A weir is a low barrier built across an open channel, river, or canal that forces water to flow over a defined crest. Engineers use weirs for three routine jobs: measuring volumetric flow, raising upstream levels for diversion, and limiting flood velocities. The overflowing sheet of water, the nappe, discharges into the air for a free weir, while a drowned nappe sits under the downstream surface and passes less water at the same head. The full derivation appears in the companion reference on weirs and flow over weirs, which develops the velocity and head relationships behind the equations here.
What Is a Weir and How Does It Work?
A weir is a barrier through which water flows over an open channel. The edge over which the water runs is the crest, and the depth of water above it is the head, written as H; for a fixed geometry, one measured head corresponds to one discharge.
The Hydraulic Function of a Weir
Weirs create a critical flow condition at the crest. Upstream the flow is slow and subcritical; approaching the crest it accelerates through critical depth and leaves in a free-falling nappe. Because the head-discharge relationship is stable and repeatable, the structure can be calibrated in the lab and trusted in the field.
Free Discharge versus Drowned Discharge
When the nappe springs clear of the crest, the weir has free discharge and the standard equations apply. When the downstream level rises above the crest, the nappe is partially submerged and the weir is drowned; the tailwater pushes back on the flow and the same upstream head passes less water. Gauging stations apply a submergence correction once the ratio of downstream to upstream head exceeds about 0.7.
Discharge varies with head raised to a power between 1.5 and 2.5, so a small head-reading error produces a larger error in the computed flow. Field teams measure the head with staff gauges, hook gauges, and optical instruments; the types of levels used in leveling range from simple dumpy levels for short reaches to digital automatic levels and the instrument choice shapes the station uncertainty budget.
Types of Weirs by Shape of Opening
The most common classification sorts weirs by the geometry of the opening, or notch. Three shapes dominate practice: rectangular, triangular, and trapezoidal.
Rectangular Weirs
The rectangular weir is the standard form: a notch with straight vertical sides and a level sill, ideal for wider flow channels carrying large discharges. Discharge relates directly to the head H, but the coefficient is influenced by crest condition and side contractions.
The Rectangular Weir Equation
A strip of thickness dh and length L at depth h below the water surface has area L x dh and theoretical velocity sqrt(2gh), so the discharge through the strip is dQ = Cd x L x dh x sqrt(2gh), where Cd is the discharge coefficient. Integrating between the crest and the water surface gives Q = (2/3) Cd L sqrt(2g) H^(3/2).
Triangular Weirs
A triangular weir, or V-notch weir, uses an inverted triangle notch. Because the flow narrows to a point at the crest, it is far more sensitive to small heads than a rectangular weir, making it the standard choice for small discharges in laboratories and irrigation turnouts. Its equation, Q = (8/15) Cd tan(theta/2) sqrt(2g) H^(5/2), shows why: head appears to the 5/2 power, so a small change in head produces a clear change in discharge.
Trapezoidal Weirs
The trapezoidal weir, best known in the Cipolletti form, adds sloping sides to the rectangular notch. The slopes are proportioned so the added discharge through the two triangular end portions compensates for the flow lost to end contractions, letting it use the simple rectangular formula without a contraction correction. It is popular in irrigation canals for combining the capacity of a rectangular weir with the stability of a triangular one.
| Feature | Rectangular weir | Triangular weir | Trapezoidal weir |
|---|---|---|---|
| Notch shape | Level sill, vertical sides | Inverted V notch | Level sill, sloping sides |
| Head exponent | H to the 1.5 power | H to the 2.5 power | H to the 1.5 power |
| Best for | Large discharges, wide channels | Small discharges, low heads | Irrigation canals, moderate flows |
Classification systems exist to match a component to its duty. A homeowner comparing patio roofing materials and cover types weighs span, drainage, and wind exposure; a hydraulic engineer weighing weir shapes weighs discharge range, head sensitivity, and sediment load. Both decisions start from the same question: what does the structure have to do?
Types of Weirs by Crest Shape
Sharp Crested and Narrow Crested Weirs
A sharp crested weir has a thin edge, usually a thin metal plate. The nappe springs clear with minimal contact, giving a stable head-discharge relationship that underpins most flow measurement standards; the edge is delicate and must be protected from debris and ice. A narrow crested weir sits between extremes: its crest is wider than a sharp edge but not wide enough for parallel critical flow to develop, so its coefficient is less stable and it appears mainly in small farm and drainage structures.
Broad Crested Weirs
A broad crested weir has a wide horizontal top long enough for the flow to run parallel to the crest and reach critical depth on it, the crest width usually exceeding the head. These weirs are robust, cheap to build in masonry or concrete, and tolerate debris and sediment far better than sharp crests. Their discharge follows Q = Cd L sqrt(g) H^(3/2) with Cd near 0.85, which collapses to the familiar Q = 1.7 L H^(3/2) in SI units.
Ogee Shaped Weirs
An ogee weir shapes the downstream face to match the underside of the nappe, so the flow leaves the crest with little separation and near-atmospheric pressure along the surface. The result is a high discharge coefficient and a stable overflow at large heads, which is why ogee profiles dominate spillways and large river weirs. Running at heads far above the design head can produce cavitation damage on the face.
Setting the crest at the design elevation is a surveyor’s job as much as a designer’s. The crest must sit at exactly the level assumed in the calculations, and the head is read from a reference datum tied to the same network; the types of leveling in surveying chosen for the task, from simple leveling to precise differential leveling, determine whether the finished crest lands within the few millimeters the equations assume.
Types of Weirs by End Contraction and Discharge Equations
Contracted and Suppressed Weirs
In a contracted weir, the notch is narrower than the channel and the nappe ends pull inward, so the side contractions reduce the effective crest length. In a suppressed weir, the notch spans the full channel width and the nappe does not contract, so the full crest length discharges.
The Discharge Coefficient
The discharge coefficient Cd accounts for losses the ideal derivation ignores: velocity of approach, friction, and streamline curvature. Cd drifts with head, crest sharpness, and contraction ratio, so published values carry their test conditions.
Practical Cd Values
For a sharp crested rectangular weir with free discharge, Cd typically falls between 0.60 and 0.62. Triangular weirs run slightly lower, about 0.58 to 0.60, while a well-formed ogee profile can reach 0.75 or higher. Broad crested weirs are usually quoted through a combined coefficient of about 1.7.
Weir Construction and Materials
The body of a weir must resist hydrostatic pressure, scour, and repeated wetting and drying. Small structures use masonry, larger ones reinforced concrete. For masonry weirs, durability depends on the types of bricks chosen, since soft or over-burnt units spall under continuous wetting and freeze-thaw cycles.
Advantages and Disadvantages of Weirs
Advantages of Weirs
- Simple and low cost: no moving parts and local materials.
- Reliable flow measurement: a calibrated crest gives repeatable data for decades.
- Level control: raising the upstream level supports diversion intakes.
- Low maintenance: fixed crests need attention mainly after floods or ice runs.
- Ecological integration: fish ladders and bypass channels can be added.
Disadvantages of Weirs
- Permanent head loss: the upstream level stays high even when no water is diverted.
- Sediment trapping: slower upstream flow drops silt that fills the pool.
- Drowned operation: once tailwater rises above the crest, gauging needs corrections.
- Afflux risk upstream: backwater can flood property and bridges during high flows.
- Debris and ice accumulation: the crest collects driftwood, and ice jams can overload it.
A weir is one of several structures used to manage a river. Where the same site must also carry traffic, engineers weigh the weir against a gated barrage and against the different types of bridges used for river crossings.
Operation, Limitations, and Location of Weirs
Operating Limits
Every weir has a design range. Below the minimum head the nappe may cling to the crest instead of springing clear, which destroys the calibration; above the maximum head the approach velocity becomes so high that the coefficient drifts. Operators track both limits: the lower is set by crest geometry and surface tension, the upper by the afflux the channel and banks tolerate.
- Record upstream and downstream water levels at fixed intervals.
- Check the crest for debris, sediment, and damage after every flood.
- Verify the nappe springs clear with air beneath it.
- Compare measured discharges against the rating table and flag drift.
- Log ice conditions and clear accumulations before they overload the crest.
Limitations and Location of Weirs
Weirs cannot store meaningful volumes of water; they are level-control structures, not reservoirs. They offer no regulation beyond what the fixed crest provides, and a drowned weir loses much of its measurement value. Sedimentation behind the crest is a slow process that eventually buries the structure unless the design includes a sluice. Site selection starts with a stable, straight reach with uniform approach flow, where the bed and banks resist scour or the design adds aprons and sheet piles; the upstream area must tolerate the afflux the weir creates.
Common Failure Modes
Weir failures develop through scour, material deterioration, and hydraulic overload. Scour at the downstream toe undermines the apron and can tip the structure. The types of failures experienced by different construction materials in structural engineering map directly onto weir distress: concrete spalls and cracks, masonry joint erosion, steel corrosion at the waterline, and timber decay all show characteristic patterns that inspection crews can identify early.
Weirs range from small farm check structures a meter wide to major river regulation works spanning hundreds of meters, in the same way building types span from single-room shelters to industrial complexes; the shared principle is matching the structure to its duty.