8.5 Flow Measurement, Weirs, Flumes & Meters

8.5 Flow Measurement, Weirs, Flumes & Meters

Every number an operator reports — chemical dose in pounds per day, detention time, surface overflow rate, loading rate, the mass loadings on a Discharge Monitoring Report — is a flow measurement multiplied by something else. Get the flow wrong and every derived value is wrong with it. The Illinois EPA treats Flow Measurement as its own examination subject: 2 questions on the Class 4, Class 3 and Class 1 exams and 4 questions on the Class 2 exam, plus its presence on the Collection System exam subject list. Under 35 Ill. Adm. Code 604.1215(h), every booster pumping station on a community water supply must be fitted with a flow rate indicator and a totalizer meter — the state assumes you can read both.

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1. Primary and Secondary Elements

Open-channel measurement always has two parts, and mixing them up is a classic exam trap.

• The primary element is the hydraulic structure — the weir plate or the flume — that forces a fixed, repeatable mathematical relationship between water depth (head) and flow rate.
• The secondary element is the device that measures that depth and converts it: a float-and-cable in a stilling well, a bubbler tube, an ultrasonic level transmitter, or a submerged pressure transducer.

A perfect transmitter on a damaged weir plate gives a confidently wrong answer. Calibration checks always start at the primary element.

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2. Weirs

A weir is an obstruction with a shaped notch; water backs up behind it and spills over, and the depth of water above the crest indicates flow. Weirs are cheap and accurate but demand a substantial head loss and are intolerant of solids, which settle in the pool upstream. They are far more common on clean-water and final-effluent channels than on raw sewage.

Installation and operating rules that show up on exams:

1. Measure head upstream, never at the crest. The water surface curves downward (draws down) approaching the weir. Head is measured in a stilling well or at a point at least 3 to 4 times the maximum expected head upstream of the weir plate.
2. Zero is the crest elevation. $H$ is measured from the crest (or the notch vertex) to the undisturbed upstream water surface.
3. The nappe must be ventilated and free-discharging. Air must reach the underside of the falling sheet. If the nappe clings to the downstream face, or if the downstream water level rises above the crest and submerges the weir, the equation no longer applies and the meter over-reads.
4. Keep the crest sharp and clean. A sharp-crested weir plate has a knife edge, typically beveled at 45 degrees on the downstream side with a flat face no more than about 1/8 inch. Corrosion, nicks, or a rag hanging on the notch change the discharge coefficient.
5. Remove upstream deposits. Grit and sludge accumulating in the approach pool raise the effective floor, change the approach velocity, and bias the reading.

Worked example. A 90-degree V-notch weir on a plant effluent channel reads a head of 0.60 ft. Flow is $Q = 2.49 \times 0.60^{2.48}$. Since $0.60^{2.48} = e^{2.48 \ln 0.60} = e^{2.48 \times (-0.5108)} = e^{-1.2668} = 0.2817$, then $Q = 2.49 \times 0.2817 = 0.701\text{ cfs}$. Converting: $0.701\text{ cfs} \times 448.8\text{ gpm/cfs} = 315\text{ gpm}$, or about 0.453 MGD ($0.701 \times 0.6463$).

Two conversions worth memorizing: 1 cfs = 448.8 gpm and 1 cfs = 0.6463 MGD.

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3. Flumes

A flume measures flow by forcing water through a converging throat, accelerating it to critical flow, and reading depth upstream. Because nothing obstructs the channel floor and velocity increases through the throat, flumes are self-cleaning — which is why they dominate raw wastewater and grit channel applications, and why Section 5.1 pairs a Parshall flume with a velocity-controlled grit chamber.

The Parshall flume

A Parshall flume is sized by its throat width (W). Its converging section, level throat floor and diverging downstream section produce a stable relationship between the upstream head $H_a$ and flow.

• For throat widths of 1 to 8 feet: $Q = 4,W,H_a^{1.522,W^{0.026}}$, with $Q$ in cfs, $W$ and $H_a$ in feet.
• For a 3-inch throat: $Q = 0.992,H_a^{1.547}$. For a 6-inch throat: $Q = 2.06,H_a^{1.58}$. For a 9-inch throat: $Q = 3.07,H_a^{1.53}$.
• $H_a$ is measured at a fixed point in the converging section, two-thirds of the way upstream from the throat crest. That location is built into the flume; a staff gauge or stilling well tap is provided there.

Submergence. Under free-flow conditions, $H_a$ alone determines the flow. When tailwater rises, the flume becomes submerged, and the downstream head $H_b$ starts to matter. The submergence ratio is $H_b/H_a$. Free flow persists up to roughly 60 percent submergence for small flumes (up to 9-inch throats) and about 70 percent for 1- to 8-foot throats. Past that, readings must be corrected downward — an uncorrected submerged flume over-reads, sometimes badly.

The Palmer-Bowlus flume is the retrofit cousin: a shaped insert dropped into an existing round sewer or manhole. It needs much less head loss and far less approach length than a Parshall, which makes it the standard choice for temporary collection-system flow studies and infiltration/inflow investigations.

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4. Closed-Pipe Meters

Straight-run requirement. Nearly all in-line meters need undisturbed flow: a common rule is 10 pipe diameters of straight run upstream and 5 downstream. Installing a meter immediately downstream of an elbow, a partially closed valve or a pump discharge builds in an error no amount of transmitter calibration will remove.

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5. Indicators, Totalizers and Charts

• A flow rate indicator reads instantaneous flow (gpm, cfs, MGD).
• A totalizer integrates flow over time and reads cumulative volume (gallons or million gallons). Daily volume is read as the difference between two totalizer readings — the totalizer never resets, so a decreasing reading means the counter rolled over or was replaced.
• A circular or strip chart recorder preserves the flow profile over time, letting an operator see diurnal peaks, wet-weather response and pump cycling that a single instantaneous reading hides.

6. Field Calibration

The reference check for any flow meter is a volumetric drawdown test. Isolate a tank, wet well or clearwell of known dimensions, run the pump or the flow for a timed interval with no other inflow, and compute:

$Q = \frac{\text{Area (sq ft)} \times \text{Drop in level (ft)} \times 7.48\text{ gal/cu ft}}{\text{Elapsed time (min)}}$

Compare the measured value against the meter reading and calculate percent error as $\frac{\text{Meter} - \text{Actual}}{\text{Actual}} \times 100$. For open-channel devices, check the physical primary element first: verify the crest or flume zero against the secondary element's zero, confirm the weir plate is level and undamaged, confirm nothing is submerging the nappe, and clear upstream deposits. Most "meter drift" complaints turn out to be a fouled stilling well, a plugged bubbler line, or a zero that walked.