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:


  • 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


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]

In inkjet printing, liquids whose Ohnesorge number is less than 1 and greater than 0.1 are jettable (1<Z<10 where Z is the reciprocal of the Ohnersorge number).[1][4]

See also[edit]

  • 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.


  1. ^ a b McKinley, Gareth H.; Renardy, Michael (2011). "Wolfgang von Ohnesorge". Physics of Fluids. 23: 127101. Bibcode:2011PhFl...23l7101M. doi:10.1063/1.3663616. 
  2. ^ Lefebvre, Arthur Henry (1989). Atomization and Sprays. New York and Washington, D.C.: Hemisphere Publishing Corp. ISBN 978-0-89116-603-0. OCLC 18560155. 
  3. ^ Ohnesorge, W (1936). "Formation of drops by nozzles and the breakup of liquid jets". Journal of Applied Mathematics and Mechanics. 16: 355–358. 
  4. ^ Derby, Brian (2010). "Inkjet Printing of Functional and Structural Materials: Fluid Property Requirements, Feature Stability, and Resolution". Annual Review of Materials Research. 40 (1): 395–414. Bibcode:2010AnRMS..40..395D. doi:10.1146/annurev-matsci-070909-104502. ISSN 1531-7331.