# Archimedes Number

on . Posted in Dimensionless Numbers

The Archimedes number, abbreviated as Ar, a dimensionless number, also called the Ar number or Archemedes' criterion, used in fluid dynamics to characterize the behavior of fluid flows around objects or in systems involving buoyancy.  It analyzes flow as it relates to a system of density differences.  It is used when dealing with gravitational settling of particles in fluid.

The Archimedes number is used primarily in the study of buoyancy driven flows, such as those involving the rise or fall of bubbles, the motion of particles in a fluid, or the behavior of fluids in tanks or pipes.  It helps determine the relative importance of buoyancy forces compared to viscous forces in a given system.  A high Archimedes number indicates that buoyancy forces dominate, while a low Archimedes number suggests that viscous forces are more significant.

## Archimedes Number formula

$$\large{ Ar = \frac{ g \; l^3 \; \rho_f \; \left( \rho_b \;-\; \rho _f \right)}{\mu^2} }$$
Symbol English Metric
$$\large{ Ar }$$ = Archimedes number $$\large{dimensionless}$$
$$\large{ g }$$ = gravitational acceleration  $$\large{\frac{ft}{sec^2}}$$   $$\large{\frac{m}{s^2}}$$
$$\large{ l }$$ = length $$\large{ft}$$ $$\large{m}$$
$$\large{ \rho_f }$$ = density of fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ \rho_b }$$ = density of the body flowing through the fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ \mu }$$ = dynamic viscosity of fluid $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$ Tags: Gravity