Laplace number

Physical key figure
Surname	Laplace number, Suratman number
Formula symbol	${\displaystyle {\mathit {La}},{\mathit {Su}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {La}}={\frac {\sigma \rho L}{\eta ^{2}}}}$
${\displaystyle \sigma }$ Surface tension ${\displaystyle \rho }$ characteristic density ${\displaystyle L}$ characteristic length ${\displaystyle \eta }$ dynamic viscosity
Named after	Pierre-Simon Laplace , PC Suratman
scope of application	viscous currents

The Laplace number (formula symbol , after the French mathematician Pierre-Simon Laplace ), also known as the Suratman number (formula symbol , after the Indian physicist and engineer PC Suratman ), is a dimensionless number of fluid dynamics . It is used, for example, to describe the deformation of drops and bubbles . ${\displaystyle {\mathit {La}}}$ ${\displaystyle {\mathit {Su}}}$

The Laplace number is defined as the product of the surface and inertia force of a fluid divided by the square of the frictional force :

${\displaystyle {\mathit {La}}={\frac {F_{O}\cdot F_{T}}{{F_{R}}^{2}}}={\frac {\sigma \cdot (\rho \cdot L)}{\eta ^{2}}}}$

With

• the surface tension in ${\displaystyle \sigma }$ ${\displaystyle \mathrm {{\frac {N}{m}}={\frac {kg}{s^{2}}}} }$
• the characteristic density ${\displaystyle \rho }$
• the characteristic length ${\displaystyle L}$
• the characteristic dynamic viscosity in . ${\displaystyle \eta }$ ${\displaystyle \mathrm {\frac {N\cdot s}{m^{2}}} }$

The key figure corresponds to the reciprocal square of the Ohnesorge number and can also be formed from the quotients of the (partly squared) Reynolds number with the capillary number or the Weber number : ${\displaystyle {\mathit {Oh}}}$ ${\displaystyle {\mathit {Re}}}$ ${\displaystyle {\mathit {Ca}}}$ ${\displaystyle {\mathit {We}}}$

${\displaystyle {\mathit {La}}={\frac {1}{{\mathit {Oh}}^{2}}}={\frac {\mathit {Re}}{\mathit {Ca}}}={\frac {{\mathit {Re}}^{2}}{\mathit {We}}}}$

Individual evidence

1. ^ Bernard Stanford Massey: Units, Dimensional Analysis and Physical Similarity . Van Nostrand Reinhold, 1971, ISBN 0-442-05178-6 , p. 119 .
2. ↑ André Trombetta: PC Suratman. In: neglectedscience. Retrieved August 7, 2014 . 
3. ^ Josef Kunes: Dimensionless Physical Quantities in Science and Engineering . Elsevier, 2012, ISBN 0-12-391458-2 , pp. 115 ( limited preview in Google Book search).