What This Solves
Calculates flow in compound channels with a main channel and one or two floodplain sections using the divided channel method.
Best Used When
- You are analyzing a natural stream with distinct main channel and overbank floodplain areas
- You need to calculate the total conveyance and velocity distribution in a compound cross-section
- You want to determine when flow begins to overtop the main channel banks into the floodplain
Do NOT Use When
- The channel has a simple cross-section without floodplains — Use Manning's Channel Calculator
- You need to compute the full water surface profile through a varying reach — Use Gradually Varied Flow Calculator
Key Assumptions
- The divided channel method (Chow) is used with separate conveyance calculations for each subsection
- Each subsection has its own roughness coefficient and geometry
- Shear stress at the interface between subsections is neglected
- The channel is prismatic along the reach being analyzed
- Water surface elevation is the same across all subsections at a given cross-section
Input Quality Notes
Roughness values for floodplain areas are highly variable and depend on vegetation, debris, and land use. Field reconnaissance is essential for selecting appropriate n values for overbank areas.
Analyze flow in a compound (two-stage) channel — a main channel with overbank floodplains or berms — using the divided channel method. Enter the area, wetted perimeter, top width and Manning’s n for each subsection to get total discharge, weighted velocity, composite roughness and the energy and momentum correction coefficients.
Division Method Reference
| Method | Description | Best Used For |
|---|---|---|
| Vertical | Vertical lines from water surface to channel bottom | Most common; main channel with floodplains |
| Horizontal | Horizontal line at bankfull elevation | Well-defined banks with distinct floodplain |
| Bisector | Bisector of angle between water surface and slope | Channels with gradual bank transitions |
Ready to Calculate
Enter subsection parameters and click Calculate to analyze compound channel flow.
For educational purposes only. Not a substitute for professional engineering judgment.
How it works
A compound channel carries water in a deep main channel and one or more shallow overbanks that usually have higher roughness and lower velocity. Treating it as one uniform section would misrepresent the flow, so the divided channel method (Chow, 1959, Chapter 7) splits the cross-section into subsections of roughly uniform roughness using vertical interfaces that are assumed to be frictionless.
For each subsection, the conveyance is computed from Manning’s equation:
Ki = (k / ni) · Ai · Ri2/3 and Qtotal = (Σ Ki) · √S
The supporting composite and distribution relationships are:
- Hydraulic radius: Ri = Ai / Pi; composite Rc = Atotal / Ptotal
- Composite roughness (Horton): nc = [Σ(Pi · ni1.5) / Ptotal]2/3
- Weighted velocity: Vavg = Qtotal / Atotal
- Froude number: Fr = Vavg / √(g · Dh), with hydraulic depth Dh = Atotal / Ttotal
- Energy / momentum coefficients: α = Σ(Vi3Ai) / (Vavg3Atotal); β = Σ(Vi2Ai) / (Vavg2Atotal)
The conveyance constant k = 1.486 for US customary units (cfs, ft) and k = 1.0 for SI units (cms, m). Gravity g is 32.174 ft/s² (US) or 9.81 m/s² (SI). Flow is classified subcritical (Fr < 1), critical (Fr ≈ 1) or supercritical (Fr > 1).
Variables
| Symbol | Meaning | Units (US / SI) |
|---|---|---|
| Q | Discharge (subsection or total) | cfs / cms |
| K | Conveyance | cfs / cms |
| A | Flow area | ft² / m² |
| P | Wetted perimeter | ft / m |
| R | Hydraulic radius (A / P) | ft / m |
| T | Top width | ft / m |
| n | Manning’s roughness coefficient | dimensionless |
| S | Longitudinal channel (energy) slope | ft/ft / m/m |
| Fr | Froude number | dimensionless |
Typical Manning’s n by subsection
Representative roughness values for the main channel and overbank subsections of a compound section. Use the lower values for clean, lined main channels and the higher values for vegetated or wooded floodplains. Values follow Chow (1959) and FHWA HEC-22.
| Surface / subsection | Manning’s n | Typical location |
|---|---|---|
| Earth channel, clean | 0.025 | Main channel |
| Earth channel with weeds | 0.030 | Main channel |
| Natural channel | 0.035 | Main channel |
| Heavy brush | 0.050 | Overbank / berm |
| Floodplain with trees | 0.060 | Overbank |
| Dense floodplain vegetation | 0.100 | Overbank |
Roughness on a vegetated floodplain varies with flow depth and season; bracket your estimate with a sensitivity check rather than relying on a single n value.
Composite roughness methods
Several published formulas combine subsection roughness into a single equivalent Manning’s n. This calculator reports the composite n using Horton’s method; the alternatives below differ in their underlying velocity or shear assumptions.
| Method | Formula | Key assumption |
|---|---|---|
| Horton (1933) | nc = [Σ(Pi ni1.5) / P]2/3 | Equal velocity in all subsections |
| Einstein–Banks (1950) | nc = [Σ(Pi ni2) / P]1/2 | Equal velocity; total force = sum of subsection forces |
| Lotter (1933) | nc = P R5/3 / Σ(Pi Ri5/3 / ni) | Total discharge = sum of subsection discharges |
| Cox (1973) | nc = [Σ(Pi ni1.5) / P]2/3 | Equivalent to Horton (perimeter-weighted) |
Assumptions & limitations
Assumptions
- Each subsection has uniform roughness
- Division lines act as frictionless boundaries (no shear transfer)
- Energy slope is constant across all subsections
- Steady, uniform flow conditions
- Manning’s equation is valid for each subsection
Limitations
- Neglects momentum exchange between main channel and overbanks
- May overestimate discharge when velocity differences are large
- Interaction losses at subsection boundaries are ignored
- Not suitable for rapidly varied flow
- Accuracy depends on measured subsection geometry
Frequently asked questions
What is a compound channel?
A compound channel is a cross-section made up of a deeper main channel flanked by one or more shallower overbank areas (floodplains or berms). Because the main channel and the overbanks usually have very different depths and roughness, they carry water at very different velocities, so the section cannot be treated as a single uniform channel. The divided channel method splits the section into subsections of roughly uniform roughness, evaluates each with Manning's equation, and sums the results.
How does the divided channel method calculate total discharge?
Each subsection is given a conveyance K = (k/n) · A · R^(2/3), where k is 1.486 in US units (1.0 in SI), n is Manning's roughness, A is the flow area and R = A/P is the hydraulic radius. The total discharge is the sum of the subsection conveyances multiplied by the square root of the channel slope: Q_total = (ΣK_i)·√S. The vertical division lines are assumed to be frictionless interfaces, so no shear is transferred between subsections.
Why is composite Manning's n needed for a compound channel?
When roughness varies across the section (for example, a smooth main channel with vegetated overbanks), a single equivalent roughness is useful for reporting an overall hydraulic radius and depth. This calculator uses Horton's method, n_c = [Σ(P_i · n_i^1.5) / P_total]^(2/3), which weights each subsection roughness by its wetted perimeter. Horton's method assumes every subsection flows at the same mean velocity.
What are the alpha and beta coefficients used for?
Because velocity is far from uniform across a compound section, the average velocity under- or over-states the true kinetic energy and momentum flux. The energy (Coriolis) coefficient alpha = Σ(V_i^3·A_i)/(V_avg^3·A_total) corrects velocity head in the energy equation and is typically 1.0–2.0 for compound channels. The momentum (Boussinesq) coefficient beta = Σ(V_i^2·A_i)/(V_avg^2·A_total) corrects momentum and is typically 1.0–1.5. Both equal 1.0 only when velocity is uniform.
What are the main limitations of the divided channel method?
The method neglects momentum exchange and interaction losses at the boundary between the fast main channel and the slower overbanks, which can cause it to overestimate total discharge when the velocity difference between subsections is large. It assumes steady, uniform flow with a single constant energy slope and is not valid for rapidly varied flow. Results are only as good as the measured subsection geometry, so confirm field areas, wetted perimeters and roughness before relying on the output.
Standards & related tools
Chow, Open-Channel Hydraulics (1959)
Chapter 7 — divided channel method and composite roughness for compound sections.
Manning’s Channel Calculator
Single-section open channel flow for simple trapezoidal and rectangular channels.
Manning’s n Reference
Roughness coefficients for natural channels, linings and floodplain cover.
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Last verified: February 2026