This lesson explains the principles in our own words. Fiscal and custody-transfer metering must follow the current editions of the standards named below, your contract and your local metrology authority, using approved flow computers.
The meter run
An orifice meter is a thin, flat plate with a sharp-edged, round hole (the bore, d) clamped across a pipe of inside diameter D. The plate forces the flow through a smaller area, so the fluid speeds up and its pressure falls. Measure that pressure difference, the ΔP, and you can calculate the flow.
- Plate and fitting. The plate sits between flanges or in a dual-chamber fitting that lets you pull it out under pressure for inspection.
- Flange taps. The ΔP is measured 1 inch (25.4 mm) upstream and downstream of the plate faces. This is the tap layout AGA 3 is built around.
- Straight pipe and a flow conditioner. The equation assumes a fully developed, swirl-free velocity profile. Elbows and valves upstream distort it, so the standard asks for long straight lengths, or shorter lengths with a tested flow conditioner.
- Secondary instruments. A ΔP transmitter, a static pressure transmitter, a temperature transmitter and often a gas chromatograph (GC) for composition, all feeding a flow computer.
The flow equation
Energy is conserved through the plate: what the fluid gains in speed it loses in pressure. Written for mass flow, every orifice standard ends up with the same shape:
- d: bore at flowing temperature (the plate grows or shrinks with temperature, so it is corrected from the measured value).
- Ev = 1/√(1 − β⁴): velocity of approach factor, with β = d/D.
- Cd: discharge coefficient. Real flow is lower than ideal because the jet contracts and loses energy. Typically about 0.60.
- Y: expansion factor. A gas expands as its pressure drops, so it is a little less dense through the bore. Y is just below 1 (1 for liquids).
- ρ1: fluid density at the upstream tap. For gas this comes from AGA 8.
The key consequence is the square root: flow is proportional to √ΔP. Double the flow and the ΔP goes up four times.
AGA 3: Cd, Y and β
AGA Report No. 3 (also published as API MPMS Chapter 14.3) is the North American standard for concentric, square-edged orifice meters. Its Part 1 holds the equations, Part 2 the plate and meter-tube specifications and installation rules. ISO 5167-2 is the international equivalent; both rest on the same large research database and give very similar results.
- Discharge coefficient. Cd is a fitted equation in β, the Reynolds number ReD and the tap positions. Because Re depends on the flow you are calculating, it is solved by iteration: guess Cd, calculate flow, calculate Re, recalculate Cd, and repeat until it settles.
- Expansion factor. Y depends on β, the ratio ΔP/P1 and the isentropic exponent k. Keep ΔP/P1 small; the equations are only valid up to a limit, and big ratios add uncertainty.
- β ratio. The equations are valid for roughly β 0.1 to 0.75. Many companies design for 0.2 to 0.6: lower β gives a bigger ΔP to measure, higher β gives less pressure loss.
- Thermal expansion. d and D are measured at a reference temperature (usually 20 °C / 68 °F) and corrected to the flowing temperature with the expansion coefficients of the plate and pipe materials.
How accurate is an orifice meter?
AGA 3 Part 1 gives a method to estimate the flow uncertainty (95 % confidence) by combining each input's uncertainty with its sensitivity, that is, how strongly it moves the flow:
- Cd (sensitivity 1): about ±0.44 % at β = 0.5 and high Reynolds number, rising at high β and at low Reynolds number.
- Bore d (sensitivity ≈ 2/(1 − β⁴)): the plate bore matters about twice as much as its own error.
- ΔP, static pressure, temperature, Z and gas analysis (sensitivity 0.5 each, because flow goes with √ΔP and √ρ).
A well-built meter run with good transmitters reaches roughly ±0.6 to ±1 % on gas. The calculator below shows each contribution as a bar, so you can see which instrument to improve first. Notice how a ΔP transmitter specified as "% of span" gets worse in % of flow as the flow falls.
AGA 8: compressibility Z
Real gas does not follow the ideal gas law exactly. The compressibility factor Z corrects it:
At 50 bar and 15 °C a typical natural gas has Z ≈ 0.88 to 0.90, so it is about 11 to 13 % denser than the ideal gas law predicts. Ignore Z and the flow is wrong by about half that (because flow goes with √ρ), plus the full error again when converting to standard volume. That is why Z is the biggest correction in gas metering.
- AGA 8 Part 1, DETAIL method. Uses the full composition (21 components: methane to decane, N₂, CO₂, H₂S, H₂, O₂, CO, water, helium, argon) in an equation of state. This is what our calculator uses.
- GROSS method. An older shortcut using relative density, heating value and CO₂ (and N₂) when no full analysis is available. It is less accurate and has a narrower range.
- AGA 8 Part 2 (GERG-2008). A newer, wider-range equation for unusual gases, high pressures and liquids.
In the calculator, switch the top selector to AGA 8 · Gas properties to use it on its own: enter pressure, temperature and composition to get Z, density, k, speed of sound, Cp/Cv, the Joule-Thomson coefficient, heating value and a Z-vs-pressure chart.
The same equation of state also gives the isentropic exponent k for the expansion factor, the speed of sound (used to check ultrasonic meters), and Z at base conditions.
Standard volume and energy
Gas is bought and sold by standard volume (or energy), not by the volume flowing in the pipe. Standard volume is the mass flow divided by the density at agreed base conditions:
- ISO / metric: 15 °C and 101.325 kPa (Sm³). Some contracts use 0 °C (Nm³).
- US gas industry: 60 °F and 14.73 psia (SCF, MSCFD, MMSCFD).
Get the base conditions wrong and the whole flow is wrong: switching from 15 °C to 0 °C changes the number by about 5.5 %. In US flow computer terms, the ratio √(Zb/Zf) is the supercompressibility factor Fpv.
AGA Report No. 5 covers converting volume or mass into energy (heating value, from the gas analysis). Energy is usually what the invoice charges for:
- Gross (superior) heating value counts the heat released when the water formed in combustion condenses; net (inferior) does not. Gas sales normally use gross.
- The heating value comes from the composition: each component's heat of combustion, weighted by its mole fraction, then divided by the real molar volume at base conditions (from AGA 8).
- Wobbe index = heating value ÷ √(relative density). Gases with the same Wobbe index give the same heat output from a burner, so it is used to check gas interchangeability.
The calculator shows gross and net heating value, Wobbe index and energy flow (GJ/h, MMBtu/d). Its values are approximate, built from public-domain NIST data, not a certified AGA 5 / GPA 2145 / ISO 6976 calculation.
Oil and other liquids
The same plate and equation work for crude oil, condensate and water, with two differences: liquids are practically incompressible, so Y = 1; and density comes from a lab analysis or an online densitometer rather than from AGA 8. Oil is much more viscous than gas, so the Reynolds number is lower and Cd changes more over the flow range. Below Re of a few thousand the equation is no longer valid, which limits orifices on heavy crude.
Live calculator
Pick an example or enter your own meter run. Switch between SI and US units, gas and oil, and between three jobs: flow from ΔP, size the bore for a required flow, or ΔP from flow. Every intermediate value is shown so you can check a flow computer step by step. Beyond natural gas it also handles other gases and vapours (molar mass, Z, k), steam (IAPWS-IF97 properties) and liquids, corner and D–D/2 tappings (ISO 5167-2), and restriction orifices with a choked-flow and cavitation check. Choose the primary device (orifice plate, venturi tube or flow nozzle) and the standard list adapts to the device and fluid: AGA 3 or ISO 5167-2 for orifices, ISO 5167-4 classical venturis (machined, as-cast, welded) and ISO 5167-3 nozzles (ISA 1932, long radius, venturi nozzle). A venturi loses only about 10–15 % of its ΔP permanently, against roughly 50–75 % for an orifice plate. It also works offline in the Instrument Apps Hub.
Video mode (for screen recording): open the scripted tour.
Calculator inputs explained
Every field in the calculator, what it means, typical values and where to find it on site. Fields only appear when the chosen device, fluid or job needs them.
Setup
| Input | What it means | Typical value / where to get it |
|---|---|---|
| AGA 3 · Orifice meter / AGA 8 · Gas properties | Full flow meter calculation, or gas properties only (Z, density, heating value) | Use AGA 8 mode to check a flow computer's Z or a GC report |
| SI / US units | Changes every unit; values are converted, not reset | SI: bar, °C, mm, Sm³/h · US: psig, °F, in, MSCFD |
| Fluid | Natural gas (AGA 8 composition), other gas / vapour (M, Z, k), steam (IAPWS-IF97) or liquid | Natural gas for sales and fuel gas; "other gas" for air, N₂, H₂, CO₂, process vapours |
| Calculate | Flow from ΔP · Size the bore · ΔP from flow · Restriction orifice | Checking a running meter → Flow from ΔP; new design → Size the bore |
| Examples | Load a complete worked case | Good starting point; then change values |
Meter run
| Input | What it means | Typical value / where to get it |
|---|---|---|
| Pipe size | Picks a standard pipe and fills in its inside diameter | From the P&ID or line list (size and schedule) |
| Pipe ID D | Measured inside diameter of the meter tube at the reference temperature | Meter tube inspection report; nominal schedule ID if not measured |
| Primary device | Orifice plate, venturi tube or flow nozzle | Instrument datasheet |
| Orifice bore / throat d | Bore (or throat) diameter at the reference temperature | Stamped on the plate tab; plate inspection certificate |
| Reference temperature | Temperature at which d and D were measured | 20 °C / 68 °F (the AGA 3 and ISO default) |
| Plate / device material, pipe material | Sets the thermal expansion used to correct d and D to flowing temperature | Usually stainless steel 316 plate, carbon steel pipe |
| Standard | Equation set; the list depends on device and fluid (AGA 3, ISO 5167-2, -3 or -4) | Natural gas sales: AGA 3; steam and process fluids: ISO 5167 |
| Pressure tappings | Flange (25.4 mm each side), corner, or D and D/2 taps (orifice only) | Visible on the fitting; flange taps are the most common |
| Static pressure measured at | Whether the pressure transmitter is on the upstream or downstream tap | Check the impulse line on site; upstream is usual |
Process
| Input | What it means | Typical value / where to get it |
|---|---|---|
| Static pressure (gauge) | Line pressure at the tap | PT reading in the DCS / flow computer |
| Atmospheric pressure | Converts gauge to absolute pressure | 101.325 kPa at sea level; lower at altitude |
| Downstream pressure P2 | Pressure after a restriction orifice (RO mode) | Process design / downstream equipment pressure |
| Vapour pressure | For the liquid cavitation and flashing check (RO mode, optional) | Fluid data sheet; water at 25 °C ≈ 3.17 kPa(a) |
| Flowing temperature | Fluid temperature at the meter | TT downstream of the device |
| Differential pressure ΔP | Measured pressure difference across the device | DP transmitter reading (convert % or mA with the span) |
| Required / maximum flow | Target flow for sizing, ΔP-from-flow or RO modes | Process design data sheet |
| Normal / minimum flow | Used to check the turndown in sizing mode | Design data; minimum should stay above about 10 % of ΔP span |
| Transmitter ΔP span (URV) | DP transmitter range for the 4–20 mA table | Transmitter datasheet or HART configuration |
Fluid properties
| Input | What it means | Typical value / where to get it |
|---|---|---|
| Composition (mole %) | Natural gas analysis, 21 components, for AGA 8 | Gas chromatograph or lab report; presets for typical gases; save your own blends |
| Base (standard) conditions | Reference P and T for standard volume | 15 °C / 101.325 kPa (ISO), 60 °F / 14.73 psia (US gas), 0 °C (Nm³): use what the contract says |
| Viscosity | Only affects the Reynolds number (small effect on C) | Natural gas ≈ 0.0103 cP; air 0.018 cP; water 0.89 cP at 25 °C; steam is calculated |
| Isentropic exponent k | Used in the gas expansion factor | From AGA 8 or IF97 automatically; air 1.40, natural gas ≈ 1.27–1.32 |
| Molar mass M, Z (other gas) | Defines density for non-natural-gas gases and vapours | Process data sheet; presets for air, N₂, H₂, CO₂, O₂, propane, ammonia |
| Liquid density (flowing and base) | Density at line conditions and at 15 °C / 60 °F | Densitometer or lab report (API gravity for crude) |
Uncertainty inputs
| Input | What it means | Typical value |
|---|---|---|
| ΔP transmitter (% of span) | Transmitter accuracy; worse in % of reading at low flow | 0.065–0.1 % of span for modern smart transmitters |
| Bore d, pipe D | Manufacturing / measurement tolerance | d ± 0.05 %, D ± 0.25 % |
| Static pressure, temperature | Secondary instrument accuracy | P ± 0.1 % of reading, T ± 0.5 °C |
| Z, gas analysis | Equation-of-state and GC uncertainty | Z ± 0.1 % (AGA 8 normal range), analysis ± 0.2 % |
Pipeline, design-pressure and relief-valve inputs are explained inside those tools: Gas Pipeline Sizing and Relief Valve Quick Check.
Sizing an orifice plate
Choose Size the bore in the calculator and enter the maximum, normal and minimum flow. A practical sizing routine:
- Pick the ΔP span at maximum flow. Common choices are 100, 200 or 250 inH₂O (25, 50 or 62.27 kPa). Higher ΔP gives better resolution at low flow but more permanent pressure loss, and must stay below the plate and fitting's structural limit.
- Calculate the bore that passes the maximum flow at that ΔP. The calculator compares all the common spans side by side and marks the best one.
- Check β. Valid range 0.1–0.75; aim for about 0.4–0.6. A β that is too high means the ΔP span is too low (or the pipe is too small); too low wastes pressure.
- Check the flow range. Because ΔP ∝ flow², minimum flow should still give at least 10 % of span (about 32 % of maximum flow). If the range is wider, plan stacked transmitters or a plate change.
- Check gas limits: ΔP/P1 ≤ 0.20 for the AGA 3 expansion factor, and a reasonable pipe velocity.
- Specify the plate: bore at 20 °C / 68 °F with its tolerance, plate thickness and bore-edge thickness, and the 45° downstream bevel when the plate is thicker than the bore edge. The calculator lists these from AGA 3 Part 2.
4–20 mA and rangeability
The DP transmitter is normally set up linear: 4 mA = 0 ΔP, 20 mA = the calibrated span (URV). The square root is taken in the flow computer or DCS, not in both. Because of the square law:
- 25 % of the ΔP span is already 50 % of the flow, and 1 % ΔP is 10 % flow.
- Below roughly 10 % ΔP (≈ 32 % flow) small transmitter errors become big flow errors. One orifice + one transmitter covers about 3:1 in flow well.
- For wider ranges, use stacked transmitters (a low-range and a high-range DP on the same taps, the flow computer switching between them) or change the plate seasonally.
Errors that cost money
- Plate fitted backwards. The bevel must face downstream. Backwards, the flow can read several percent or more low.
- Worn or rounded edge, dirt, liquid or wax on the plate. A rounded edge lets more flow through for the same ΔP, so the meter reads low. Inspect plates on a schedule.
- Bent (dished) plate after a pressure surge or slug. Check flatness during inspection.
- Wrong bore or pipe ID in the flow computer. The flow goes with about d²: 1 % error in d is roughly 2 % in flow.
- Old gas composition. If the GC fails and the flow computer keeps an old analysis, Z, density and energy are all off.
- Pulsation from reciprocating compressors. ΔP is averaged as √(average ΔP) instead of the average of √ΔP, which over-reads (square-root error).
- Leaking manifold or equalising valve, wet or blocked impulse lines, and transmitter zero drift at low ΔP.
- Wrong base conditions or unit setup between the flow computer, SCADA and the contract.
Worked example
A 6-inch Schedule 40 meter run (D = 154.05 mm at 20 °C) with a 76.2 mm stainless steel plate measures pipeline-quality gas at 49 bar(g) and 15 °C, with 25 kPa ΔP. The calculator gives:
- β ≈ 0.495, Ev ≈ 1.031
- From AGA 8: Z ≈ 0.896 at flowing conditions, ≈ 0.998 at base conditions
- AGA 3: Cd ≈ 0.603 at ReD ≈ 3.2 million; Y ≈ 0.998
- Flow ≈ 14,250 kg/h ≈ 20,000 Sm³/h ≈ 0.48 million Sm³/d
- Uncertainty with good transmitters (0.1 % ΔP span, 0.1 % P, ±0.5 °C, 0.2 % gas analysis) ≈ ±0.5 %, dominated by Cd
Load it with the "6 in gas · 50 bar" example above and check each step yourself, then change the composition and watch Z and the flow change.
Q&A quiz
Standards and sources
- AGA Report No. 3 / API MPMS Chapter 14.3: Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids (Parts 1–4).
- AGA Report No. 8: Thermodynamic Properties of Natural Gas and Related Gases (Part 1 DETAIL and GROSS; Part 2 GERG-2008).
- AGA Report No. 5: Natural Gas Energy Measurement.
- ISO 5167-1 and -2: Measurement of fluid flow by means of pressure differential devices: orifice plates.
- NIST AGA8 reference code (public domain): github.com/usnistgov/AGA8, used for the calculator's AGA 8 DETAIL engine.
- AGA 3 Part 1, 3rd edition (1990), made public through incorporation by reference (law.resource.org): the calculator's AGA 3 discharge coefficient reproduces its Cd tables to within table rounding.
The standards are copyrighted and sold by AGA, API and ISO. This page summarises the ideas only; buy the current editions for design and fiscal work. Related: DP Transmitters for Flow · How Flow Meters Work · Square Root Extraction.