Archimedes Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Archimedes Number

Archimedes number ( \(Ar\) ) (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

\(Ar = \frac { g    l^3   \rho_f \left( \rho_b \;-\; \rho _f \right)}    {\mu^2} \)          \( Archimedes number  \;=\;  \frac { gravitational \; acceleration \;\;x\;\;   length^3  \;\;x\;\;  fluid \; density  \;  \left( \; density \; of \; body  \;-\; fluid \; density \;  \right)}    { dynamic \; viscosity^2} \)

Where:

\(Ar\) = Archimedes number

\(g\) = gravitational acceleration 

\(l\) = length

\(\rho_f\) = fluid density

\(\rho_b\) = density of the body flowing through the fluid

\(\mu\) = dynamic viscosity of the fluid

 

Tags: Equations for Gravity