The short answer
Open Channel Flow Measurement
Open channel flow is measured by placing a primary device, a flume or a weir, in the channel and measuring the liquid level upstream of it. The primary device has a known head-discharge relationship, so the level, called the head, converts to flow by an equation or a table. The level is measured by an ultrasonic, radar, or submerged pressure sensor at a specific point defined by the device, and the conversion is done in the flow meter or the controller.
Key points
- Flow comes from level. The primary device makes the relationship known; the sensor measures the head.
- The head must be measured at the point the device defines, not wherever is convenient.
- A Parshall flume passes solids and tolerates some submergence; a weir is more accurate and traps solids.
- Submergence, approach turbulence, and a wrong zero are the three common errors.
- For a permit flow, calibrate the head measurement against a physical gauge and keep the records.
The principle
In a closed pipe, flow is velocity times area, and the area is known. In an open channel the depth changes with the flow, so both are unknown. The solution is a primary device: a structure of known shape placed in the channel that forces the flow through a control section where depth and flow have a fixed, calculable relationship. Measure the depth upstream of that section, called the head, and the relationship gives the flow.
Everything about open channel measurement follows from that. The primary device must be built to the standard dimensions so that the published relationship applies. The head must be measured where the standard says. The channel must deliver water to the device the way the standard assumes. When those three are true the measurement is good to a few percent, which is why flumes and weirs are the accepted method for permit flow at treatment plants.
Flumes
A flume is a narrowing of the channel with a drop in the floor that accelerates the flow to critical depth. The Parshall flume is the standard in North American water and wastewater, available in throat widths from one inch to fifty feet, with published equations for each size.
Q = C × Hₐⁿ
- Q = flow, in cubic feet per second
- Hₐ = head measured at the specified point in the converging section, in feet
- C and n = constants for the throat width. For a 6 inch Parshall flume, Q = 2.06 × Hₐ^1.58. For throat widths of 1 to 8 feet, Q = 4 × W × Hₐ^(1.522 × W^0.026) with W in feet
The head is measured at a point two-thirds of the converging section length upstream from the throat, on the sidewall, where the standard puts the staff gauge. A sensor over the throat or over the approach channel reads a different level and a wrong flow. On a prefabricated flume the measuring point is marked; on a cast-in-place flume it is in the drawings, and it is worth checking against the standard dimensions.
- Free flow
- Downstream water is low enough that it does not affect the head. The single upstream measurement is valid. Parshall flumes stay in free flow up to a submergence ratio, downstream depth over upstream head, of about 50 to 60 percent for the small sizes and 70 to 80 percent for larger ones.
- Submerged flow
- Downstream backs up into the throat. The single measurement reads high. A correction requires a second level measurement in the throat, which is possible but rarely done well. Keep the flume in free flow by design.
- Palmer-Bowlus and other flumes
- Flumes designed to sit in a round pipe or a manhole, with a flat throat, used where a Parshall would not fit. Lower accuracy, easier installation, and their own equations.
Weirs
A weir is a plate across the channel with a notch of known shape. Water pools behind it and spills over the notch, and the head above the notch bottom gives the flow. Weirs are more accurate than flumes when installed correctly and are simpler to build, but they trap solids and grease behind the plate, need a larger drop in the channel, and must have air under the falling water.
| Weir | Equation (Q in cfs, H and L in feet) | Notes |
|---|---|---|
| V-notch, 90° | Q = 2.49 × H^2.48 | Best at low flows; the standard for small streams and plant effluent under a few cfs |
| Rectangular, contracted | Q = 3.33 × (L − 0.2H) × H^1.5 | L is the notch width; the contraction term accounts for the sides |
| Rectangular, suppressed | Q = 3.33 × L × H^1.5 | The notch spans the full channel width; the nappe must be ventilated |
| Cipolletti, trapezoidal | Q = 3.367 × L × H^1.5 | Sides slope 1 horizontal to 4 vertical to offset the contraction |
The head on a weir is measured upstream at a distance of at least four times the maximum head, where the water surface is level, not at the plate where the surface is already dropping toward the crest. The zero is the elevation of the notch bottom or crest, and it is set by measurement, not by assumption.
Measuring the head
- Ultrasonic
- The traditional choice: a transducer above the channel measuring the distance to the surface. Affected by temperature gradients, foam, and turbulence; needs its dead band above the highest water level; a sunshade helps.
- Radar
- The same geometry, less affected by temperature and vapor, and now the default for new installations.
- Submerged pressure
- A transducer in a stilling well or on the channel floor. Simple and unaffected by the air above, but it fouls and needs regular cleaning in wastewater.
- Bubbler
- A tube to the channel floor with a small air flow; the back pressure equals the head. Nothing electrical in the water, tolerant of grease and solids, and common at older plants.
- Float in a stilling well
- The reference method for calibration and the mechanism in older chart recorders. A stilling well connected to the channel at the measuring point damps waves.
Whatever the sensor, the zero is the elevation of the flume floor at the measuring point or the weir crest, and the sensor is set to read zero head at that elevation. Check it against a staff gauge or a tape at commissioning and on a schedule. Every inch of zero error on a small flume is a flow error of several percent that is invisible in the trend.
Where it goes wrong
| Problem | Effect | Check |
|---|---|---|
| Sensor at the wrong point | Systematic error at all flows | Measure the sensor location against the standard dimensions |
| Zero set wrong | Large error at low flow, smaller at high flow | Staff gauge reading against the meter at several flows |
| Submergence | Reads high; worse as downstream level rises | Compare downstream depth to the head; look for a level water surface through the throat |
| Solids or grease behind a weir | Raises the apparent head; reads high | Inspect and clean; consider a flume |
| Approach turbulence | Noisy head, unstable reading | Straight, uniform approach channel of at least ten channel widths; baffles upstream if needed |
| Foam or floating debris | Ultrasonic and radar read the surface of the foam | Sunshade, foam control, or a submerged sensor |
| Flume built to the wrong dimensions | Unknown coefficient | Field-measure the throat and converging section against the standard |
Frequently asked questions
- Which is better for a wastewater plant, a flume or a weir?
- A Parshall flume for raw wastewater and anywhere solids are present, because it is self-cleaning and tolerates some submergence. A V-notch or rectangular weir for clean effluent at low flow, where its accuracy is better and nothing collects behind it.
- Can I calculate flow in the PLC instead of a flow meter?
- Yes. Read the head from a level transmitter, apply the flume or weir equation with a low-head cutoff, and totalize. The dedicated open channel flow meter does the same thing with the equations built in and a certified totalizer, which matters for permit reporting.
- How accurate is open channel flow?
- A properly built and installed Parshall flume with a well-calibrated head measurement is within about 3 to 5 percent. A weir can reach 2 percent. In practice, errors in the head measurement and in the installation dominate, and a flume that has never been checked can be off by 10 percent or more.
- How do I verify the flow meter for a permit?
- Verify the head: compare the meter reading with a staff gauge at the measuring point at several flows, and record it. Then verify the conversion with a known head against the published table. A dye dilution or velocity-area test is the independent check where the primary device itself is in doubt.
Related topics
- Radar Level MeasurementNon-contact and guided wave radar, why it handles a wet well better than most alternatives, and the installation details that decide whether it works.
- Ultrasonic Level MeasurementNon-contact level by time of flight: how the sensor works, the blanking zone and beam angle, temperature compensation, the surfaces and vapors that defeat it, mounting rules, and what to do when it loses its echo.
- Hydrostatic Level MeasurementMeasuring level from the pressure of the liquid above a sensor: submersible transducers, bubblers, and base-mounted transmitters, the density assumption behind all of them, venting, installation, and what makes them drift.
- Magnetic FlowmetersFaraday's law applied to a pipe: how a mag meter works, the conductivity and full-pipe requirements, and why grounding decides whether it reads.
- Analog Scaling: Raw Counts to Engineering UnitsThe arithmetic that turns an analog card reading into feet, psi, or gallons per minute — plus the range mismatches that silently corrupt it.
- Ultrasonic FlowmetersTransit-time and Doppler ultrasonic flow measurement: how each works, which liquids each suits, clamp-on versus wetted transducers, the pipe data the meter needs, the accuracy to expect, and the installation details that decide whether to trust the reading.
Direct contact
Have a controls question?
Reach Eric Sullivan directly about anything on this site, a controls or automation topic, or one of his personal projects.