U-Channel Hydraulics
Non-full flow in a U-shaped channel with a curved circular bottom and straight trapezoid walls. Central angle θ = 180° − 2α; straight-wall depth H2 = H − (r − r·cos θ/2).
| No. | Bottom radius r | Side angle α (°) | Water depth H (m) | Slope i | Roughness n | Straight depth H2 (m) | Central θ (°) | Chord (m) | Area A (m²) | Wetted X (m) | Radius R (m) | v (m/s) | Flow Q (m³/s) |
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Max velocity
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m/s
Total discharge ΣQ
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m³/s
Max hydraulic radius
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m
For H2 > 0: area A = r²/2·[π·(1−α/90) − sin 2α] + H2·(2r·cos α + H2·tan α), wet perimeter X = π·r·(1−α/90) + 2·H2/cos α. For H2 ≤ 0 (arc only): A = r²·acos((r−H)/r) − (r−H)·r·sin(acos((r−H)/r)), X = 2r·acos((r−H)/r). Manning velocity v = (A/X)^(2/3)·√i/n, discharge Q = A·v. Units: r, H in m, i as a fraction (e.g. 1/2000).