Uncare number

Physical key figure
Surname	Uncare number
Formula symbol	${\displaystyle {\mathit {Oh}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Oh}}={\frac {\eta }{\sqrt {L\rho \sigma }}}}$
${\displaystyle \eta }$ dynamic viscosity ${\displaystyle L}$ characteristic length ${\displaystyle \rho }$ density ${\displaystyle \sigma }$ Surface tension
Named after	Wolfgang von Unesorge
scope of application	Fluid atomization

The Ohnesorge number (after Wolfgang von Ohnesorge , who introduced it in his dissertation in 1935; symbol :) is a dimensionless number in physics . It describes the influence of toughness on the deformation of drops and bubbles : ${\displaystyle {\mathit {Oh}}}$

${\displaystyle {\mathit {Oh}}={\frac {\text{Reibungskraft}}{\sqrt {{\text{Trägheitskraft}}\cdot {\text{Oberflächenkraft}}}}}={\frac {\eta }{\sqrt {L\cdot \rho \cdot \sigma }}}={\frac {\sqrt {\mathit {We}}}{\mathit {Re}}}={\frac {1}{\sqrt {\mathit {Su}}}}}$

With

• ${\displaystyle \eta }$dynamic viscosity (in SI units Pa s ) (causes friction force ) ${\displaystyle \cdot }$
• ${\displaystyle L}$ characteristic length (e.g. bubble diameter ) (in SI units, m)
• ${\displaystyle \sigma }$ Surface tension (in SI units N / m)
• ${\displaystyle \rho }$ Density of the liquid of the drop (in SI units kg / m ³ )
• ${\displaystyle {\mathit {We}}}$ Weber number (records the two most important forces that act on a falling drop: inertia and surface force)
• ${\displaystyle {\mathit {Re}}}$ Reynolds number
• ${\displaystyle {\mathit {Su}}}$ Suratman number .

There are basically six forces acting on a falling drop:

• Inertia of liquid and gas
• Viscosity of liquid and gas
• Gravity and surface force of the liquid.

The ratio of the no-worries number to the Reynolds number is important in the characterization of fluid atomization , a field of process engineering . For this purpose, the non-care number is plotted against the Reynolds number in the double logarithmic non-care diagram, so that the states "dropping", "waving" and "atomizing" can be differentiated (see liquid jet ).

Web links

• Gareth H. McKinley, Michael Renardy: by Wolfgang von Ohnesorge, 2011 (pdf) (with explanations on the number of Ohnesorge)