# Atwood Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Atwood number, abbreviated as A, a dimensionless number, describes density difference between two adjacent fluids with a common interface.  Atwood number is an important parameter in the study of Rayleigh–Taylor instability and Richtmyer–Meshkov instability.  In Rayleigh–Taylor instability, the penetration distance of heavy fluid bubbles into the light fluid is a function of acceleration time scale.

## ATwood number formula

 $$\large{ A = \frac { \rho_1 \;-\; \rho_2 } { \rho_1 \;+\; \rho_2 } }$$

### Where:

 Units English Metric $$\large{ A }$$ = Atwood number $$\large{ dimensionless }$$ $$\large{ \rho_1 }$$ (Greek symbol rho) = density of heavier fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ \rho_2 }$$ (Greek symbol rho) = density of lighter fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$