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The Ohnesorge number (Oh) is a
dimensionless number Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...
that relates the viscous forces to
inertia Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newto ...
l and
surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
forces. The number was defined by Wolfgang von Ohnesorge in his 1936 doctoral thesis. It is defined as: : \mathrm = \frac = \frac \sim \frac Where * ''μ'' is the dynamic viscosity of the liquid * ''ρ'' is the density of the liquid * ''σ'' is the surface tension * ''L'' is the characteristic length scale (typically drop diameter) * Re is the
Reynolds number In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ...
* We is the
Weber number The Weber number (We) is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It is named ...


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. English translation: In
inkjet printing Inkjet printing is a type of computer printing that recreates a digital image by propelling droplets of ink onto paper or plastic substrates. Inkjet printers were the most commonly used type of printer in 2008, and range from small inexpensi ...
, liquids whose Ohnesorge number are in the range 0.1 < ''Oh'' < 1.0 are jettable (1


See also

*
Laplace number The Laplace number (), also known as the Suratman number (), is a dimensionless number used in the characterization of free surface fluid dynamics. It represents a ratio of surface tension to the momentum-transport (especially dissipation) inside ...
- There is an inverse relationship, \mathrm = 1/\sqrt, between the
Laplace number The Laplace number (), also known as the Suratman number (), is a dimensionless number used in the characterization of free surface fluid dynamics. It represents a ratio of surface tension to the momentum-transport (especially dissipation) inside ...
and the Ohnesorge number. It is more historically correct to use the Ohnesorge number, but often mathematically neater to use the
Laplace number The Laplace number (), also known as the Suratman number (), is a dimensionless number used in the characterization of free surface fluid dynamics. It represents a ratio of surface tension to the momentum-transport (especially dissipation) inside ...
.


References

Dimensionless numbers of fluid mechanics Fluid dynamics {{fluiddynamics-stub