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ISO 5167 Orifice Plate Calculator

Compute ISO 5167-2 orifice-plate discharge with Reader–Harris/Gallagher C from β, Re_D, and tapping. Runs locally. Not tank orifice C_d A √(2gH), not given C_d=0.61, not ISA 1932 nozzle, not venturi C_d=0.98.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 5/5 tests · Production surface contract 1/1 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
ISO 5167-2 incompressible orifice-plate discharge from D, d or β, Re_D, tapping, and Δp. Invert Δp. Report Reader–Harris/Gallagher C from β, Re_D, and tapping.
Scope
ISO 5167-2 orifice plate: Q = C E A2 √(2Δp/ρ); Reader–Harris/Gallagher C from β, Re_D, and tapping; incompressible ε=1; C is reported, not an input
Verification
Engine tested · 5/5 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Evidence
5 property · Production surface contract 1/1 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 163 remain CURRENT) @ 2026-09-17T23:16:16.380Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

DischargeQ = C E A2 √(2Δp / ρ)
Approachβ = d/D · E = 1/√(1 − β⁴)
RHG C (corner L1=L2′=0)C = 0.5961 + 0.0261 β² − 0.216 β⁸ + 0.000521 (10⁶ β / Re_D)^0.7 + (0.0188 + 0.0063 A) β^3.5 (10⁶ / Re_D)^0.3
iSI. Incompressible ε=1. C is reported from β, Re_D, and tapping; do not send C_d. Do not send query v — that is calculation_version. D-D/2 tappings are out of scope.

How to use

1

Enter pipe D and bore d

Pipe D in [50 mm, 1000 mm] and bore d ≥ 12.5 mm. REST may send D+beta instead of d. This is not a nozzle D1+D2 pair.

2

Enter Re_D

Pipe Reynolds number on D. Do not send ρ, μ, and v to wrap the Reynolds page.

3

Choose tapping and enter Δp

Corner tappings are the default. Flange uses L1=L2′=25.4 mm/D. Invert on the Δp tab. Read C on the C tab without Δp.

Example calculations

Common configurations with formula and result.

ϟ

β=0.5, Re_D=10⁶, 10 kPa, corner

D=0.1 m, d=0.05 m, Δp=10 kPa, ρ=1000 kg/m³, corner tappings

C from Reader–Harris/Gallagher, Q=C E A2 √(2Δp/ρ)
C≈0.60378 · Q≈0.005476 m³/s
ϟ

Same β via D+beta

D=0.1 m, beta=0.5

d=β D
same C

ISO 5167 Orifice Plate calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
ISO 5167-2 orifice plate. Incompressible Q = C E A2 √(2Δp/ρ) with E=1/√(1−β⁴). C is the Reader–Harris/Gallagher coefficient from β, Re_D, and tapping (corner default, flange optional). β∈[0.10,0.75], D∈[50 mm, 1000 mm], d≥12.5 mm. Not tank Q=C_d A √(2gH), not a given C_d=0.61, not ISA 1932, not a venturi with C_d=0.98.
What it calculates
ISO 5167-2 incompressible orifice-plate discharge from D, d or β, Re_D, tapping, and Δp. Invert Δp. Report Reader–Harris/Gallagher C from β, Re_D, and tapping.
Inputs
  • mode?
  • D
  • d|beta
  • Re_D
  • tapping?
  • dP?
  • rho?
  • Q?
Outputs
  • Q?
  • D
  • d
  • beta
  • E
  • A1
  • A2
  • C
  • Cd
  • Re_D
  • tapping
  • v1?
  • v2?
  • rho?
  • dP?
  • mode
  • model
Formula
Q = C E A2 √(2Δp/ρ); Reader–Harris/Gallagher C from β, Re_D, tapping (corner L1=L2′=0; flange L1=L2′=0.0254/D)
Assumptions
  • ISO 5167-2 orifice plate: Q = C E A2 √(2Δp/ρ); Reader–Harris/Gallagher C from β, Re_D, and tapping; incompressible ε=1; C is reported, not an input
  • Corner tappings default (L1=L2′=0); flange L1=L2′=25.4 mm/D; β∈[0.10,0.75]; D∈[50 mm,1000 mm]; d≥12.5 mm; Re_D≥5000 (β≤0.56) or 16000 β² (β>0.56)
  • Not tank orifice C_d A √(2gH), not given C_d=0.61, not ISA 1932 nozzle, not venturi C_d=0.98, not Q=Av, not Darcy f, not D-D/2 tappings, not compressible ε
Units
  • SI; D, d in m; Q in m³/s; Δp in Pa; ρ in kg/m³; Re_D dimensionless
Boundary conditions
  • missing D, d/beta, Re_D, Δp, Q, or ρ when required → MISSING_REQUIRED_INPUT
  • D outside [50 mm, 1000 mm], d < 12.5 mm, β outside [0.10,0.75], or Re_D below the ISO floor → VALUE_OUT_OF_RANGE
  • C_d given, nozzle D1+D2, tank H, A or v, Darcy f, μ, Cv/Kv, K, ε, kind, D-D/2 tapping → MIXED_INPUT_ENCODING
  • mode=Cd or unknown mode → INVALID_MODE
Example
D=0.1 d=0.05 Re_D=1e6 dP=10000 rho=1000 corner → C≈0.60378 Q≈0.005476
Validation cases

4 published on this page · 5/5 tests · Production surface contract 1/1 · View evidence

  • D=0.1 d=0.05 Re_D=1e6 dP=10000 rho=1000 → C≈0.60378 Q≈0.005476
  • D=0.1 d=0.05 Re_D=1e6 Cd=0.61 → MIXED_INPUT_ENCODING
  • D1=0.1 D2=0.05 Re_D=1e6 dP=10000 rho=1000 → MIXED_INPUT_ENCODING
  • mode=Cd D=0.1 d=0.05 Re_D=1e6 → INVALID_MODE
Sources
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute ISO 5167-2 orifice-plate discharge from β, Re_D, tapping, and Δp. C is computed, not supplied.

Supported and not supported

Supported — Q from D, d or β, Re_D, tapping, and Δp · invert Δp · C from β, Re_D, and tapping · API physics.fluid.iso_orifice

Not supported — tank C_d A √(2gH), given C_d=0.61, ISA 1932 nozzle, venturi C_d=0.98, Q=Av, Darcy f, compressible ε, D-D/2 tappings

Agent / API notes

Capability id: physics.fluid.iso_orifice · tool id: iso-orifice · pin 1.0.0.

{ "D": 0.1, "d": 0.05, "Re_D": 1000000, "dP": 10000, "rho": 1000 }

Modes: flow (default), pressure, coefficient. Optional tapping: corner (default) or flange. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/iso-orifice. There is no /calc/fluid.

Other calculators in this family: Orifice discharge, ISO 5167 nozzle, Venturi meter, Flow rate .

Q Orifice discharge › Q ISO 5167 nozzle › Q Venturi meter › Q Flow rate ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this the tank orifice page?

No. Tank Q=C_d A √(2gH) with a given C_d is /calc/physics/orifice-discharge. Sending H here is MIXED_INPUT_ENCODING. This page computes C from β and Re_D.

Is C_d = 0.61?

No. A given sharp-edged C_d (default 0.61) is /calc/physics/orifice-discharge. Sending C_d here is MIXED_INPUT_ENCODING. At β=0.5 and Re_D=10⁶ this page reports C≈0.60378, not 0.61.

Is this an ISA 1932 nozzle?

No. ISO 5167-3 ISA 1932 is /calc/physics/iso-nozzle (D1+D2, C≈0.97656 at this β and Re). Sending D1 and D2 here is MIXED_INPUT_ENCODING.

Is this a venturi meter?

No. A classical venturi with a given C_d (default 0.98) is /calc/physics/venturi. Sending C_d here is MIXED_INPUT_ENCODING.

Are D-D/2 tappings supported?

No. This seed is corner (default) or flange. D-D/2 is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. Sending A or v is MIXED_INPUT_ENCODING.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine isoOrifice wrapper.