16.4 Flow Measurement Devices: Meters, Weirs & Flumes

Closed Conduit Devices

The Differential Pressure Relationship

For venturi, orifice, and nozzle meters:

$Q \propto \sqrt{\Delta P}$

Flow varies with the square root of the differential pressure. Two consequences:

• Turndown is limited. At 10 percent of full-scale flow the differential is only 1 percent of full-scale differential, which is often below the transmitter's usable accuracy. Differential pressure meters are poor at very low flow.
• A leak in one impulse line produces a false differential and therefore a false flow. Impulse lines and their isolation valves must be maintained and blown down.

Installation

Nearly every meter needs straight, undisturbed pipe upstream and downstream to develop a symmetric velocity profile - commonly 5 to 10 diameters upstream and 2 to 5 downstream, more after two elbows in different planes or after a partly closed valve. Installing a meter immediately after an elbow is the most common installation error and can produce errors of several percent that no calibration will remove.

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Open Channel Devices

Open channel flow is computed from head - the depth of water above a reference - using a rating equation specific to the device. Level is measured, flow is calculated.

Weirs

(Q in ft³/s, L and H in feet.)

Worked example. A 90° V-notch weir with a head of 0.75 ft: Q = 2.5 x 0.75^2.5 = 2.5 x 0.4871 = 1.22 ft³/s = 546 gpm

Weir requirements: the crest must be level and sharp-edged; the nappe must be fully ventilated (air beneath the sheet of falling water), or the nappe clings to the weir plate and the reading is wrong; the head must be measured upstream of the drawdown, typically at a distance of at least 4 times the maximum head; and the approach channel must be free of turbulence. Weirs accumulate solids upstream, which raises the approach velocity profile and biases the reading - a decisive disadvantage in wastewater.

Flumes

$Q = C H_{a}^{n}$

where the coefficient C and exponent n depend on the throat width. For a 1-foot Parshall flume, Q ≈ 4.00 H^1.522 (Q in ft³/s, H in feet).

Worked example. A 1-ft Parshall flume with H_a = 0.90 ft: Q = 4.00 x 0.90^1.522 = 4.00 x 0.8523 = 3.41 ft³/s = 2.20 MGD

[!IMPORTANT] Submergence invalidates the rating. Every weir and flume rating assumes free flow - that downstream conditions do not back water up into the measuring section. A Parshall flume has a defined submergence limit (commonly about 70 percent for small flumes, ratio of downstream to upstream head); above it, a submergence correction is required and the accuracy degrades. Backwater from a downstream obstruction, a high receiving water, or a plugged channel is one of the most common causes of a badly wrong wastewater flow reading, and it is invisible unless someone looks at the channel.

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Calibration and Verification

Drop test example. A rectangular clearwell 40 ft x 25 ft drops 1.6 ft in 12 minutes with the inlet closed. Volume = 40 x 25 x 1.6 = 1,600 ft³ = 11,968 gal Flow = 11,968 / 12 = 997 gpm, which is compared to the meter's indication.

Calibrate on a defined schedule - annually for master and source meters, and after any repair, relocation, or process change. Document the result.

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Failure Modes That Produce Plausible Wrong Numbers

[!WARNING] A flow error corrupts every calculation that uses it. Chemical dose in mg/L, pounds per day of BOD, F/M ratio, mean cell residence time, CT, surface overflow rate, and every compliance report are all computed from flow. An operator who trusts an uncalibrated flow meter will chase phantom process problems for months. When process numbers stop making sense, verify the flow meter before changing anything else.