Sediment Transport & Shear Stress

Source file: sediment_transport.html

Purpose

Evaluates the boundary (bed) shear stress in a channel and compares it against an allowable/critical shear stress threshold to assess channel bed and bank stability against scour and erosion — a tractive force (permissible shear stress) design check.

Governing Equation

τ₀ = γ × R × S

Where: - τ₀ — boundary (mean) shear stress at the channel bed (N/m²) - γ — unit weight of water = 9810 N/m³ (fixed constant) - R — hydraulic radius of the channel section (m) - S — energy slope (approximated by the bed slope for uniform/gradually varied flow)

Inputs

Input	Symbol	Notes
Hydraulic radius	`R`	m — from the channel's cross-sectional area and wetted perimeter
Energy slope	`S`	dimensionless (m/m)
Allowable bed shear stress	`τ_c`	N/m² — the critical/permissible shear stress for the channel lining or bed material (from tractive force tables, e.g., for a given soil, riprap size, or vegetation cover)

Solution Method

Direct (non-iterative) calculation: 1. Compute τ₀ = γ × R × S. 2. Compare τ₀ to the user-supplied allowable limit τ_c: - If τ₀ ≤ τ_c → Stable (No Scour Risk) - If τ₀ > τ_c → Unstable (Scour/Erosion Expected)

Outputs

Calculated boundary shear stress (τ₀, N/m²)
Erosion risk status (Stable / Unstable)

Notes & Limitations

This tool computes the average boundary shear stress across the whole wetted perimeter; actual local shear stress on the channel bed versus side slopes differs (bed shear is typically higher than side-slope shear for trapezoidal channels — some design guides apply correction factors, e.g., ~0.97–1.0 for bed and ~0.75–0.78 for sides, which are not applied here).
R and S must be supplied by the user (typically obtained from a Manning's/GVF channel analysis) — this calculator does not derive them from channel geometry itself.
The allowable shear stress τ_c must be selected externally from tractive-force/permissible-velocity tables appropriate to the bed/lining material; it is not looked up automatically.