Sediment Transport Rate Calculator

The Shields parameter (tau-star) is a dimensionless measure of the shear stress exerted by flow relative to the gravitational force on a sediment particle: tau* = tau / ((rho_s - rho_w) x g x d), where tau is bed shear stress, rho_s is sediment density, rho_w is water density, g is gravity, and d is grain diameter. At the critical Shields parameter (approximately 0.047 for sand), sediment begins to move.

The Meyer-Peter and Muller (1948) formula is an empirical bedload transport equation: q_b* = 8 x (tau* - tau*_c)^1.5, where q_b* is dimensionless bedload transport rate, tau* is the Shields parameter, and tau*_c is the critical Shields parameter (approximately 0.047). It is validated for coarse sediment transport (gravel) and is widely used by USGS and in fluvial geomorphology.

Bedload is sediment that moves along the bed by rolling, sliding, or saltating (hopping). Suspended load is sediment carried in suspension in the water column. Bedload transport dominates in coarse-grained rivers (gravel beds); suspended load dominates in fine-grained rivers (sand and silt). Total sediment discharge = bedload + suspended load.

Bed shear stress (tau) is the tangential force per unit area exerted by flowing water on the channel bed. For uniform open-channel flow: tau = rho_w x g x R x S, where R is hydraulic radius (m) and S is energy slope (dimensionless). Shear stress increases with flow velocity, depth, and channel slope.

The Meyer-Peter and Muller equation was derived from flume experiments with coarse sediment (gravel). It should be applied with caution for fine sand, non-uniform sediment mixtures, or bedforms like dunes. For fine sediment and sand-bed rivers, equations such as those of van Rijn (1984) are more appropriate. The USGS provides guidance on sediment transport method selection.