (m). *

\sigma

is the

( N/m). The modified Weber number, :

\mathrm^*=\frac

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

\mathrm^*=\frac

, where :

E_\mathrm=\frac

and :

E_\mathrm=\pi l^2 \sigma

Applications

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.

Mathematical expression

Applications

References

Further reading