Archimedes Number

Archimedes number, abbreviated as Ar, a dimensionless number, analyzes flow as it relates to a system of density differences.  It is used when dealing with gravitational settling of particles in fluid.

 

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	\(\large{dimensionless}\)
\(\large{ \rho_f }\) = 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	\(\large{\frac{lbf-sec}{ft^2}}\)	\(\large{ Pa-s }\)
\(\large{ g }\) = gravitational acceleration	\(\large{\frac{ft}{sec^2}}\)	\(\large{\frac{m}{s^2}}\)
\(\large{ l }\) = length	\(\large{in}\)	\(\large{mm}\)