# Archimedes number

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]:

${\displaystyle \mathrm {Ar} ={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}}$

where:

• ${\displaystyle g}$ is the local external field (for example gravitational acceleration), m/s2,
• ${\displaystyle \rho _{\ell }}$ is the density of the fluid, kg/m3,
• ${\displaystyle \rho }$ is the density of the body, kg/m3,
• ${\displaystyle \mu }$ is the dynamic viscosity, kg/ms,
• ${\displaystyle L}$ is the characteristic length of body, m.

## 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.