Bagnold Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

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

\(\large{ Ba = \frac{ \rho \; d^2 \; \lambda^{\frac{1}{2}} \; \dot {\gamma} }{ \mu }  }\) 

Where:

 Units 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 \(\large{\frac{lbf}{in^2}}\) \(\large{ Pa }\)

 

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