Sediment Transport Rate Calculator
Free Sediment transport rate Calculator for hydrology & water resources. Enter variables to compute results with formulas and detailed steps.
Formula
tau = rho*g*d*S; theta = tau/((rho_s-rho_w)*g*D); qb = 8*(theta-theta_c)^1.5*sqrt((s-1)*g*D^3)
Where tau is bed shear stress, rho is water density, g is gravity, d is flow depth, S is slope, theta is Shields parameter, D is grain diameter, and qb is bedload transport rate per unit width.
Worked Examples
Example 1: Gravel-Bed River Transport
Problem: A 15 m wide river with velocity 1.5 m/s, depth 2.0 m, slope 0.002, and median grain size 10 mm.
Solution: tau = 1000 x 9.81 x 2.0 x 0.002 = 39.24 Pa\ntau_c = 0.047 x 1650 x 9.81 x 0.01 = 7.61 Pa\ntheta = 39.24 / (1650 x 9.81 x 0.01) = 0.2424\nphi = 8 x (0.2424 - 0.047)^1.5 = 0.5285
Result: Shear: 39.24 Pa | Shields: 0.2424 | Active Transport
Example 2: Sand-Bed Stream
Problem: A 10 m wide stream with velocity 0.8 m/s, depth 1.0 m, slope 0.001, grain size 1 mm.
Solution: tau = 1000 x 9.81 x 1.0 x 0.001 = 9.81 Pa\ntheta = 9.81 / (1650 x 9.81 x 0.001) = 0.606\ntheta >> theta_c: active transport
Result: Active Transport | Shields: 0.606 | Shear: 9.81 Pa
Frequently Asked Questions
What is sediment transport rate and why is it important?
Sediment transport rate quantifies the mass or volume of sediment particles moved by flowing water per unit time, typically in kg/s or tonnes/day. It is fundamental in fluvial geomorphology because it determines river erosion rates, delta building, reservoir filling, and landscape reshaping. Understanding transport rates is essential for designing stable channels, predicting reservoir lifespans, and managing downstream ecology. Engineers need accurate estimates for bridge scour, river restoration, and dredging operations.
What is the Shields parameter and how does it predict sediment motion?
The Shields parameter is a dimensionless ratio of fluid force on a sediment grain to gravitational resistance, defined as theta = tau / ((rho_s - rho_w) * g * D). When theta exceeds the critical value of approximately 0.047 for turbulent flow, sediment grains begin to move. Albert Shields determined this critical value empirically in 1936 through flume experiments and it remains one of the most important thresholds in sediment transport mechanics. The actual critical value varies slightly with grain Reynolds number and bed configuration.
How does the Meyer-Peter and Muller formula calculate bedload transport?
The Meyer-Peter and Muller (1948) formula expresses dimensionless bedload transport as phi = 8 * (theta - theta_c)^1.5, where theta is the Shields parameter and theta_c is the critical value for incipient motion. The dimensional rate per unit width is obtained by multiplying phi by sqrt((rho_s/rho_w - 1) * g * D^3). The formula works best for uniform gravel and coarse sand in the 0.4 to 29 mm range, assuming bedload transport dominates over suspended load, which is typical for gravel-bed rivers.
What is the difference between bedload and suspended load transport?
Bedload transport involves particles that roll, slide, or saltate along the channel bed while maintaining frequent contact with the bottom. Suspended load consists of finer particles carried within the water column by turbulent eddies without touching the bed for extended periods. The distinction depends on the ratio of settling velocity to shear velocity. In sand-bed rivers, suspended load often constitutes 90 percent or more of total transport, whereas in gravel-bed rivers, bedload may be the dominant mode.
How does grain size affect sediment transport calculations?
Grain size is the single most important sediment property affecting transport because it determines both the threshold for motion and the transport mode. Larger grains require greater shear stress due to their greater submerged weight. The critical Shields parameter varies with grain diameter through the grain Reynolds number. In natural rivers with mixed sizes, the median diameter D50 is commonly used, but the full distribution affects hiding and exposure effects where small particles sheltered between large ones require more stress than predicted by their individual size.
What role does channel slope play in sediment transport?
Channel slope directly controls the gravitational component driving transport through tau = rho * g * d * S. Steeper channels generate higher shear stresses for the same depth, enabling transport of larger particles and greater quantities. Mountain streams with slopes of 0.01 to 0.10 can transport boulders during floods, while lowland rivers with slopes of 0.0001 to 0.001 primarily transport sand and silt. Slope also influences subcritical versus supercritical flow through the Froude number, affecting bedform development.