Cauchy number

The Cauchy number (after Augustin Louis Cauchy ) is one of the dimensionless key figures in physics . It gives the ratio of the inertial forces to the elastic forces in solid bodies : ${\displaystyle \mathrm {Ca} }$

${\displaystyle \mathrm {Ca} ={\frac {F_{traeg}}{F_{el}}}={\frac {\rho \cdot (\omega \,l)^{2}}{E}}}$

in which

• ${\displaystyle \rho }$the density ,
• ${\displaystyle \omega }$the angular frequency ,
• ${\displaystyle l}$the characteristic length and
• ${\displaystyle E}$mean the modulus of elasticity .

The Cauchy number is used in the investigation of elastic oscillation processes . It is also used in the similarity theory : two processes that take place mainly under inertia and elastic forces are mechanically similar if their Cauchy numbers match.

See also

• Mach number , the dimensionless number of speed, which indicates the ratio of inertial forces to compression forces.