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].