Bagnold number
The 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. The Bagnold number is defined by B a = ρ d 2 λ 1 / 2 γ ˙ μ {\displaystyle \mathrm {Ba} ={\frac {\rho d^{2}\lambda ^{1/2}{\dot {\gamma }}}{\mu }}} , where ρ {\displaystyle \rho } is the particle density, d {\displaystyle d} is the grain diameter, γ ˙ {\displaystyle {\dot {\gamma }}} is the shear rate and μ {\displaystyle \mu } is the dynamic viscosity of the interstitial fluid.