Laplace number

The Laplace number (La), also known as the Suratman number (Su), is a dimensionless number used in the characterization of free surface fluid dynamics. It represents a ratio of surface tension to the momentum-transport (especially dissipation) inside a fluid. It is named after Pierre-Simon Laplace and Indonesian physicist P. C. Suratman.^[1]

It is defined as follows:^[2]

${\displaystyle \mathrm {La} =\mathrm {Su} ={\frac {\sigma \rho L}{\mu ^{2}}}}$

where:

• σ = surface tension
• ρ = density
• L = length
• μ = liquid viscosity

Laplace number is related to Reynolds number (Re) and Weber number (We) in the following way:^[2]

${\displaystyle \mathrm {La} ={\frac {\mathrm {Re} ^{2}}{\mathrm {We} }}}$

• Ohnesorge number - There is an inverse relationship, ${\displaystyle \mathrm {La} =\mathrm {Oh} ^{-2}}$, between the Laplace number and the Ohnesorge number.