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# Ohnesorge number

The Ohnesorge number, Oh , is a dimensionless number that relates the viscous and surface tension force.

It is defined as: $Oh = \frac{ \mu}{ \sqrt{\rho \sigma L }}$

Where

• μ is the liquid viscosity
• ρ is the liquid density
• σ is the surface tension
• L is the characteristic length scale (typically- drop diameter)

## Applications

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.[1] [2]

## References

1. ^ Lefebvre, Arthur Henry (1989), , New York and Washington, D.C.: Hemisphere Publishing Corp., ISBN 978-0-89116-603-0, OCLC 18560155
2. ^ 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, $Oh = 1/\sqrt{La}$, 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.