Bagnold number


he Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first identified by Ralph Alger Bagnold.
In flows with small Bagnold numbers (Ba < 40), viscous fluid stresses dominate grain collision stresses, and the flow is said to be in the 'macro-viscous’ regime. Grain collision stresses dominate at large Bagnold number (Ba > 450), which is known as the 'grain-inertia’ regime. A transitional regime falls between these two values.

Related formulas


BaBagnold number (dimensionless)
ρParticle density (kg/m3)
dGrain diameter (m)
λLinear concentration (dimensionless)
γShear rate ((1/s))
μDynamic viscosity of the interstitial fluid (kg/(m*s))