Introduction to Open Channel Flow

Open channel flow occurs whenever water flows with a free surface exposed to the atmosphere. This includes rivers, streams, ditches, gutters, culverts flowing partially full, and storm sewers not under pressure. Understanding open channel flow is fundamental to nearly every aspect of drainage design.

Open Channel vs. Pipe Flow

The key distinction is the free surface. In pipe flow (pressurized conduits), the flow cross-section is fixed and the driving force is the pressure difference. In open channel flow, the water surface is free to adjust, and gravity is the driving force.

This free surface makes open channel flow more complex than pipe flow because the depth — and therefore the cross-sectional area — can change along the channel and over time.

Flow Classification

Open channel flow is classified in several ways:

By Time Variation

• Steady flow: Depth and velocity don’t change with time at a given location. Most design calculations assume steady flow.
• Unsteady flow: Depth and velocity change with time (e.g., a flood wave passing through a channel). Hydrograph routing deals with unsteady flow.

By Spatial Variation

• Uniform flow: Depth and velocity are constant along the channel length. This requires a constant slope, cross-section, and roughness. Uniform flow is the basis for most design calculations.
• Varied flow: Depth changes along the channel. This can be gradually varied (gentle changes over long distances) or rapidly varied (abrupt changes like hydraulic jumps).

By Froude Number

The Froude number is the most important dimensionless parameter in open channel flow:

Where:

• V = flow velocity (ft/s or m/s)
• g = gravitational acceleration (32.2 ft/s² or 9.81 m/s²)
• D = hydraulic depth = A/T (flow area divided by top width)

The Froude number determines the flow regime:

Uniform Flow and Manning’s Equation

Uniform flow is the idealized condition where gravitational forces driving the flow are exactly balanced by friction forces resisting it. The depth remains constant — this is called normal depth.

Manning’s equation is the standard tool for calculating uniform flow:

Where:

• Q = discharge (cfs)
• n = Manning’s roughness coefficient
• A = flow area (ft²)
• R = hydraulic radius = A/P (ft)
• S = channel bed slope (ft/ft)

The constant 1.486 applies to US customary units. For SI units, the constant is 1.0.

Hydraulic Radius

The hydraulic radius is a measure of channel efficiency:

Where P is the wetted perimeter — the length of the channel cross-section in contact with water. A higher hydraulic radius means less friction per unit of flow area, which means more efficient flow.

For a given area, a semicircular cross-section has the maximum hydraulic radius (most efficient). In practice, trapezoidal channels with a bottom width roughly equal to the depth provide a good balance of efficiency and constructability.

Calculate channel flow with the Manning’s Channel Calculator →

Critical Flow and Specific Energy

Specific Energy

Specific energy is the energy per unit weight of water measured relative to the channel bottom:

Where y is the flow depth and V²/2g is the velocity head. For a given discharge, there is a unique relationship between depth and specific energy.

Critical Depth

At critical depth, the specific energy is at its minimum for a given discharge. This is the depth where Fr = 1. For a rectangular channel:

Where b is the channel width.

Critical depth is important because:

• It represents the transition between subcritical and supercritical flow
• It occurs at channel transitions (slope changes, contractions)
• It controls flow at free overfalls and certain structures

Calculate critical depth →

Practical Applications

Gutter Flow

Street gutters are triangular open channels formed by the pavement cross-slope and the curb face. Gutter flow analysis uses Manning’s equation with the triangular cross-section geometry to determine spread width and capacity.

Calculate gutter flow →

Swales

Vegetated swales are trapezoidal or parabolic channels designed for both conveyance and water quality treatment. Their high Manning’s n values (0.03–0.15 depending on vegetation) mean they require wider, flatter cross-sections compared to lined channels.

Design a swale →

Culverts

Culverts can operate as open channels (inlet or outlet control with partially full flow) or as pressurized conduits. The transition between these regimes depends on headwater depth, barrel geometry, and tailwater conditions.

Storm Sewers

Storm sewer pipes flowing partially full are analyzed as circular open channels. Manning’s equation with the appropriate geometric relationships for circular sections determines the capacity at any given depth.

Common Mistakes in Practice

1. Assuming uniform flow everywhere. Real channels have varying slopes, cross-sections, and obstructions. Uniform flow is a design simplification — verify that actual conditions approximate the assumption.

2. Ignoring supercritical flow. Steep slopes can produce supercritical flow that erodes unlined channels. Always check the Froude number.

3. Using wrong Manning’s n. Roughness values for new, clean channels differ significantly from aged, vegetated conditions. Design for the worst case.

4. Neglecting tailwater effects. Downstream water levels can back up flow, increasing depth upstream. This is especially important at confluences and outfalls.

References

1. Chow, V. T. (1959). Open-channel hydraulics. McGraw-Hill.

2. Sturm, T. W. (2010). Open channel hydraulics (2nd ed.). McGraw-Hill.

3. Federal Highway Administration. (2013). Urban drainage design manual (3rd ed., Hydraulic Engineering Circular No. 22). U.S. Department of Transportation.

4. Mays, L. W. (Ed.). (2010). Water resources engineering (2nd ed.). Wiley.