Source file: manning_calculator.html
Given a target discharge, sizes a trapezoidal open channel (bed width and flow depth) that carries that discharge at a specified slope and roughness, then reports the resulting geometry and hydraulic properties.
Manning's Equation for uniform open-channel flow:
Q = (k / n) × A × R^(2/3) × S^(1/2)
Where:
- Q — discharge (m³/s or cfs)
- n — Manning's roughness coefficient
- A — flow cross-sectional area
- R — hydraulic radius = A / P
- S — bed (energy) slope
- k — unit conversion constant: 1.0 for SI (metric), 1.486 for US Customary units
For a trapezoidal channel with bed width b, side slope z (horizontal : vertical), and flow depth y:
A = (b + z·y) × yP = b + 2y√(1 + z²)R = A / PT_w = b + 2zyT_b = b + 2z(y + F_b), where F_b is freeboardD = y + F_b| Input | Symbol | Notes |
|---|---|---|
| Unit system | — | Metric (m, m³/s) or US Customary (ft, cfs) |
| Target discharge | Q |
Design flow the channel must convey |
| Manning's roughness | n |
Typical range 0.010–0.035 depending on lining |
| Bed slope | S |
Longitudinal channel slope |
| Side slope | z |
Horizontal run per 1 unit vertical rise |
| Freeboard | F_b |
Additional depth above design water surface for safety margin |
The calculator does not solve directly for a unique (b, y) pair — Manning's equation alone is under-determined (one equation, two unknowns: b and y). It resolves this by adding a second constraint: assume the "most efficient" or near-square channel shape by searching for the combination where bed width ≈ flow depth (b ≈ y).
Algorithm:
1. Loop candidate depths y from 0.05 up to 20 (step 0.01).
2. For each y, use bisection search (25 iterations, b bounded between 0.01 and 100) to find the bed width b that makes the computed discharge Q_calc match the targetQ.
3. Track the (b, y) pair from all candidate depths where |b − y| is smallest (i.e., closest to a square-ish channel).
4. Report that best-fit geometry as the final design.
This is a heuristic design choice (near-square trapezoidal section), not the industry-standard "most hydraulically efficient section" formula, but it produces a single practical geometry rather than an infinite family of solutions.
b), water depth (y)T_w) and at bank level (T_b)D)P), area (A), hydraulic radius (R)Q_act) — should closely match the target QThis page can receive a discharge value from the Rational Method calculator via URL parameters (?q=...&units=metric), auto-populating the target discharge field and unit system on load.