Ohnesorge number

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

It is defined as\[ \mathrm{Oh} = \frac{ \mu}{ \sqrt{\rho \sigma L }} = \frac{\sqrt{\mathrm{We}}}{\mathrm{Re}} \sim \frac{\mbox{viscous forces}}{\sqrt{{\mbox{inertia}} \cdot {\mbox{surface tension}}}} \]

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.

See also

• 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.

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