Sediment Transport Rate Calculator
Free Sediment transport rate Calculator for hydrology & water resources. Enter variables to compute results with formulas and detailed steps.
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Adjust values & calculateFormula
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.
Last reviewed: December 2025
Worked Examples
Example 1: Gravel-Bed River Transport
Example 2: Sand-Bed Stream
Background & Theory
The Sediment Transport Rate Calculator applies the following established principles and formulas. Earth science calculators draw on a wide range of measurement scales and physical principles that quantify natural phenomena across geological, atmospheric, and hydrological systems. Earthquake magnitude is most precisely described by the Moment Magnitude Scale (Mw), which replaced the original Richter scale for larger events. Mw is calculated as Mw = (2/3) log10(M0) − 10.7, where M0 is the seismic moment in dyne-centimeters. The Richter scale, while still referenced colloquially, is a local magnitude (ML) measurement derived from peak seismograph amplitude at a standard 100 km distance. Wind intensity is classified using the Beaufort Scale, a 13-point empirical scale (0–12) relating wind speed in knots to observable sea and land effects, with Beaufort 12 corresponding to hurricane-force winds above 64 knots. Tropical cyclone intensity is further categorized by the Saffir-Simpson Hurricane Wind Scale, which assigns Categories 1 through 5 based on sustained wind speed, correlating with expected structural damage. Mineral hardness is quantified on the Mohs scale (1–10), comparing scratch resistance relative to reference minerals from talc (1) to diamond (10). Soil composition analysis measures the proportions of sand, silt, and clay by particle size, alongside organic matter content, bulk density, and porosity, which together determine engineering and agricultural suitability. Seismic wave velocity in rock varies by material: P-waves travel at approximately 5–7 km/s in granite and 1.5 km/s in water, while S-waves travel at roughly 60% of P-wave speeds. Atmospheric pressure decreases with altitude according to the barometric formula: P = P0 × exp(−Mgh / RT), where M is molar mass of air, g is gravitational acceleration, h is altitude, R is the universal gas constant, and T is temperature in Kelvin. Standard sea-level pressure is 101,325 Pa. Tidal calculations use harmonic analysis of gravitational forcing by the Moon and Sun, with the principal lunar semidiurnal tidal constituent (M2) having a period of approximately 12.42 hours.
History
The history behind the Sediment Transport Rate Calculator traces back through the following developments. The systematic study of Earth's structure and processes spans millennia, but the scientific foundations were laid in the seventeenth century. In 1669, Danish naturalist Nicolas Steno published his principles of stratigraphy, establishing the laws of superposition, original horizontality, and lateral continuity — foundational rules for reading rock layers that remain in use today. Scottish geologist James Hutton introduced the concept of uniformitarianism in 1788, proposing that geological processes observable in the present have operated throughout Earth's history at broadly consistent rates. This idea of deep time challenged prevailing biblical chronologies and set the stage for modern geology. Charles Lyell systematized these ideas in his landmark three-volume work Principles of Geology, published beginning in 1830, which directly influenced Charles Darwin's thinking on biological evolution during the voyage of the Beagle. The nineteenth century saw growing curiosity about continental shapes, but a coherent theory awaited Alfred Wegener, a German meteorologist who proposed continental drift in 1912, arguing that the continents had once formed a supercontinent he called Pangaea. His evidence included matching fossil records and geological formations across the Atlantic, but his mechanism was disputed for decades. The theory gained acceptance in the 1960s when seafloor spreading was confirmed through paleomagnetic studies, and plate tectonics emerged as the unifying framework of modern geoscience. The United States Geological Survey was established by Congress in 1879 to classify public lands and examine the geological structure, mineral resources, and products of the national domain. The twentieth century brought instrumental advances, including the global seismograph network deployed after World War II, initially to monitor nuclear tests, which dramatically improved earthquake detection and characterization. Satellite Earth observation began in earnest with the Landsat program launched in 1972, enabling continuous global monitoring of land use, glacier retreat, and vegetation patterns. Today, GPS networks, LIDAR scanning, and ocean-floor mapping provide centimeter-scale precision for tracking tectonic motion, sea level rise, and volcanic deformation in near real time.
Frequently Asked Questions
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy