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A flow estimate starts with the boundary.
Manning’s relationship connects channel geometry, hydraulic radius, bed slope, and roughness to an estimated mean velocity. Multiplying mean velocity by flow area gives discharge.
Governing equation
Q = (1/n) A R2/3 S1/2. For a rectangular channel, A = by and R = A/(b + 2y).
Worked example using the starting values
For b = 2 m, y = 0.8 m, S = 0.005 m/m and n = 0.03, A = 1.60 m² and R = 1.60/(2 + 2 × 0.8) = 0.444 m. Manning’s equation gives mean velocity 1.373 m/s and discharge 2.196 m³/s (about 2.20 m³/s). These are uniform-flow estimates for the entered geometry and boundary, not a flood-capacity or freeboard result.
Assumptions and common slips
The calculation assumes a rectangular section and steady uniform flow, with the entered bed slope used as the energy slope. Roughness n must represent the actual channel condition. A frequent unit error is entering 0.5 for a 0.5% slope: use 0.005 m/m; because velocity varies with the square root of slope, the mistaken entry would make the estimate ten times larger.
Keep the water problem wider than Q.
- Check freeboard, overtopping, entrance and exit conditions, structures, bends, and transitions.
- Check whether the selected roughness represents the actual boundary, vegetation, sediment, joints, and maintenance state.
- Consider unsteady, backwater, gradually varied, or rapidly varied flow where the steady-uniform assumption is not appropriate.