text: The Weber number appears in the incompressible Navier-Stokes equations through a free surface boundary condition.
  For a fluid of constant density  and dynamic viscosity , at the free surface interface there is a balance between the normal stress and the curvature force associated with the surface tension:
  Where  is the unit normal vector to the surface,  is the Cauchy stress tensor, and  is the divergence operator. 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  is the Froude number,  is the Reynolds number, and  is the Weber number. The influence of the Weber number can then be quantified relative to gravitational and viscous forces.