Archimedes number

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The 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]


  • is the local external field (for example gravitational acceleration), m/s2,
  • is the density of the fluid, kg/m3,
  • is the density of the body, kg/m3,
  • is the dynamic viscosity, kg/ms,
  • is the characteristic length of body, m.

References[change | change source]

  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.