Bagnold Number

Bagnold number, abbreviated as Ba, a dimensionless number, is used in the field of sediment transport and geomorphology to characterize the relative importance of bedload transport (particles rolling, sliding, or saltating along the bed of a river or channel) compared to suspended sediment transport (particles carried within the water column). 

Bagnold number Interpretation

• When Ba < 1  -  Suspended sediment transport dominates, and particles are mostly carried within the water column.
• When Ba > 1  -  Bedload transport dominates, and particles are primarily moved along the bed by rolling, sliding, or saltation.

The Bagnold number is particularly useful in understanding the dynamics of sediment transport in fluvial and coastal environments, as well as in the study of sediment deposition, erosion, and the formation of various landforms, including sand dunes, river beds, and river deltas.

 

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 the particle	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ d }\) = diameter of the grain	\(\large{in}\)	\(\large{mm}\)
\(\large{ \lambda }\)  (Greek symbol lambda) = linear concentration	\(\large{dimensionless}\)
\(\large{ \dot {\gamma} }\)   (Greek symbol gamma) = shear rate	\(\large{\frac{lbf}{in^2}}\)	\(\large{ Pa }\)
\(\large{ \mu }\)  (Greek symbol mu) = dynamic viscosity of the interstitial fluid	\(\large{\frac{lbf-sec}{ft^2}}\)	\(\large{ Pa-s }\)