The Ohnesorge number, Oh , is a dimensionless number that relates the viscous and surface tension force.
It is defined as:
μ is the liquid viscosity
ρ is the liquid density
σ is the surface tension
L is the characteristic length scale (typically- drop diameter)
The Ohnesorge number for a 3 mm diameter rain drop is typically ~0.002. Larger Ohnesorge numbers indicate a more influence of the viscosity .
This is often used to relate to free surface fluid dynamics such as dispersion of liquids in gases and in spray technology.
^Lefebvre, Arthur Henry (1989), , New York and Washington, D.C.: Hemisphere Publishing Corp., ISBN 978-0-89116-603-0, OCLC 18560155
^ Ohnesorge, W (1936). "Formation of drops by nozzles and the breakup of liquid jets". Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) [Applied Mathematics and Mechanics]16: 355-358. Berlin: Akademie Verlag.
Laplace number - There is an inverse relationship, , between the Laplace number and the Ohnesorge number. It is more historically correct to use the Ohnesorge number, but often mathematically neater to use the Laplace number.