Archimedes number

Archimedes' number is named after the Greek Archimedes.

In viscous fluid dynamics, the Archimedes number (Ar) [1] is used when the motion of fluids is affected by density differences. It is a dimensionless number, the ratio of gravitational forces to viscous forces.[2]

The relationship and has the form:[3]

[math]\displaystyle{ \mathrm{Ar}=\frac{g L^3\rho_\ell(\rho-\rho_\ell)}{\mu^2} }[/math]

where:

  • [math]\displaystyle{ g }[/math] is the local external field (for example gravitational acceleration), [math]\displaystyle{ m/s^2 }[/math],
  • [math]\displaystyle{ \rho_\ell }[/math] is the density of the fluid, [math]\displaystyle{ kg/m^3 }[/math],
  • [math]\displaystyle{ \rho }[/math] is the density of the body, [math]\displaystyle{ kg/m^3 }[/math],
  • [math]\displaystyle{ \mu }[/math] is the dynamic viscosity, [math]\displaystyle{ kg/ms }[/math],
  • [math]\displaystyle{ L }[/math] is the characteristic length of body, [math]\displaystyle{ m }[/math].

References

  1. Do not confuse it with Archimedes' constant, π)
  2. Wypych, George (2014). Handbook of Solvents, Volume 2 - Use, Health, and Environment (2nd ed.). ChemTec Publishing. p. 657.
  3. Harnby, N; Edwards, MF; Nienow, AW (1992). Mixing in the Process Industries (2nd ed.). Elsevier. p. 64.