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Van Rijn Bedload Saltation Sediment Transport Calculator

Van Rijn’s 1984 bedload formulation describes the rolling, sliding, and saltating motion of river sand and gravel particles close to the alluvial bed.

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?

Van Rijn’s 1984 bedload formulation describes the rolling, sliding, and saltating motion of river sand and gravel particles close to the alluvial bed.

Unlike classic excess shear stress models, Van Rijn introduces a dimensionless grain parameter D* and a transport stage parameter T that accounts for grain-related skin friction.

This tool computes volumetric and mass sediment transport rates per unit channel width in kg/(m·s) and daily transport in tonnes/(m·day).

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

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Van Rijn Bedload Saltation Sediment Transport Calculator Formula & Variables

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

D_* = 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 primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

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

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

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

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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