In differential pressure flow measurement, a primary element such as an orifice plate, a nozzle or a Venturi narrows the fluid path and creates a pressure drop. A transmitter measures that difference and the flow is obtained from its square root. It is an old, standardized and widespread technique, with clear limits on range and installation.
The principle
When a fluid that fills a pipe passes through a restriction, its velocity increases and its static pressure drops. The pressure difference between a point upstream and one at the restriction or downstream depends on the flow, and that dependence can be described with the Bernoulli equation and experimentally determined coefficients. A primary element creates the restriction and a differential pressure transmitter measures the drop. The flow is calculated from it.
The most common primary elements are the orifice plate, the flow nozzle and the Venturi tube. The orifice plate is the most used for its low cost and simplicity: a thin plate with a hole, installed between flanges.
The relationship between flow and differential pressure
Mass flow through an orifice plate is proportional to the discharge coefficient C, the expansibility factor ε (for gases), the orifice area and the square root of the product of the fluid density and the differential pressure. In general form:
q = C / √(1 − β⁴) · ε · (π/4) · d² · √(2 · ρ · Δp)
where β is the ratio of the orifice diameter to the pipe diameter, d is the orifice diameter, ρ the density and Δp the differential pressure. What matters for instrumentation is the consequence: flow is proportional to the square root of Δp. Once the plate is installed, it is enough to measure the pressure difference, take its square root and multiply it by a constant to obtain an acceptable flow.
Illustrative example. A differential pressure transmitter is calibrated from 0 to 100 kPa, and that range corresponds to 100 % of maximum flow.
| Flow (% of maximum) | Differential pressure (% of range) | Signal without square root | Signal with square root |
|---|---|---|---|
| 100 % | 100 % | 20 mA | 20 mA |
| 70.7 % | 50 % | 12 mA | 15.3 mA |
| 50 % | 25 % | 8 mA | 12 mA |
| 25 % | 6.25 % | 5 mA | 8 mA |
| 10 % | 1 % | 4.16 mA | 5.6 mA |
Without the square root, a 12 mA signal does not mean 50 % of flow but 70.7 %. With the square root applied in the transmitter or in the controller, the signal is linear with flow. A frequent mistake is to apply the square root twice, or not at all.
The 10 % row shows the low-range problem: a differential pressure of 1 % of the range is a small signal, and a zero that has drifted even slightly becomes a large flow error.
Primary elements and how to choose
| Element | Characteristic | Used when |
|---|---|---|
| Orifice plate | Cheap, easy to replace, higher permanent pressure loss | Clean fluids, installations where the loss is acceptable |
| Flow nozzle | Lower loss than the orifice, more expensive | Steam and high flows |
| Venturi tube | Recovers almost all the pressure, lowest permanent loss | Large pipes and fluids with fine suspended solids, where the loss counts |
The discharge coefficient of a typical orifice plate is between 0.6 and 0.85 depending on the geometry and the tap position. When the plate and its installation comply with the ISO 5167 standard, the flow is calculated without calibrating the meter individually; that standard is a paid document and only its general scope is cited here.
Pressure taps
Where the upstream and downstream pressure is taken changes the coefficient. The most common configurations are:
- Flange taps: 25.4 mm (one inch) from each face of the plate, in special flanges.
- Corner taps: immediately before and after the plate.
- D and D/2 taps: one pipe diameter upstream and half a diameter downstream.
The choice is set by the design of the element, and the transmitter must be connected to the correct taps.
Installation: what makes or breaks accuracy
The formula assumes developed flow, without swirl or a distorted profile. An orifice plate only works well with a fully developed flow profile. To achieve that, straight pipe runs are required upstream and downstream, whose length depends on the beta ratio and on the preceding fitting: an elbow, a valve or a reducer. On the order of 20 to 40 diameters upstream is recommended depending on the Reynolds number, or a flow conditioner. The exact values for a specific case come from the calculation according to the standard.
Other installation aspects:
- Full pipe. The method assumes a single-phase fluid and a full pipe. A gas with condensate or a liquid with bubbles alters the measurement.
- Plate orientation. The sharp edge faces upstream, and a damaged or worn edge changes the coefficient.
- Impulse lines. The small tubes that carry the pressure from the taps to the transmitter must be short, with adequate slope, without air pockets in liquids or condensate in gases. A three-valve or five-valve manifold allows the transmitter to be isolated and equalized to check the zero without taking it out of service.
- Transmitter position. For liquids, below the taps; for gases, above. This is a general rule that is verified in the design.
Limits of the method
- Permanent pressure loss. An orifice plate recovers less pressure than a Venturi; the permanent loss is about the differential pressure multiplied by (1 − β^1.9).
- Limited flow range. Because of the square relationship, the useful range is bounded, and below a certain percentage the reading is unreliable.
- Wear. The plate edge rounds over time and changes the coefficient, especially with abrasive fluids.
- Dirty or viscous fluids. They suit the sharp-edged plate poorly; the coefficients vary with viscosity and at low flow.
- Compensation. In gases and steam, density changes with pressure and temperature; for an accurate mass flow it is compensated with additional transmitters.
Mass flow and compensation in gases and steam
The flow formula includes the fluid density. In a nearly incompressible liquid, the density changes little with pressure and is taken as constant, with a temperature correction if needed. In a gas or steam, the density depends on the operating pressure and temperature, so the flow calculated with a fixed density drifts when those conditions change.
Illustrative example. A compressed air line was designed at 7 bar with a given density. If the real operating pressure drops to 6 bar and there is no compensation, the real density is lower than the assumed one, and so is the true mass flow. But the instrument keeps calculating with the design value and shows a flow higher than the real one. That is why, for balances or billing, the meter carries an additional pressure transmitter and a temperature transmitter, and the density calculation is done in the controller or in a flow computer. The error of not compensating can be several percent, depending on how far operation departs from the design.
Common mistakes
- Applying the square root twice, or not at all.
- Installing the plate backwards or with a damaged edge.
- Measuring without the straight runs the calculation calls for, or with a partly open valve right before the plate.
- Leaving air in the impulse lines of a liquid, or liquid in those of a gas.
- Changing the transmitter range without updating the maximum flow calculation in the system.
- Confusing the high and low pressure sides of the transmitter, giving a negative or zero reading.
- Not compensating for pressure and temperature in gas or steam.
- Reading total flow on a run when the flow is low, without checking the low-accuracy zone.
Checklist
- Element calculation sheet: diameter, beta ratio, taps and maximum flow with its Δp.
- Plate installed with the correct orientation and its identification engraved.
- Straight runs conforming to the calculation, or a flow conditioner.
- Impulse lines short, sloped and leak-free.
- Transmitter range equal to the calculation, with the square root applied only once.
- Zero checked with the manifold equalized.
- Density compensation defined for gas or steam.
- Instrument fault alarm for an out-of-range signal.
- Range, tag and calculation recorded.
How we help
A poorly adjusted differential pressure flowmeter gives no warning: it delivers a plausible figure with a 10 or 20 % error, which later shows up in balances and invoices. In design, our engineering design and studies service leaves the calculation sheets and loop drawings consistent with the equipment, remotely and worldwide. In the field, testing and commissioning checks the zero, the range and the response of each loop up to the control system, in Colombia or elsewhere on request. To check the signal of each transmitter up to the screen, see point-to-point signal testing; for process supervision, substation SCADA and HMI system.
Related guides
- Point-to-point signal testing
- Substation SCADA and HMI system
- Valve sizing: Cv and Kv
- Pt100 and thermocouples: differences and how to choose
- Level and pressure measurement: technologies and selection
References
- ISO 5167 (series), Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full (paid standard, cited by title; general scope only).
- Wikipedia, “Orifice plate” (CC BY-SA 4.0), accessed 2026-11-05.
- Kuphaldt, T. R., Lessons in Industrial Instrumentation, chapter on flow (CC BY 4.0).
Frequently asked questions
Why is the flow signal extracted with a square root?
Because flow is proportional to the square root of the differential pressure. If the flow doubles, the pressure difference is multiplied by four. That is why the transmitter or the controller must apply the square root so the signal is linear with flow.
What is the beta ratio?
It is the ratio of the orifice diameter to the inside diameter of the pipe. It enters the flow formula and the discharge coefficient, and it defines how much the path narrows: the lower the beta, the higher the differential pressure and the higher the permanent loss.
How many straight pipe runs does an orifice plate need?
It depends on the beta ratio and on the upstream fittings, such as elbows, valves or reducers. The ISO 5167 standard sets the runs for each case, and they can be shortened with a flow conditioner. They are not estimated by eye: they come from the calculation of the element.
What happens to the reading when the flow is very low?
Differential pressure falls with the square of the flow, so at low flows the signal is very small and is affected by noise and zero drift. That is why differential pressure measurement has a limited useful range, which can be extended with two transmitters of different ranges.