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Open Channel Flow Measurement with Weirs and Flumes
An open-channel level sensor measures head, which a validated primary-element rating converts to flow. Head error is amplified by the rating’s slope. The complete uncertainty also includes the weir or flume geometry, coefficient, approach conditions and datum survey.
The formula decides the error sensitivity
For a 90° V-notch weir under free-flow conditions, an illustrative SI approximation is:
Q = 1.38 × h^2.5 (Q in m³/s, h in metres). This coefficient is an assumed example, not a universal rating; use the approved equation or calibration for the actual notch and installation.
Rectangular-weir and flume ratings also depend on their exact geometry and hydraulic conditions. A simple rectangular-weir approximation may use a head exponent near 1.5, but its coefficient and contraction corrections must be established. For a rating Q = C × h^n, the first-order sensitivity to a small head error is:
ΔQ/Q ≈ n × (Δh/h)
where n is the exponent. A 1% head error at n = 2.5 is a 2.5% flow error.
Worked example. A 90° V-notch weir with h = 0.20 m: Q = 1.38 × 0.2^2.5 = 1.38 × 0.0179 ≈ 0.0247 m³/s ≈ 89 m³/h. Now a 10 mm level error — easily produced by a misplaced ruler, a foam layer or an uncalibrated sensor — gives ΔQ/Q = 2.5 × (0.01/0.2) = 12.5%, or 11 m³/h of imaginary flow. At h = 0.40 m the same 10 mm is only 6.25%. The lesson is structural: weir systems lose accuracy exactly in the low-flow range where environmental compliance reporting usually cares most.
Head must be measured in still water, at the right point
The formula assumes head is the level upstream of the device, measured in a zone where the water surface is calm and representative:
Location: upstream of the drawdown curve — for a V-notch, at the specified head station; for a traditional fully contracted 90° V-notch, at least four times the maximum head upstream, and never in the plunge zone near the notch.
Stilling: provide a suitable approach section or approved stilling arrangement without distorting the primary-element hydraulics. Ripples increase scatter; a radar does not universally read their peak. Validate the time-averaged head and the instrument response.
Zero: the weir crest or flume floor elevation is the zero, and it must be surveyed, not assumed from a drawing. A 5 mm zero error is a permanent flow bias at every head.
Non-contact radar or ultrasonic instruments avoid an immersed sensor, but require a rigid mounting and a clear path. A 3 mm bracket displacement can become a direct head error. Pressure sensors add a density assumption and may be affected by sediment, fouling or a blocked pressure port; settled material is not automatically added to the water head as its full density.
Free flow is a condition, not a hope
A free-flow rating is valid only within its specified hydraulic conditions. Verify nappe ventilation and tailwater limits for a weir, and the size-specific submergence limit and head stations for a flume. Submerged-flow corrections exist for some designs but are not interchangeable with the free-flow rating.
If the channel can back up — tides, gate operations, storm events — either measure downstream head as well and correct for submergence, or choose a different measurement principle. A formula applied to drowned conditions quietly produces confident, wrong numbers.
Choosing between weir and flume
| Condition | Weir consideration | Flume consideration |
|---|---|---|
| Clean water | Suitable designs can provide a useful calibrated rating | Select the required range and available head |
| Solids or sediment | Inspect for deposition or crest blockage | Some geometries pass solids better; inspection is still needed |
| Small flows | Appropriate notch angle and validated minimum head | Use a design rated for the required minimum flow |
| Limited available head | Check upstream rise and permanent loss | A suitable design may reduce head loss |
| Retrofit | Plate, approach pool and datum work | Geometry, head station and civil modifications |
Choose the primary element from the required flow range, head loss, solids, tailwater and applicable reporting method. A V-notch can be useful for small clean flows; a suitable flume may pass solids better, but no design is maintenance-free.
Questions from open channel projects
Q1. Can the level sensor sit directly over the weir?
No. It must sit upstream at the specified stilling location, or read through a stilling well connected to the channel. Above the notch it measures the drawdown, which is exactly what the formula forbids.
Q2. Is a radar sensor accurate enough?
Millimetre-level radar is available, but the mounting and zero survey usually dominate. Budget the installation rigidity and the surveyed datum before shopping for sensor specs.
Q3. What about very low flows?
Surface tension, nappe behaviour and head uncertainty become important near the lower rating limit. Use the validated minimum head for that notch and approach geometry. A different notch angle or primary element may be needed; do not claim compliance-quality flow below the validated range.
Related technical guides
- Radar Level Transmitter Accuracy: What the Datasheet Number Does Not Tell You
- Radar Level Transmitter Output Signals: Choosing the Right One
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