Laplace number

{{Short description|Dimensionless parameter in fluid mechanics}}

The Laplace number ({{math|La}}), also known as the Suratman number ({{math|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.{{Cite book |last=Massey |first=Bernard Stanford |url=https://www.google.fr/books/edition/Measures_in_Science_and_Engineering/ebEeAQAAIAAJ?hl=en&gbpv=0&bsq=Measures%20in%20science%20and%20engineering%20:%20their%20expression,%20relation,%20and%20interpretation%20by%20Massey,%20B.%20S.%20(Bernard%20Stanford) |title=Measures in Science and Engineering: Their Expression, Relation, and Interpretation |date=1986 |publisher=E. Horwood |isbn=978-0-470-20331-6 |language=en}}

It is defined as follows:{{cite journal |last1=Balakotaiah |first1=V. |last2=Jayawardena |first2=S. S. |last3=Nguyen |first3=L. T. |title=Studies on Normal and Microgravity Annular Two Phase Flows |journal=Proceedings of the Fourth Microgravity Fluid Physics and Transport Phenomena Conference |date=1999 |url=https://ntrs.nasa.gov/api/citations/20010004266/downloads/20010004266.pdf |access-date=27 May 2024}}

:$\backslash mathrm\{La\}\; =\; \backslash mathrm\{Su\}\; =\; \backslash frac\{\backslash sigma\; \backslash rho\; L\}\{\backslash mu^2\}$

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:{{r|Balakotaiah_99}}

:$\backslash mathrm\{La\}\; =\; \backslash frac\{\backslash mathrm\{Re\}^2\}\{\backslash mathrm\{We\}\}$