Open Channel Flow

Open channels carry water with a free surface: rivers, canals, drains, culverts and sewers. Learn uniform flow (Manning), Froude number, specific energy and critical depth, hydraulic jumps, weirs and channel design.

Most water moves by gravity in open channels — irrigation canals, storm drains, sewers, rivers and spillways. Unlike pipes, the water surface is free, so depth changes with flow and the channel's slope and roughness decide velocity.

Designing a channel means choosing its size, shape, slope and lining so it carries the design flow without overtopping, eroding or depositing sediment.

An analogy

A river is like traffic on a sloping road: steeper and smoother means faster; rougher and flatter means slower and deeper for the same number of cars per minute.

Uniform flow and Manning

In a long channel with constant slope, gravity balances friction and depth becomes constant (normal depth). Manning's n: smooth concrete 0.012–0.015, earth channels 0.022–0.030, natural rivers 0.030–0.050+.

Froude number and flow regimes

Subcritical flow (Fr < 1) is deep and slow; disturbances travel upstream. Supercritical flow (Fr > 1) is shallow and fast (spillways, steep chutes). Critical flow (Fr = 1) gives minimum specific energy and is used for flow measurement (flumes).

Specific energy and hydraulic jumps

Specific energy E = y + V²/2g relative to the bed. For each E above minimum, two depths are possible (alternate depths). When supercritical flow meets subcritical conditions, a hydraulic jump forms — turbulent, dissipating energy — deliberately used in stilling basins below spillways.

Gradually varied flow and design

Near structures and slope changes, depth varies gradually (backwater curves M1, M2, S1…), computed by the standard step method (HEC-RAS). Channel design balances hydraulic efficiency (best section: rectangle with b = 2y; trapezoid half-hexagon), permissible velocities (no erosion/no silting), freeboard and lining cost.

Formulas

• Manning's equation: V = (1/n) R^(2/3) S^(1/2), Q = V A
• Froude number: Fr = V / √(g y) (< 1 subcritical, > 1 supercritical)
• Critical depth (rectangular): y_c = (q²/g)^(1/3), q = Q/b
• Hydraulic jump: y₂/y₁ = ½(√(1 + 8Fr₁²) − 1), h_L = (y₂ − y₁)³/(4y₁y₂)
• Rectangular sharp-crested weir: Q = (2/3) C_d b √(2g) H^(3/2)

Worked example: Discharge in a concrete canal

Given: Rectangular, b = 3 m, y = 1.2 m; n = 0.015, S₀ = 0.001

Find: V, Q and Fr.

• A = 3.6 m², P = 5.4 m, R = 0.667 m
• V = (1/0.015) × 0.667^(2/3) × 0.001^(1/2) = 1.61 m/s
• Q = 5.79 m³/s; Fr = 1.61/√(9.81 × 1.2) = 0.47 (subcritical)

Answer: Q ≈ 5.8 m³/s, subcritical

Worked example: Hydraulic jump in a stilling basin

Given: y₁ = 0.3 m, V₁ = 8 m/s

Find: Fr₁, y₂ and energy loss.

• Fr₁ = 8/√(9.81 × 0.3) = 4.66
• y₂ = 0.15 × (√(1 + 8 × 21.75) − 1) = 1.83 m
• h_L = (1.53)³/(4 × 0.3 × 1.83) = 1.64 m

Answer: y₂ ≈ 1.83 m, h_L ≈ 1.64 m

Common mistakes

• Wrong: Using the Darcy pipe equation for open channels without care. — Right: Use Manning (or Chézy) with appropriate n and hydraulic radius.
• Wrong: Ignoring supercritical flow at slope changes. — Right: Check Fr; design transitions and stilling basins for jumps.

Applications

• Irrigation & drainage: Lined canals sized by Manning with freeboard.
• Urban stormwater: Road gutters, culverts and trunk drains.
• Spillways & river engineering: Energy dissipation, flood levels and bridge afflux.

Key takeaways

• Manning: V = (1/n)R^(2/3)S^(1/2).
• Fr decides sub-/supercritical behaviour.
• Critical depth minimises specific energy.
• Hydraulic jumps dissipate energy in stilling basins.

Going further

• HEC-RAS: Standard software for 1D/2D river hydraulics, floodplain mapping and bridge hydraulics.
• Sediment transport: Shields criterion and regime theory for stable alluvial channels.
• Culvert hydraulics: Inlet vs outlet control determines headwater levels.