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Van Rijn Bedload Saltation Sediment Transport Calculator

Calculate unit bedload sediment transport rates, dimensionless grain sizes, critical Shields thresholds, and transport stage parameters using Van Rijn (1984).

Median sand particle diameter (d50).

Average water depth of the alluvial channel.

Cross-sectional average stream flow velocity.

Calculated Result
0.1977 kg/(m·s)

Unit Mass Bedload Rate

Daily Transport per Unit Width

17.08 tonnes/(m·day)

Transport Stage Parameter (T)

6.373

Dimensionless Grain Size (D*)

16.4

Actual Shear Velocity (u*)

0.0484 m/s

Calculation Breakdown

  1. Dimensionless Grain Parameter (D*)D* = d50 · [(s - 1)·g / ν²]^(1/3) => 16.4
  2. Critical Shields & Shear Velocityθ_cr = 0.0302; u*_cr = √(θ_cr·(s-1)·g·d50) => 0.0178 m/s
  3. Transport Stage Parameter (T)T = (u* / u*_cr)² - 1 => 6.373
  4. Van Rijn Bedload Transport Rate (qb)qb = 0.053 · √((s-1)·g·d50³) · D*^(-0.3) · T^(2.1) => 0.1977 kg/(m·s)

Sediment Transport Metrics

Interactive visualization based on your current inputs

Value
0.04.18.21216Grain D*Transport Stage TTransport (kg/m·s ×100)Daily (tonne/m·day)ParameterValue

What Is the Van Rijn Bedload Saltation Sediment Transport Calculator?

Calculate unit bedload sediment transport rates, dimensionless grain sizes, critical Shields thresholds, and transport stage parameters using Van Rijn (1984).

The Van Rijn Bedload Saltation Sediment Transport Calculator is an analytical tool in the construction domain designed to evaluate Median Grain Diameter (d50), Mean Flow Depth (h), Mean Flow Velocity (ū) using verified mathematical equations. It provides reproducible, deterministic calculations for academic, professional, and practical applications.

How Does the Van Rijn Bedload Saltation Sediment Transport Calculator Work?

This calculator computes results by taking input values for Median Grain Diameter (d50), Mean Flow Depth (h), Mean Flow Velocity (ū) and applying the governing equation: Transport stage parameter T captures excess effective skin friction over critical entrainment threshold, driving non-linear bedload saltation.. Values are checked for dimensional consistency and processed through standard arithmetic routines.

Van Rijn Bedload Saltation Sediment Transport Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

D∗=d50[(s−1)gν2]1/3,T=(u∗′)2−(u∗,cr)2(u∗,cr)2,qb=0.053(s−1)gd503D∗−0.3T2.1D_* = d_{50} \left[\frac{(s-1)g}{\nu^2}\right]^{1/3}, \quad T = \frac{(u_*^\prime)^2 - (u_{*,cr})^2}{(u_{*,cr})^2}, \quad q_b = 0.053 \sqrt{(s-1)g d_{50}^3} D_*^{-0.3} T^{2.1}

Transport stage parameter T captures excess effective skin friction over critical entrainment threshold, driving non-linear bedload saltation.

How to Use the Van Rijn Bedload Saltation Sediment Transport Calculator

  1. Enter your value for Median Grain Diameter (d50) in mm.
  2. Enter your value for Mean Flow Depth (h) in m.
  3. Enter your value for Mean Flow Velocity (ū) in m/s.
  4. Verify your input parameters to ensure they match your design or problem specifications.
  5. Review the calculated results, intermediate mathematical steps, and graphical visualization below.

Step-by-Step Example Calculation

Meandering Sand River Channel

Input Values:

medianGrainDiameterMm:0.65
waterDepthM:2.2
meanFlowVelocityMps:1.15
Worked Steps: With D* = 16.4 and critical shear velocity 0.019 m/s, transport stage parameter T = 3.65 yields a bedload transport rate of 0.086 kg/(m·s) or 7.43 tonnes/(m·day).

Understanding Your Result

The calculated output gives the primary solution for Van Rijn Bedload Saltation Sediment Transport under the specified conditions. Use this value to compare against standard design tolerances, benchmarks, or reference ranges in construction.

Factors That Affect the Result

  • Input precision and measurement accuracy of Median Grain Diameter (d50), Mean Flow Depth (h), Mean Flow Velocity (ū).
  • Operating conditions, environmental parameters, and specific construction tolerances.
  • Boundary constraints and deviations from nominal theoretical model assumptions.

When Should You Use This Calculator?

  • When performing technical analysis or dimensioning related to Van Rijn Bedload Saltation Sediment Transport.
  • To cross-verify manual calculations or theoretical models in construction.
  • For preliminary estimates before conducting detailed field measurements or laboratory testing.

Assumptions & Limitations

  • Van Rijn bedload applies to grain sizes from 0.1 mm to 2.0 mm (fine to coarse sands).
  • Grain-related shear velocity u*’ excludes form drag from sand dunes and ripples, focusing purely on skin friction driving bedload.

Frequently Asked Questions

Why does Van Rijn separate bedload from suspended sediment load?+
Bedload moves in continuous contact with or bouncing along the bed within a thin saltation layer (~few grain diameters), governed by gravity and grain friction, while suspended load is diffused throughout the water column by turbulence.
How does water temperature affect bedload transport?+
Warmer water has lower kinematic viscosity ν, increasing the dimensionless particle parameter D* and slightly modifying the critical Shields threshold.

Calculation Accuracy & Reference Note

This calculator implements verified mathematical formulas for Van Rijn Bedload Saltation Sediment Transport Calculator. Always verify critical results against official domain standards and manufacturer documentation.

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