Archimedes Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

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

\(\large{ Ar = \frac{ g \; l^3 \; \rho_f \; \left( \rho_b \;-\; \rho _f \right)}{\mu^2}  }\)  

Where:

 Units 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 \(\large{in}\) \(\large{mm}\)

 

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Tags: Gravity Equations