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). 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 Interpretation
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Low Bagnold Number (Ba << 1) - Viscous forces dominate over inertial forces. This typically occurs in slow-moving, highly viscous flows or with very small particles. Sediment transport might be limited or occur via creep or suspension rather than saltation (bouncing motion).
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High Bagnold Number (Ba >> 1): - Inertial forces dominate over viscous forces. This is common in fast-moving flows (strong winds or turbulent water) with larger grains. Saltation or bedload transport (rolling/sliding of grains along the surface) becomes significant.
Bagnold Number formula |
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\( Ba \;=\; \dfrac{ \rho \cdot d \cdot v^2 }{ \mu }\) (Bagnold Number) \( \rho \;=\; \dfrac{ Ba \cdot \mu }{ d \cdot v^2 }\) \( d \;=\; \dfrac{ Ba \cdot \mu }{ \rho \cdot v^2 }\) \( v \;=\; \sqrt{ \dfrac{ Ba \cdot \mu }{ \rho \cdot d } }\) \( \mu \;=\; \dfrac{ \rho \cdot d \cdot v^2 }{ Ba }\) |
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| Symbol | English | Metric |
| \( Ba \) = Bagnold Number | \(dimensionless\) | \(dimensionless\) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( d \) = Characteristic Grain Size | \(in\) | \(mm\) |
| \( v \) = Flow Velocity (Often the Shear Velocity in Sediment Transport ) | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( \mu \) (Greek symbol mu) = Fluid Dynamic Viscosity | \(lbf-sec\;/\;ft^2\) | \(Pa-s \) |
