Bagnold Number

Bagnold number, abbreviated as Ba, a dimensionless number, is the ratio of grain collision stresses to various fluid stresses in a granular flow with interstitial Newtonian fluid.

 

Bagnold Number formula
\(\large{ Ba = \frac{ \rho \; d^2 \; \lambda^{\frac{1}{2}} \; \dot {\gamma} }{ \mu }  }\)
Symbol	English	Metric
\(\large{ Ba }\) = Bagnold number	\(\large{dimensionless}\)
\(\large{ \rho }\)   (Greek symbol rho) = density of particle	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ d }\) = diameter of grain	\(\large{in}\)	\(\large{mm}\)
\(\large{ \mu }\)  (Greek symbol mu) = dynamic viscosity	\(\large{\frac{lbf-sec}{ft^2}}\)	\(\large{ Pa-s }\)
\(\large{ \lambda }\)  (Greek symbol lambda) = linear concentration	\(\large{dimensionless}\)
\(\large{ \dot {\gamma} }\)   (Greek symbol gamma) = shear rate	\(\large{\frac{lbf}{in^2}}\)	\(\large{ Pa }\)