# Ohnesorge number

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The **Ohnesorge number** (**Oh**) is a dimensionless number that relates the viscous forces to inertial and surface tension forces. The number was defined by Wolfgang von Ohnesorge in his 1936 doctoral thesis.^{[1]}

It is defined as:

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)- Re is the Reynolds number
- We is the Weber number

## Applications

The Ohnesorge number for a 3 mm diameter rain drop is typically ~0.002. Larger Ohnesorge numbers indicate a greater 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.^{[2]}^{[3]}

## See also

- 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.