The short answer
Differential Pressure Flow Measurement
Differential pressure flow measurement places a restriction such as an orifice plate or a venturi in the pipe and measures the pressure drop across it. Flow is proportional to the square root of that differential, so the transmitter or the controller must take the square root, and the useful turndown is limited to about 4:1 or 5:1 before the low-end signal disappears into noise. It is robust, well understood, and inexpensive in large sizes, but the mag meter has replaced it for most conductive liquids.
Key points
- Flow varies with the square root of differential pressure. Half the flow is a quarter of the DP.
- Turndown is about 4:1 for an orifice, better for a venturi with a good transmitter. Beyond that, the reading is noise.
- Take the square root once, in the transmitter or the controller, never in both.
- Impulse lines cause more DP flow problems than the element or the transmitter.
- Still the right choice for steam, gas, large pipes, and non-conductive liquids. A mag meter wins on most water.
How it works
Put a restriction in a pipe and the fluid speeds up to get through it. Speeding up costs pressure, so the pressure just downstream of the restriction is lower than just upstream. Bernoulli relates the two: the pressure difference is proportional to the square of the velocity, which means velocity, and therefore volumetric flow, is proportional to the square root of the differential pressure.
Q = K × √(ΔP / ρ)
- Q = volumetric flow
- K = a constant for the element, pipe size, and units, from the flow calculation or the element data sheet
- ΔP = differential pressure across the element
- ρ = fluid density
The square root is the defining feature of the method and the source of most of its limits. At 100 percent flow the differential is 100 percent of range. At 50 percent flow it is 25 percent of range. At 25 percent flow it is about 6 percent, and at 10 percent flow it is 1 percent of range, which is inside the noise and drift of the transmitter. That is why DP flow turndown is quoted around 4:1 for an orifice plate: below a quarter of full-scale flow the measurement is unreliable.
The primary elements
| Element | Permanent pressure loss | Straight run needed | Where it is used |
|---|---|---|---|
| Orifice plate | High, roughly 50 to 90 percent of the differential depending on the bore ratio | Long: 10 to 40 diameters upstream depending on the fitting, about 5 downstream | Steam, gas, clean liquids, anywhere cost and replaceability matter more than pumping energy |
| Venturi | Low, roughly 10 to 20 percent of the differential | Shorter than an orifice | Large water lines, raw water and effluent, where pumping cost matters and the meter stays for decades |
| Flow nozzle | Between the two | Similar to an orifice | High velocity steam and gas; erosive service where a plate would wear |
| Averaging pitot tube | Very low | Similar to an orifice | Large ducts and pipes where an insertion element is the only practical option; low differentials |
| Wedge and cone | Moderate | Short | Dirty liquids, slurries, and installations without straight run |
The transmitter and the square root
The DP transmitter measures the differential, typically in inches of water column, and outputs 4-20 mA. The square root has to be taken somewhere. Transmitters can output a signal already proportional to flow, and controllers can take the square root of a linear DP signal. Do one or the other. A signal square-rooted twice reads right at zero and full scale and wrong everywhere between, and the error is subtle enough to survive commissioning.
Whichever device takes the square root, a low-flow cutoff is set below it. Near zero differential the square root function amplifies noise enormously: 0.1 percent of DP range is 3 percent of flow range. The cutoff forces flow to zero below a small differential, typically around 1 percent of DP range, and the totalizer stops counting noise.
Impulse lines
The two pressure taps connect to the transmitter through impulse lines, and those lines are where most DP flow measurements fail. The rules are few and they matter.
- Both lines must be full of the same fluid at the same temperature, so that their static heads cancel. A bubble in one line on liquid service, or condensate in one line on gas service, is a differential that has nothing to do with flow.
- On liquid service, taps on the side of the pipe or below the centerline, with lines sloping continuously down to the transmitter, so gas rises back to the pipe. On gas service, taps on top, lines sloping up, so liquid drains back.
- Lines are short, of equal length, and routed together. A line in the sun and one in the shade have different densities.
- A three-valve or five-valve manifold at the transmitter, so it can be zeroed with the equalizing valve open and both lines blocked, and vented or drained.
- On dirty water and wastewater, diaphragm seals or purged lines replace open impulse lines, or the element is chosen so that no impulse lines are needed.
Installation and straight run
The element assumes a fully developed, symmetrical velocity profile. Elbows, valves, and pumps upstream distort it, and the distortion changes the differential for a given flow. The standards give required straight pipe lengths for each upstream fitting: for an orifice plate the requirement can reach 40 pipe diameters after a partially open valve and is rarely less than 10. Flow conditioners shorten the requirement. When the straight run is not available, the meter reads wrong by an amount that cannot be calibrated out because it depends on flow.
Against the mag meter
For a conductive liquid, which includes all water and wastewater, the electromagnetic flowmeter has no pressure loss, no moving parts, full-bore turndown of 20:1 or more, a linear output, and no impulse lines. It has replaced the orifice plate for nearly all utility water flow. The DP element remains the right choice where the mag meter does not work: steam, gases, hydrocarbons, and non-conductive liquids. It also remains on large existing venturis, which are accurate, need no power, and last longer than the transmitters bolted to them.
Frequently asked questions
- Why does my DP flowmeter read flow when the pump is off?
- The impulse lines are not balanced: a bubble, a difference in temperature, or a line that has partially drained gives a standing differential. Open the equalizing valve and check the zero. If the zero is right with the manifold equalized and wrong when it is in service, the lines are the problem.
- Can I extend the turndown with two transmitters?
- Yes. A high-range and a low-range transmitter on the same taps, with the controller switching between them, gives 10:1 or better. Smart transmitters with very good low-end performance achieve some of this alone; a venturi with a modern transmitter can do 8:1 or 10:1.
- The plate was replaced and the flow reads differently. Why?
- The bore diameter, the plate thickness, the edge sharpness, and the orientation all matter. A plate installed backwards, with the bevel upstream, reads low by several percent. A plate with a rounded edge from erosion or a different bore from the sizing sheet changes the coefficient. Compare the new plate to the sizing sheet, not to the old plate.
- Do I need to measure temperature and pressure too?
- For liquids at steady temperature, no. For gases and steam, density changes with pressure and temperature, and the flow calculation must be compensated with both measurements, either in a multivariable transmitter or in the controller.
Related topics
- 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.
- Pressure TransmittersGauge, absolute, and differential pressure transmitters: how they sense, how range, turndown, and accuracy specifications work, the process connection and its accessories, and the installation errors that show up as calibration problems.
- 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.
- Filtering Analog InputsHow to damp a noisy analog input in the controller without hiding a real process change: the first-order filter, the moving average, the median, where each belongs, and what never to filter.
- 4-20 mA Signals from the Instrument SideHow a 4-20 mA current loop is powered and wired at the transmitter, why the loop resistance budget matters, and how to check a loop with a meter.
- 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
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