Engineering & Technology · Water, Hydraulic & Coastal Infrastructure

Open channels, rivers, sediment and river engineering

An open channel has a free surface, so a change in flow can also change depth. A river adds an erodible bed, banks, sediment supply and habitat: its geometry is part of the response rather than a permanently fixed pipe.

Review fluid continuity, pressure and hydraulic head, energy per unit weight, groundwater/ground interaction, and area under a rate–time graph. Use SI units, with 1 L/s=.001 m³/s and 1 h=3600 s. Water density 1000 kg/m³ and g = 9.81 m/s² are declared where used. New channel, coastal and hydrological terms are introduced in the lessons.

Back to the chapter

After reading, you can

Explain open-channel flow regimes and connect river hydraulics to sediment supply and changing geometry.

Distinguish flow geometry from material roughness

Discharge is Q=AV, where A is flow area and V mean velocity. Hydraulic radius Rh=A/P uses wetted perimeter P and helps describe frictional effects. Hydraulic depth D=A/T uses top surface width T and appears in free-surface wave and critical-flow relationships. These lengths are not interchangeable.

For a rectangular channel of width b and depth y, A=by, T=b and D=y. Its hydraulic radius is by/(b+2y), generally smaller than y. Irregular rivers require their actual cross-sections and suitable roughness and boundary assumptions; one average depth cannot describe every flow path.

Compare flow speed with surface-wave propagation

Froude number Fr=V/√(gD) compares the flow speed with a gravity-wave speed in the elementary model. Subcritical flow has Fr<1; small disturbances can propagate upstream relative to the ground. In supercritical flow, Fr>1, they cannot in this model. Critical flow has Fr=1. These describe a flow state, not a universal label for the entire river.

For a rectangular section with discharge per width q=Q/b, specific energy relative to the bed is E=y+q²/(2gy²) when the velocity correction factor is one. The depth term increases with y, while the velocity-head term falls. Their sum has a minimum at critical depth yc=(q²/g)^(1/3). The plotted curve is a relation at one section, not a water-surface profile along a sloping channel.

Friction, contractions, backwater and changing bed level affect actual profiles. A hydraulic jump can dissipate energy between a shallow fast state and a deeper slower state while momentum and boundary forces require their own account. Equal discharge does not mean equal depth, velocity or erosive effect.

Horizontal water depth y .4–3 m; graph axes 0–3 m. Vertical specific energy E 0–3.5 m. Rectangular width4 m and discharge9 m³/s give q=2.25 m²/s; E=y+q²/(2g y²), velocity correction factor1, g9.81. Minimum at yc=(q²/g)^(1/3)≈.8021 m and E≈1.2032 m. At y1.5 m: velocity1.5 m/s, Froude≈.3910 and E≈1.6147 m. No friction slope, sediment law or complete water-surface profile is implied.

Retain the sediment account

Sediment arrives from upstream, tributaries, banks and the bed. Transport depends on the flow and the material available, including grain size. If more sediment enters a reach than leaves, its stored sediment increases unless another removal path is included. Deposition can reduce storage or alter flood levels; erosion can undermine a foundation or change habitat.

River engineering may use bank protection, channel changes, crossings, grade controls or restoration. Each can affect upstream and downstream water levels, sediment continuity and ecological connections. A channel that passes one design discharge in its initial geometry may change through deposition, scour, vegetation or debris. Maintain surveys and sediment evidence alongside water-level and discharge records.

Identify a constructed channel state and sediment residual

Take a rectangular width 4 m, depth 1.5 m and discharge 9 m³/s. Area is 6 m² and V=1.5 m/s. Hydraulic depth is 1.5 m, but hydraulic radius is 6/(4+3)=.8571 m. With g=9.81, Fr≈.391, a subcritical state in this model.

Discharge per width is 2.25 m²/s. Critical depth is about .802 m and minimum specific energy about 1.203 m. At the supplied depth, E=1.5+1.5²/(2×9.81)≈1.6147 m. A different depth could have the same specific energy; the relation alone does not decide which state the boundaries establish.

Separately suppose a reach receives 20 tonnes of sediment per day and exports 12, with no other exchange. Its stored sediment increases by 8 tonnes/day. That mass balance does not specify the deposition location or bed-elevation change without grain, density and geometry information. These values are invented, not a river survey.

Try the reasoning

Why are hydraulic depth and hydraulic radius different?
Show the answer and reasoning
They divide area by different boundaries: top width versus wetted perimeter.
Does the specific-energy curve show the bed slope?
Show the answer and reasoning
No. It compares possible depths at one fixed discharge per width relative to the local bed.
Can a water-only calculation establish long-term channel capacity?
Show the answer and reasoning
No. Sediment, banks, vegetation, debris and evolving geometry can change the hydraulic state.

What to carry forward

Use the correct depth measure and flow regime, then include the sediment and geometry changes that the water model omits.

References

Teaching resources and research supporting this lesson’s explanations and examples.