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ORIFICE PLATE SIZING CALCULATOR

ISO 5167-2:2022 concentric orifice plate sizing for liquid, gas, vapour and steam. Reader-Harris/Gallagher discharge coefficient. DP transmitter range recommendation.

ISO 5167-2:2022 Liquid / Gas / Steam Bore · Flow · Differential DP Transmitter Range PDF Report
1
Tag · Pipe · Meter
Identification
Enter flow rates + dP range → calculates orifice bore
Pipe Data
— select pipe above
Meter Setup
Operating Conditions
2
Fluid Properties
Fluid Phase
Liquid Properties
Volume-fraction weighted SG and viscosity. For preliminary engineering only.
COMPONENTVOL %
TOTAL 0.0%
3
Flow · Differential
Flow Rates
Differential Pressure
R
Calculation Results
ISO 5167-2:2022
ENTER INPUTS IN COLUMNS 1–3
THEN CLICK CALCULATE

RESULTS APPEAR HERE

ISO Orifice Plate Types — Reference Guide

ISO 5167-2:2022 · Annex A (Eccentric, Segmental) · Annex B (Quadrant Edge, Conic Entry) · ISA-RP3.2

ISO 5167-2:2022 defines eight orifice plate and tap type combinations. Each plate type has a mandated tap type, a specific discharge coefficient equation, a valid β range, and a valid Reynolds number range. The tap clock position (top / side / bottom on the pipe) is always determined by the fluid phase — regardless of plate type — per ISA-RP3.2 and ISO/TR 15377.

CONCENTRIC — FLANGE TAPS
StandardISO 5167-2:2022 main body
Cd equationReader-Harris/Gallagher (full RHG)
Tap positionL₁ = L₂ = 25.4 mm from plate face
β range0.20 – 0.75
ReD min5,000
ApplicationMost common type. Clean fluids, general process service. Preferred for standard installations worldwide.
CONCENTRIC — CORNER TAPS
StandardISO 5167-2:2022 main body
Cd equationRHG with L₁ = L₂ = 0
Tap positionAt plate faces (L₁ = L₂ = 0)
β range0.20 – 0.75
ReD min5,000
ApplicationSmall diameter pipes where 25.4 mm flange spacing is impractical. Common in European practice and small bore applications.
CONCENTRIC — RADIUS TAPS (D & D/2)
StandardISO 5167-2:2022 main body
Cd equationRHG with L₁ = 1D, L₂ = 0.47D
Tap position1D upstream, D/2 downstream
β range0.20 – 0.75
ReD min5,000
ApplicationGood accuracy across the full β range. Less sensitive to upstream flow disturbances than flange taps.
CONCENTRIC — PIPE TAPS (2½D & 8D)
StandardISO 5167-2:2022 main body
Cd equationRHG with L₁ = 2.5D, L₂ = 8D
Tap position2.5D upstream, 8D downstream
β range0.20 – 0.75
ReD min5,000
ApplicationOlder American practice. Taps in existing pipe fittings. Higher permanent pressure loss than radius or flange taps.
QUADRANT EDGE — CORNER TAPS  ISO 5167-2 Annex B.1
Cd equationFixed Cd = 0.7749 — constant, independent of Re
Tap typeCorner taps only — mandated by ISO 5167-2 Annex B.1
β range0.245 – 0.600
ReD range500 – 100,000
ApplicationViscous liquids and low Reynolds number service (fuel oils, heavy process fluids). The quarter-circle entry profile maintains stable Cd where sharp-edge plates are inaccurate.
CONIC ENTRY — CORNER TAPS  ISO 5167-2 Annex B.2
Cd equationFixed Cd = 0.734 — constant
Tap typeCorner taps only — mandated by ISO 5167-2 Annex B.2
β range0.100 – 0.316
ReD range50 – 4,000
ApplicationExtremely low Reynolds number service — laminar and transitional flow in very viscous fluids (polymers, adhesives, heavy oils). The 45° conical entry creates a stable vena contracta under laminar conditions.
ECCENTRIC — FLANGE SIDE TAPS  ISO 5167-2 Annex A.1
Cd equationRHG equation (same as concentric flange taps)
Tap typeFlange side taps only — 3 or 9 o'clock position
β range0.300 – 0.800
ReD min10,000
Bore — liquidOffset to bottom — solids and debris pass through without accumulating
Bore — gasOffset to top — liquid condensate drains away from measurement path
ApplicationDirty liquids, slurries, two-phase fluids where a concentric bore would accumulate solids or gas pockets at the measurement point.
SEGMENTAL — FLANGE TAPS  ISO 5167-2 Annex A.2
Cd equationRHG equation (same as concentric flange taps)
Tap typeFlange taps only — mandated by ISO 5167-2 Annex A.2
β range0.300 – 0.800
ReD min10,000
Bore — liquidFlat chord at bottom — full pipe cross-section keeps slurry moving
Bore — gasFlat chord at top — prevents liquid accumulation above bore
ApplicationHeavy slurries and dirty services. The semicircular bore provides a larger open area at the pipe wall compared to eccentric — better for high-solids content flows.

Tap Clock Position by Fluid Phase

The clock position of the taps on the pipe circumference is governed by the fluid phase — not the plate type. This rule applies to all concentric, quadrant edge, and conic entry plates. Eccentric and segmental plates always use side taps regardless of medium; the bore orientation handles phase separation instead.

FLUID PHASE TAP POSITION STANDARD / BASIS REASON
Gas / Vapour Top — 12 o'clock ISA-RP3.2, ISO/TR 15377 Prevents liquid accumulation in impulse lines, which creates a false dP reading
Liquid (clean) Bottom — 6 o'clock ISA-RP3.2, ISO/TR 15377 Prevents gas pockets forming in impulse lines, which cause measurement errors
Steam Side — 3 or 9 o'clock ISA-RP3.2 Condensate pots equalise impulse lines; side taps prevent both condensate slugs and steam flashing
Eccentric / Segmental Side — always ISO 5167-2 Annex A Tap position fixed by standard; bore orientation (not tap position) provides phase separation

What is an Orifice Plate?

An orifice plate is a thin plate with a precisely machined hole (bore) inserted into a pipeline. As fluid flows through the bore, kinetic energy increases and static pressure drops. This differential pressure is proportional to the square of the flow rate and forms the basis of orifice plate flow measurement.

Orifice plates are the most widely used primary flow element in the process industries due to their simplicity, low cost, proven reliability and established international standards. They are used for liquids, gases, vapours and steam across a wide range of pipe sizes and flow conditions.

Complete Input Field Guide

Every input field explained — what it means, what value to enter, and how it affects the calculation.

COLUMN 1 — PIPE, METER SETUP & IDENTIFICATION

INSTRUMENT TAG

Optional. Enter the instrument tag number (e.g. FE-1001). Appears in the PDF report header and file name. Does not affect calculation.

CALCULATION MODE

Calculate Bore: Enter flow rates + max dP → tool sizes the bore diameter. Most common mode for new designs.
Calculate Flow: Enter existing bore + max dP → tool calculates the flow at that dP. Use for checking existing plates.
Calculate dP: Enter existing bore + flow → tool calculates the differential pressure. Use for transmitter range verification.

NOMINAL PIPE SIZE (NPS) & SCHEDULE

Select the pipe size and wall thickness schedule. The tool automatically fills the inside diameter D from ASME B36.10M pipe data. If your pipe has a non-standard ID (e.g. lined pipe, actual measured ID), select "Custom ID" and enter the measured inside diameter directly. Always use the actual measured bore — small errors in D cause large errors in flow.

PLATE / TAP TYPE

Concentric Flange Taps: Standard choice for most applications. Taps 25.4 mm from plate faces.
Corner Taps: For small pipes where 25.4 mm spacing is impractical.
Quadrant Edge: Viscous liquids, Re 500–100,000. Fixed Cd = 0.7749.
Conic Entry: Very viscous fluids, Re 50–4,000 only. Fixed Cd = 0.734.
Eccentric: Dirty liquids and slurries. Bore offset to bottom (liquid) or top (gas).
Segmental: Heavy slurries. Semicircular bore, flat chord at bottom for liquid.

ELEMENT & PIPE MATERIAL

Used to calculate the thermal expansion factor Fa. At operating temperatures different from 20°C, the bore and pipe ID change slightly. Fa corrects for this per ISO 5167-2. For most ambient-temperature applications the correction is negligible (<0.01%). At high temperatures (>200°C) or cryogenic service it becomes significant. Select the actual material of the orifice plate and the pipe separately — they may differ.

UPSTREAM DISTURBANCE TYPE

The fitting or obstruction immediately upstream of the orifice plate. This determines the minimum straight pipe length required between that fitting and the orifice plate. If multiple disturbances are present, use the one requiring the longest straight run. The tool reads ISO 5167-2:2022 Table 1 directly based on this selection and the calculated beta ratio. If your upstream piping is unknown or very complex, use Two 90° bends — different planes as a conservative default.

COLUMN 2 — OPERATING CONDITIONS & FLUID PROPERTIES

OPERATING PRESSURE

The upstream static pressure P₁ at the orifice plate, at maximum flow conditions. Used to: (1) calculate gas density for compressible flow, (2) compute the dP/P₁ ratio for the choked flow and cavitation checks, (3) calculate gas expansion factor Y. Enter as gauge pressure (barg) or absolute pressure (bara/kPaa/psia) — select the unit. For gas service this is critical — a 10% error in pressure gives a ~5% error in flow.

OPERATING TEMPERATURE

The fluid temperature at the orifice plate. Used to: (1) calculate gas density via ideal gas law, (2) interpolate liquid viscosity between the two reference temperatures from the database, (3) calculate the thermal expansion factor Fa for bore correction. For steam, the operating pressure auto-calculates saturation temperature. For superheated steam enter the actual steam temperature.

LIQUID — SPECIFIC GRAVITY (SG)

Relative density of the liquid compared to water at 15°C. SG = ρ_fluid / ρ_water. Water = 1.0, light hydrocarbons ≈ 0.55–0.75, heavy oils ≈ 0.85–0.98. Select a fluid from the database to auto-fill SG, or enter directly. SG must be at actual operating conditions, not at standard conditions — for hot or pressurised liquids, use the density at operating P and T.

LIQUID — VISCOSITY

Dynamic viscosity in cP (= mPa·s). Affects the pipe Reynolds number ReD, which directly enters the RHG discharge coefficient equation. For most clean liquids (water, light hydrocarbons) at moderate temperatures the effect on Cd is small. For viscous fluids (heavy oils, glycols) at low temperatures the effect is large — consider Quadrant Edge plate if Re < 10,000. Select from database for automatic temperature interpolation.

GAS — MOLECULAR WEIGHT (MW)

Molar mass of the gas in g/mol. Used with P and T to calculate density via ideal gas law: ρ = P·MW/(Z·R·T). Common values: Air = 28.97, Methane = 16.04, Natural Gas ≈ 16–20 (varies by composition), Propane = 44.1, CO₂ = 44.01, Hydrogen = 2.016, Nitrogen = 28.01. For gas mixtures use the Gas Mixture Builder to calculate blended MW by Kay's rule. Even a small error in MW propagates directly to a proportional error in density and flow.

GAS — COMPRESSIBILITY (Z)

Real gas compressibility factor. Z = 1.0 for ideal gas. For most gases at low pressure (<10 barg) Z ≈ 0.97–1.00 and the error from using Z=1 is small. At high pressures (>50 barg) or near the critical point Z can deviate significantly — use an equation of state (Peng-Robinson, SRK) or NIST data to find the correct Z. For natural gas at pipeline conditions (40–80 barg, 0–50°C), Z ≈ 0.87–0.94.

GAS — Cp/Cv RATIO (k / κ)

Isentropic exponent. Used to calculate: (1) gas expansion factor Y — the correction for compressible flow through the orifice, (2) sonic velocity and critical pressure ratio for choked flow check. Common values: Air = 1.40, Methane = 1.31, Propane = 1.14, CO₂ = 1.30, Hydrogen = 1.41, Steam ≈ 1.135. Higher k → less compressibility effect, higher sonic velocity. Error in k has moderate effect on Y at high dP ratios.

BASE CONDITIONS (Standard P & T)

The reference conditions used to express standard volume flow (Sm³/hr, SCFH etc). Default: 101.325 kPaa, 15°C per ISO 5024. Different industries use different standards — oil & gas often uses 14.696 psia / 60°F (US), or 101.325 kPaa / 0°C (IUPAC). Only affects how standard volume results are displayed — does not change bore sizing or mass flow calculations.

COLUMN 3 — FLOW RATES & DIFFERENTIAL PRESSURE

MAXIMUM FLOW

The highest flow rate the meter must measure. The orifice bore is sized so that at this flow rate, the differential pressure equals the Max dP Range you enter. Typically set to 110–125% of normal flow to allow margin. In bore mode this is a required input. In flow/differential mode it is optional — used only to calculate the flow table.

NORMAL FLOW

The expected operating flow rate. Used to calculate the normal operating dP, which is used for: (1) DP transmitter range recommendation — targets normal dP at 40–65% of transmitter span for good accuracy, (2) Reynolds number display (shown at normal flow per industry convention). Typically 60–80% of maximum flow.

MINIMUM FLOW

The lowest flow rate the meter must reliably measure. Used only for the flow table display — shows the minimum dP at this flow. Helps verify that minimum flow is above the ReD minimum for the selected plate type. Orifice plates have poor turndown (typically 3:1 to 4:1 on flow = 9:1 to 16:1 on dP) — if minimum flow is very low, consider a different meter type.

MAX DIFFERENTIAL PRESSURE (TRANSMITTER RANGE)

This is the DP transmitter measurement span — not the allowable pressure loss. The bore is sized so that at maximum flow, the differential pressure equals this value. The tool then checks this value against three limits:
dP/P₁ < 0.25 for liquids — above this, cavitation or flashing risk
dP/P₁ < critical pressure ratio for gas — above this, flow is choked (sonic) and the orifice equation is invalid
Transmitter range recommendation — tool selects from standard range series (25, 50, 100, 160, 250 mbar...) targeting normal dP at 40–65% of span
Typical starting point: try 250 mbar (100 inH₂O) for most liquid applications, 500 mbar for gas.

WARNINGS, ERRORS & HOW TO FIX THEM

⚠ ERROR: Beta ratio out of range (0–1)

Cause: The calculated bore is larger than the pipe ID or negative.
Fix: Increase the max dP range, decrease the max flow rate, or select a larger pipe size. Beta must be between 0.20 and 0.75 for standard plates.

⚠ WARNING: Beta below minimum

Cause: Bore is too small relative to pipe — very high dP or very low flow.
Fix: Reduce max dP range, or select a smaller pipe size. For standard plates β min = 0.20. A very small beta gives high permanent pressure loss and poor Cd accuracy.

⚠ WARNING: Beta above maximum

Cause: Bore is too large — very low dP or very high flow for the pipe size.
Fix: Increase max dP range, or select a larger pipe size. For standard plates β max = 0.75. High beta gives poor signal strength and increased sensitivity to upstream disturbances — requires longer straight run.

⚠ WARNING: Reynolds number below minimum

Cause: Fluid is too viscous, pipe is too small, or flow rate is too low for the RHG equation to be valid.
Fix options: (1) Select a larger pipe size to increase velocity, (2) increase flow rate, (3) switch to Quadrant Edge plate (valid Re 500–100,000) or Conic Entry plate (valid Re 50–4,000) for viscous service.

⚠ WARNING: High dP/P ratio — cavitation risk (liquid)

Cause: dP/P₁ > 0.25. The pressure at the vena contracta drops so low that it approaches the vapour pressure, causing flashing or cavitation. This damages the plate and creates inaccurate readings.
Fix: (1) Reduce max dP (increase beta — reduce dP range), (2) increase operating pressure P₁, (3) check vapour pressure input is correct. If the process cannot be changed, a Venturi meter (lower dP loss) may be required.

⚠ WARNING: CHOKED FLOW — sonic at bore (gas)

Cause: dP/P₁ ≥ critical pressure ratio = (2/(κ+1))^(κ/(κ-1)). Gas velocity at the bore has reached the speed of sound — the orifice equation completely breaks down. Flow does not increase with further increase in dP.
Fix: (1) Significantly reduce max dP range, (2) increase beta (larger bore), (3) increase operating pressure. If choked flow is the actual process condition, a critical flow nozzle (ISO 9300) is the correct meter type, not an orifice plate.

ⓘ WARNING: High Mach number at bore (Ma > 0.25)

Cause: Gas velocity at the bore exceeds 25% of sonic velocity. Compressibility effects are significant and the gas expansion factor Y correction becomes important.
Fix: Review Y factor result. If Ma > 0.3, consider reducing dP range or increasing beta. The Y equation in ISO 5167-2 is valid up to about dP/P₁ = 0.40 — beyond this use a Venturi meter.

ⓘ WARNING: Pipe diameter below 50 mm

Cause: ISO 5167-2 specifies a minimum pipe diameter of 50 mm for the standard orifice plate equations. Below this, manufacturing tolerances become a significant percentage of the bore diameter, increasing uncertainty.
Fix: If the small pipe is unavoidable, apply extra manufacturing tolerances and increase uncertainty estimate. Consider a different meter type (rotameter, Coriolis, magnetic) for very small pipes.

ⓘ WARNING: Quadrant/Conic gas expansion Y not validated

Cause: ISO 5167-2 Annex B does not provide a gas expansion factor Y for Quadrant Edge or Conic Entry plates — these were designed primarily for liquid service.
Fix: For gas service with these plates, use the Y result as an approximation only and confirm with the plate manufacturer. Consider using a standard concentric plate for gas applications.

⚠ NOTE: Pipe taps — NOT in ISO 5167-2:2022

ISO 5167-2:2022 change: Pipe taps (2.5D upstream, 8D downstream) were removed from ISO 5167-2:2022. They are no longer a recognised tap type under this standard. For pipe tap applications use AGA Report No.3 (natural gas) or ASME MFC-3M instead.
This tool: Pipe taps are retained for checking and documenting existing installations using the AGA-3/Stolz equation. Cd is calculated per ASME MFC-3M, not ISO 5167-2. Use flange taps for all new designs.

ⓘ INFO: Eccentric / Segmental plate installation notes

For eccentric plates, the bore centre offset and orientation (top/bottom) is shown in the Eccentric Plate Geometry result section. For segmental plates, the chord width and height are shown in the Segmental Plate Geometry section — these are the actual plate fabrication dimensions. The installation diagram shows the correct bore orientation for the selected fluid phase.

⚠ WARNING: Plate Thickness Conflict (ISO 5167-2 Sec.7.1)

Cause: ISO 5167-2:2022 Sec.7.1 requires a minimum plate thickness e_min = max(3 mm, 0.005×D) to give the plate mechanical rigidity. It also requires a maximum thickness e_max = 0.05×D (for β≤0.65) or 0.02×D (for β>0.65) so the plate is thin enough not to disturb the vena contracta. For small pipes (D≤50 mm) at high beta ratios, e_min can exceed e_max — making it physically impossible to satisfy both constraints with a standard plate.
Fix: Select a larger pipe size to increase D, or reduce the beta ratio (increase the max dP range). Alternatively, consult the plate manufacturer — special thin-plate designs exist for small-bore high-beta applications.

ⓘ INFO: Flow Uncertainty (ISO 5168:2005)

The flow uncertainty is computed using the full ISO 5168:2005 quadrature propagation formula: δW/W = √[(δCd)² + (2δd)² + (2δD)² + (δρ/2)² + (δΔP/2)²]. The factor of 2 on bore d and pipe D arises because W ∝ d² and W ∝ D⁻². Assumed component uncertainties: δCd = 0.5% (standard concentric plates, Re≥10,000), δd = 0.07% (ISO-tolerance machined bore), δD = 0.10% (pipe schedule data), δρ = 0.20% liquid / 0.50% gas, δΔP = 0.10% (calibrated transmitter).
For custody transfer applications: obtain δCd from the vendor certificate, measure pipe ID on-site (reduces δD to ~0.03%), and use a calibrated transmitter with known δΔP. These improvements can reduce total uncertainty to below 0.3%.

TARGETING A GOOD BETA RATIO

The beta ratio β = d/D is the single most important design parameter. The target range for good engineering practice is 0.40 ≤ β ≤ 0.65:

BETA RANGE PRESSURE LOSS dP SIGNAL STRAIGHT RUN RECOMMENDATION
β < 0.20 Very high Very strong Minimum Below ISO limit — avoid
0.20 – 0.39 High Strong Short Acceptable — high loss, good signal
0.40 – 0.65 Moderate Good Moderate Optimal range — best balance
0.65 – 0.75 Low Weak Long Acceptable — low loss but needs more straight run
β > 0.75 Very low Very weak Maximum Above ISO limit — avoid

To adjust beta: increase max dP range to decrease beta (smaller bore), or decrease max dP range to increase beta (larger bore). Alternatively change the pipe size.

ISO 5167 — Discharge Coefficient (Cd)

This calculator implements the Reader-Harris/Gallagher (RHG) equation per ISO 5167-2:2022, which is the internationally recognised standard for the discharge coefficient of concentric orifice plates. The RHG equation was first standardised in ISO 5167-2:2003 and confirmed unchanged in the 2022 revision.

READER-HARRIS/GALLAGHER EQUATION — ISO 5167-2:2022 EQ.1
Cd = 0.5961 + 0.0261β² − 0.216β⁸ + 0.000521(10⁶β/ReD)0.7
+ (0.0188 + 0.0063A)β³·⁵(10⁶/ReD)0.3
+ (0.043 + 0.080e−10L₁ − 0.123e−7L₁)(1 − 0.11A)β⁴/(1 − β⁴)
− 0.031(M₂ − 0.8M₂1.11.3
where: A = (19000β/ReD)0.8 · L₁ = L₂ = 25.4/D (mm) for flange taps · M₂ = 2L₂/(1−β)
Small pipe correction (D < 71.12 mm): Cd += 0.011(0.75 − β)(2.8 − D/25.4)

Beta Ratio (β = d/D)

Ratio of orifice bore (d) to pipe inside diameter (D). Valid range per ISO 5167: 0.20 to 0.75. Optimal engineering range: 0.40 to 0.65 for balanced accuracy and pressure loss.

Pipe Reynolds Number (ReD)

ReD = ρvD/μ. ISO 5167 valid range: ReD ≥ 5,000. The Cd equation converges through iteration since ReD depends on velocity which depends on flow area which depends on Cd. This tool uses 200 iterations.

Mass Flow Rate Equation

ISO 5167-2:2022 — MASS FLOW EQUATION
ṁ = Cd · E · (π/4) · d² · Y · √(2ΔP · ρ₁)
ṁ = mass flow rate (kg/s)
Cd = discharge coefficient (dimensionless)
E = velocity of approach factor = 1/√(1−β⁴)
d = orifice bore diameter (m)
Y = gas expansion factor (1.0 for liquid)
ΔP = differential pressure (Pa)
ρ₁ = upstream fluid density (kg/m³)
β = d/D = beta ratio

Gas Expansion Factor Y — ISO 5167-2:2022 Eq.4

Y = 1 − (0.351 + 0.256β⁴ + 0.93β⁸) × [1 − (1 − ΔP/P₁)1/κ]

Y corrects for the reduction in gas density as it expands through the orifice bore. For liquids Y = 1.0. For gases at moderate differentials (ΔP/P₁ < 0.25) Y is typically 0.97 to 0.99. κ is the isentropic exponent (Cp/Cv ratio).

Tap Types and L₁/L₂ Parameters

The tap type determines where the pressure is measured upstream (L₁) and downstream (L₂) of the orifice plate. These values directly enter the RHG discharge coefficient equation and must match the actual installation.

TAP TYPE L₁ L₂ TYPICAL USE
Flange Taps 25.4/D 25.4/D Most common — standard process plant
Corner Taps 0 0 Small bore pipes, D < 50 mm
Radius Taps (D-D/2) 1.0 0.47 Custody transfer, higher accuracy
Pipe Taps (2½D-8D) 2.5 8.0 Older installations, US practice

Straight Run Requirements — ISO 5167-2:2022 Table 1

Minimum straight pipe lengths upstream and downstream of the orifice plate, in pipe diameters (D), for each upstream disturbance type and beta ratio. Always use the largest value applicable to your actual piping configuration. For multiple disturbances, use the value for the most demanding one.

Quadrant Edge and Conic Entry plates (ISO 5167-2 Annex B): Fixed 10D upstream, 5D downstream — independent of beta ratio and upstream disturbance.

UPSTREAM DISTURBANCE β≤0.20 β≤0.25 β≤0.30 β≤0.35 β≤0.40 β≤0.45 β≤0.50 β≤0.60 β≤0.67 β≤0.75
Single 90° bend 6666101014182044
Two 90° bends — same plane 6666101014182044
Two 90° bends — different planes 66615151534444444
Reducer (2D→D over 1.5D–3D) 555555891012
Expander (0.5D→D over D–2D) 10101010222228363636
Gate valve (fully open) 9999999121224
Globe / angle valve (fully open) 18181818181818181818
Thermometer pocket / well 445566791118
Downstream (all disturbances) 4444445678

All values in pipe diameters (D). Highlighted values indicate where the disturbance type demands significantly more straight run than a single bend — pay special attention to out-of-plane bends and expanders at high beta ratios. Source: ISO 5167-2:2022 Table 1.

Permanent Pressure Loss

ΔPw/ΔP = (√(1 − β⁴(1 − Cd²)) − Cdβ²) / (√(1 − β⁴(1 − Cd²)) + Cdβ²)

Exact ISO 5167-2:2022 Sec.6.4 formula. The permanent pressure loss is the net energy permanently lost to turbulence and friction downstream of the orifice plate — it cannot be recovered. It is always less than the measured differential pressure ΔP.

Note: A simplified approximation ΔPw ≈ ΔP × (1 − β1.9) is sometimes seen in literature but has errors of up to 5.9% at β = 0.75. This tool uses the exact formula. At β = 0.5 approximately 70% of ΔP is permanently lost; at β = 0.7 approximately 51% is lost. This is the key disadvantage versus Venturi meters which recover 85–90% of differential, but orifice plates are far cheaper to install and maintain.

DP Transmitter Range Selection

Selecting the correct DP transmitter range is as important as sizing the orifice bore. The orifice plate has a square-root relationship between differential pressure and flow:

Q ∝ √ΔP
ΔPnormal = ΔPmax × (Qnormal/Qmax
% Flow = √(ΔP / ΔPrange) × 100

This tool recommends a transmitter range from the standard instrument range series (25, 50, 100, 160, 250, 400, 630, 1000 mbar...) such that the normal flow differential falls between 40% and 65% of the transmitter range. This gives adequate turndown (typically 3:1 to 4:1 on flow) while maintaining good accuracy at normal flow. The square-root relationship means a 3:1 flow turndown requires a 9:1 dP turndown — the key limitation of orifice plate meters.

Gas Mixture Properties — Calculation Methods

For gas mixtures, the bulk properties (MW, Cp/Cv, viscosity) must be calculated from the individual component properties and their mole fractions. This tool uses the following mixing rules.

Molecular Weight — Kay's Rule (Exact for Ideal Gas)

MWmix = Σ (yi × MWi)

Where yi is the mole fraction of component i. This is exact for ideal gas mixtures and is the same equation used in all process simulation software. Mole fraction = mole percent / 100.

Cp/Cv Ratio — Mole-Weighted Cp

Cpmix = Σ(yi × MWi × Cpi) / MWmix
Cvmix = Cpmix − R/MWmix
kmix = Cpmix / Cvmix

Where R = 1.9859 BTU/(lbmol·°F) = 8.314 J/(mol·K). Cp values are from the InstruCalc fluid database at average process temperature. The k ratio is critical for gas expansion factor Y calculation.

Viscosity — Wilke's Method (1950)

μmix = Σ [ yi × μi / Σj(yj × φij) ]
φij = [1 + (μij)0.5 × (MWj/MWi)0.25]² / [8(1 + MWi/MWj)]0.5

Wilke's method (1950) is the industry standard for gas mixture viscosity and is used in HYSYS, PRO/II and other process simulators. It gives results within 2% of experimental values for most non-polar gas mixtures at low to moderate pressures.

Viscosity vs Temperature — Log-Linear Interpolation

ln(μ) = ln(μ₁) + [(T − T₁)/(T₂ − T₁)] × [ln(μ₂) − ln(μ₁)]

Viscosity varies exponentially with temperature (Walther's equation). Log-linear interpolation between the two database reference temperatures gives significantly better accuracy than simple linear interpolation, especially over large temperature ranges. The interpolated value is shown with a note indicating the reference temperatures used.

Standard Volume Flow vs Actual Volume Flow

For gas flow measurement, flow rates are commonly expressed in standard (or normal) conditions rather than at actual flowing conditions. This allows comparison of gas quantities independent of operating pressure and temperature.

STANDARD TO ACTUAL VOLUME CONVERSION
Qactual = Qstd × (Pbase/Pflow) × (Tflow/Tbase) × (Zflow/Zbase)
ṁ = Qstd × ρbase
ρbase = Pbase × MW / (R × Tbase)

Base conditions per ISO 5024: Pbase = 101.325 kPaa (14.696 psia), Tbase = 15°C (59°F). Units: sm³ = standard cubic metres at base conditions. The tool converts standard volume to mass flow internally using base density.

Frequently Asked Questions

Why does viscosity matter for orifice plate sizing?

Viscosity determines the pipe Reynolds number ReD = ρvD/μ, which directly enters the RHG discharge coefficient equation. At high Re (above 10⁶) Cd is nearly independent of ReD so viscosity has little effect. At lower Re (below 10⁵) — typical for viscous liquids, small pipes, or low flow rates — viscosity significantly affects Cd and therefore the calculated bore diameter. If Re falls below 5,000 (the ISO 5167 minimum for standard plates), consider switching to a Quadrant Edge plate (Re 500–100,000) or Conic Entry plate (Re 50–4,000).

Is this suitable for custody transfer calculations?

This tool implements the full ISO 5167-2:2022 RHG equation and is suitable for preliminary engineering and instrument specification. For legal custody transfer applications, the final calculation must be performed by the flow element vendor using certified software, and the plate must be manufactured and inspected to ISO 5167 tolerances. For natural gas custody transfer, AGA Report 3 (which uses the same RHG equation) applies.

What is the difference between permanent pressure loss and differential pressure?

The differential pressure ΔP is the measured pressure difference between the upstream and downstream taps — this is the signal used to calculate flow. Most of this is recovered as the flow expands after the orifice. The permanent pressure loss ΔPw is computed from the exact ISO 5167-2:2022 Sec.6.4 formula using Cd and β — it represents the energy permanently lost to turbulence and friction, a real operating cost. At β = 0.5, about 70% of ΔP is permanently lost; at β = 0.7 about 51% is lost. Venturi meters recover 85–90% by contrast, but cost much more.

When should I use eccentric or segmental plates instead of concentric?

Use eccentric or segmental plates when solids, slurries, or a second phase (gas in liquid, liquid in gas) are present. A concentric bore accumulates solids at the bottom of the pipe and creates gas pockets at the top — both cause measurement errors and plate erosion. Eccentric plates shift the bore toward the pipe wall (bottom for liquid/slurry, top for gas) to keep the measurement path clear. Segmental plates use a semicircular bore with the open segment at the bottom (liquid) or top (gas), providing a larger solids-handling cross-section. Both types use the same RHG Cd equation as concentric plates with flange taps.

How do I size the DP transmitter range?

The tool automatically recommends a transmitter range from the standard instrument series (25, 50, 100, 160, 250, 400, 630, 1000 mbar...) targeting normal flow dP at 40–65% of the transmitter span. This gives a turndown of approximately 3:1 to 4:1 on flow (9:1 to 16:1 on dP). The orifice plate's square-root relationship limits practical turndown — if you need more, consider a multi-range transmitter or a different meter technology. The DP range you enter determines the bore size: increasing it gives a smaller bore (lower beta), decreasing it gives a larger bore (higher beta).

Is this suitable for custody transfer calculations?

This tool implements the full ISO 5167-2:2022 RHG equation and is suitable for preliminary engineering and instrument specification. For legal custody transfer applications, the final calculation must be performed by the flow element vendor using certified software, and the plate must be manufactured and inspected to ISO 5167 tolerances. For natural gas custody transfer, AGA Report 3 (which uses the same RHG equation) applies.

Standards and References

ISO 5167-2:2022

Measurement of fluid flow by pressure differential devices — Part 2: Orifice plates. Second edition, replaces 2003. Key 2022 changes: pipe taps removed from scope; revised plate edge thickness for β < 0.20; corrected spacing for two 45° bends; flow calibration section added. RHG discharge coefficient equation and Y expansion factor are unchanged from 2003.

ISO 5168:2005

Measurement of fluid flow — Procedures for the evaluation of uncertainties. Used for the flow uncertainty percentage calculation.

ISO 5024:1999

Petroleum liquids and gases — Measurement — Standard reference conditions. Base conditions for standard volume: 101.325 kPaa, 15°C.

ASME B36.10M

Welded and Seamless Wrought Steel Pipe. Pipe inside diameter schedule data for NPS ½ to NPS 24, all standard schedules.

Reader-Harris & Gallagher (1998)

A new equation for the orifice discharge coefficient. Presented at the 1998 FLOMEKO Conference. Forms the basis of ISO 5167-2:2022.

Wilke C.R. (1950)

A viscosity equation for gas mixtures. Journal of Chemical Physics, 18(4):517–519. Used for gas mixture viscosity calculation.

AGA Report No.3 / ASME MFC-3M

AGA Report No.3 (American Gas Association) and ASME MFC-3M cover pipe tap orifice meters, which are outside the scope of ISO 5167-2:2022. The AGA-3/Stolz equation is used in this tool for pipe tap Cd calculation.

For preliminary engineering and instrument specification. For custody transfer and safety-critical applications, verify with your flow element vendor.  |  © EkaTools.com