Bagnold Number

on . Posted in Dimensionless Numbers

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

\( Ba \;=\;  \tau \; D \;/\; \rho \; g \; d^2 \) 
Symbol English Metric
\( Ba \) = Bagnold number \(dimensionless\)
\( \tau \)  (Greek symbol tau) = shear stress  \(lbf\;/\;in^2\) \(Pa\)
\( D \) = characteristic grain size \(in\) \(mm\)
\( \rho \)  (Greek symbol rho) = density of granular material \(lbm\;/\;ft^3\) \(kg\;/\;m^3\)
\( g \) = gravitational acceleration  \(ft\;/\;sec^2\) \(m\;/\;s^2\)
\( \mu \)  (Greek symbol mu) = depth of the flowing granular material \(ft\) \( m \)


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Tags: Liquid Open Channel