Short answer: at low flow, neither the plate nor the transmitter alone sets orifice measurement quality; the two do it together. Flow rate is proportional to the square root of the differential pressure (DP). When flow halves, DP drops to one quarter; when flow falls to one tenth, DP falls to one hundredth. If transmitter uncertainty is stated as a percentage of span, the absolute DP error stays constant, so it grows relative to the shrinking DP, and roughly half of that relative error carries through to flow. The beta ratio (β = d/D) decides how much DP a given flow produces; the transmitter range decides how well that DP is read.
This is a first approximation that assumes a constant discharge coefficient and expansibility factor. In reality the discharge coefficient changes with Reynolds number, and for gases the expansibility factor changes with the ratio of DP to static pressure. For custody transfer or fiscal metering, uncertainty is calculated with all its components following the ISO 5167-1 approach and the project specification; the example below does not replace that calculation or sizing software.
What do beta ratio and transmitter range control?
· Beta ratio: At the same flow, a smaller beta produces a higher DP, which improves readability at low flow but also raises permanent pressure loss. A larger beta means lower DP and lower permanent loss, but a smaller signal for the transmitter at low flow.
· Transmitter range: Usually set to the DP at maximum flow. If uncertainty is stated as a percentage of span, the error band grows relative to DP at low flow; some transmitters state uncertainty as a percentage of reading, which behaves differently. Which definition applies is checked in the product data sheet for the selected range.
· Calculation chain: The flow computer uses the discharge coefficient, expansibility factor, beta ratio, bore diameter and density together with DP. Whenever the plate is changed or the transmitter is re-ranged, the flow computer parameters must be updated as well.
Beta limits should be read from the standard actually applied. The publication abstract of API MPMS 14.3.2 / AGA 3 Part 2 states that the standard is based on beta ratios of 0.10–0.75 and that discharge coefficient uncertainty is lowest between 0.2 and 0.6. For ISO 5167-2:2022, the BSI summary states that the standard does not cover pipe sizes below 50 mm or above 1 000 mm, or pipe Reynolds numbers below 5 000; the summary gives no numeric beta range. Project calculations rely on the full text of the applicable standard.
Worked example: DP and uncertainty from 100% to 10% flow
The following example scenario only illustrates the mechanism; it is not a real project, product or design value. The calculation was checked independently in Python.
· DP across the plate at maximum flow: 250 mbar; transmitter range 0–250 mbar.
· Assumed transmitter uncertainty: 0.1% of span, i.e. a constant 0.25 mbar at every flow. This is an assumed value, not a product accuracy.
· DP = 250 mbar × (flow / maximum flow)²; discharge coefficient, expansibility factor and density held constant.
· Approximate relative uncertainty carried to flow = 0.5 × ΔDP/DP. Only the transmitter contribution is included; ambient temperature and static pressure effects, long-term stability, discharge coefficient uncertainty, dimensional tolerances and density calculation are excluded.
· For comparison, a second low-range transmitter: 0–25 mbar, with the same assumption of 0.1% of span (0.025 mbar).
Educational flow–DP example (assumed values; transmitter contribution only)
Flow (% of maximum) | DP (mbar) | 0–250 mbar: ΔDP/DP (%) | 0–250 mbar: effect on flow (%) | 0–25 mbar: effect on flow (%) |
100 | 250 | 0.1 | ≈ 0.05 | Over range |
50 | 62.5 | 0.4 | ≈ 0.2 | Over range |
25 | 15.625 | 1.6 | ≈ 0.8 | ≈ 0.08 |
10 | 2.5 | 10 | ≈ 5 | ≈ 0.5 |
The table shows three things. First, a 10:1 change in flow means a 100:1 change in DP; at 10% flow the single transmitter uses only 1% of its span. Second, under the same assumption the uncertainty carried to flow rises from about 0.05% at 100% flow to about 5% at 10% flow. The approximate formula reaches its limit here: the exact expression √(1 + ΔDP/DP) − 1 gives 4.88%, so the trend is the same. Third, the second transmitter ranged 0–25 mbar can measure up to about 31.6% flow and reduces the contribution at 10% flow to about 0.5%.
How much does changing beta change DP?
If the discharge coefficient is held constant, DP at the same flow scales with (1 − β⁴)/β⁴. Using this educational ratio, reducing beta from 0.6 to 0.4 raises DP by about 5.7 times; in the example above, 2.5 mbar at 10% flow becomes about 14 mbar. However, DP at maximum flow rises by the same factor, which requires the transmitter range to be reselected and increases permanent pressure loss. Because the real discharge coefficient varies with beta and Reynolds number, the exact value is calculated with the standard equations.
Which low-flow option makes sense under which conditions?
Conditional decision matrix for low-flow options
Option | When it makes sense | Points to watch |
Single transmitter ranged to maximum DP | Flow stays in a narrow band, or low-flow periods are not significant for measurement | Uncertainty grows quickly at low flow; the low-flow cutoff must be chosen deliberately |
Seasonal re-ranging of the transmitter | Flow stays in a low band for long seasonal periods | Over-range at high flow; change records, flow computer parameters and contract compliance |
Stacked high/low range transmitters | Flow varies over a wide band within the same operating period | Switch point and hysteresis are defined in the flow computer; the low-range transmitter's tolerance to high DP is confirmed in product data; each transmitter is calibrated separately |
Changing to a plate with a different beta ratio | Flow level changes markedly by period and plate changes suit operations | Permanent pressure loss and transmitter range are rechecked; calculations and records are updated for each plate; fitting type determines how easily the plate can be changed |
Parallel meter runs | Flow range is too wide for one run and measurement must be uninterrupted | Space, cost and run switching logic |
Different metering technology | Required turndown cannot reasonably be met with the DP method | Technology selection is a separate evaluation |
Measured DP is not the same as permanent pressure loss
The DP read by the transmitter is the difference between the upstream and downstream taps. Part of this pressure is recovered downstream of the plate; the unrecovered part is the permanent pressure loss, which shows up as a cost at the compressor, regulator or pump. As beta gets smaller, measured DP rises and so does permanent loss. Choosing a smaller beta for low flow must therefore be weighed against the permanent loss allowed at maximum flow. The 2022 edition of ISO 5167-1 includes annexes on turndown and permanent pressure loss; numeric values come from the applicable standard and the project calculation.
A restriction orifice is a separate element: it is used to create a calculated pressure drop in a line and is not intended for measurement. Using a restriction plate as if it were a metering plate is not a valid way to solve a low-flow problem.
Limits of this approach
· At low flow the Reynolds number falls and the discharge coefficient changes; according to the BSI summary, ISO 5167-2 does not cover pipe Reynolds numbers below 5 000.
· Pulsating flow, two-phase flow or the supersonic region are outside the standard's scope; the logic of the example does not apply there.
· Total transmitter performance is more than reference accuracy; ambient temperature, static pressure and long-term stability effects are read separately in the product data.
· Near zero DP, the square-root function amplifies small signal noise; the low-flow cutoff threshold is set by the contract and project requirements.
· Plate edge damage, deposits or incorrect installation increase error regardless of transmitter selection.
· The example is not an uncertainty budget; design decisions are made with an ISO 5167 or AGA 3 calculation and the project specification.
Data to provide for a quotation or review
· Minimum, normal and maximum flow and the approximate time spent in each band (seasonal profile if any).
· Operating pressure and temperature ranges; gas composition or operating density.
· Pipe inside diameter and meter run layout.
· Allowable permanent pressure loss.
· Existing plate bore or beta ratio, transmitter ranges and flow computer configuration.
· Purpose of the measurement (process control or custody transfer), target uncertainty and contract terms.
· Fitting type and how plate changes can be done in operation.
Related pages
· Orifice plate: Plate types and bore sizing for the process conditions.
· Differential pressure (DP) transmitters: Product information on range selection and square-root output.
· Orifice metering systems and DP flow meters: Plate, fitting, transmitter and flow computer treated as one system.
· Selecting single-chamber, dual-chamber and double-isolation orifice fittings: How practical plate changes are in operation depends on the fitting type.
· Orifice or ultrasonic for natural gas metering?: Technology comparison when the DP method cannot meet the required turndown.
Frequently asked questions
Does reducing the beta ratio always solve a low-flow problem?
No. It raises DP at low flow, but it also raises DP and permanent pressure loss at maximum flow by the same factor. Transmitter range, allowable pressure loss and the standard's limits must be checked together.
Stacked transmitters or a plate change?
If flow fluctuates over a wide band within the same period, stacked transmitters are usually the better fit. If flow stays at different levels for long periods and the fitting design suits plate changes, a plate with a different beta ratio can be considered.
If transmitter accuracy is stated as a percentage of reading, does the problem disappear?
The transmitter contribution grows more slowly at low DP, but discharge coefficient variation, the Reynolds number limit and other uncertainty components remain. The DP range over which the percentage-of-reading definition applies is checked in the product data.