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Physics calculator

ISO 5167 Nozzle Calculator

Compute ISO 5167-3 ISA 1932 nozzle discharge with C from β and Re_D, not a given C_d. Runs locally. Not a venturi wrap with C_d=0.98, not orifice C_d=0.61, not Q=Av, and not Darcy.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q = C E A2 √(2Δp/ρ) with ISA 1932 C from β and Re_D; plus pressure and coefficient solves; + O3 mpmath tabulated discharge.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Q = C E A2 √(2Δp/ρ) with ISA 1932 C from β and Re_D; plus pressure and coefficient solves; + O3 mpmath tabulated discharge.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not given C_d, not RHG orifice, not venturi type C, not long-radius, not Q=Av, not Darcy, not compressible ε.
Numerical scope
O2: ISO 5167-3 ISA 1932 Q=C E A2 √(2Δp/ρ), C from β and Re_D vs a separate-module identity (≤2 ULP). Not given C_d, not RHG orifice, not venturi type C, not long-radius, not Q=Av, and not Darcy. ≤2 ULP vs O3 applies only to the published tabulated ISO-nozzle vectors. Not given C_d, not RHG orifice, not venturi type C, not long-radius, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
ISO 5167-3 ISA 1932 incompressible nozzle discharge from D1, D2 or β, Re_D, and Δp. Invert Δp. Report C from β and Re_D.
Scope
ISO 5167-3 ISA 1932 nozzle: Q = C E A2 √(2Δp/ρ); C from β and Re_D; incompressible ε=1; C is reported, not an input
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q = C E A2 √(2Δp/ρ) with ISA 1932 C from β and Re_D; plus pressure and coefficient solves; + O3 mpmath tabulated discharge.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-27.o2-o3
Verification revision
2026-09-27.o2-o3 · 1/1 property · digest af75580f8d95
Legacy regression
6/6 tests · Production surface contract 6/6
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
4/4 golden · 1/1 CVP boundary · 2/2 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
Sources
Evidence
1 legacy golden · legacy regression suite · 4/4 oracle-backed golden · 2/2 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

DischargeQ = C E A2 √(2Δp / ρ)
Approachβ = D2/D1 · E = 1/√(1 − β⁴)
ISA 1932 CC = 0.9900 − 0.2262 β^4.1 − (0.00175 β² − 0.0033 β^4.15)(10^6/Re_D)^1.15
iSI. Incompressible ε=1. C is reported from β and Re_D; do not send C_d. Do not send query v — that is calculation_version.

How to use

1

Enter D1 and D2

Inlet D1 ≥ 50 mm and throat D2. REST may send D1+beta instead of D2. This is not an orifice d+D pair.

2

Enter Re_D

Pipe Reynolds number on D1. Do not send ρ, μ, and v to wrap the Reynolds page.

3

Enter Δp and ρ

Inlet-to-throat differential pressure. 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

D1=0.1 m, D2=0.05 m, Δp=10 kPa, ρ=1000 kg/m³

C from ISA 1932, Q=C E A2 √(2Δp/ρ)
C≈0.97656 · Q≈0.008856 m³/s
ϟ

Same β via D1+beta

D1=0.1 m, beta=0.5

D2=β D1
same C

ISO 5167 Nozzle calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
ISO 5167-3 ISA 1932 nozzle. Incompressible Q = C E A2 √(2Δp/ρ) with E=1/√(1−β⁴). C is computed from β and Re_D, not supplied. β∈[0.30,0.80], Re_D∈[7×10⁴,10⁷], D≥50 mm. Not a venturi tube with given C_d=0.98, not a sharp-edged orifice with C_d=0.61.
What it calculates
ISO 5167-3 ISA 1932 incompressible nozzle discharge from D1, D2 or β, Re_D, and Δp. Invert Δp. Report C from β and Re_D.
Inputs
  • mode?
  • D1
  • D2|beta
  • Re_D
  • dP?
  • rho?
  • Q?
Outputs
  • Q?
  • D1
  • D2
  • beta
  • E
  • A1
  • A2
  • C
  • Cd
  • Re_D
  • v1?
  • v2?
  • rho?
  • dP?
  • mode
  • model
Formula
Q = C E A2 √(2Δp/ρ); C = 0.9900 − 0.2262 β^4.1 − (0.00175 β² − 0.0033 β^4.15)(10^6/Re_D)^1.15
Assumptions
  • ISO 5167-3 ISA 1932 nozzle: Q = C E A2 √(2Δp/ρ); C from β and Re_D; incompressible ε=1; C is reported, not an input
  • C = 0.9900 − 0.2262 β^4.1 − (0.00175 β² − 0.0033 β^4.15)(10^6/Re_D)^1.15; β∈[0.30,0.80]; Re_D∈[7e4,1e7]; D≥50 mm
  • Not a venturi wrap with given C_d=0.98, not orifice C_d=0.61, not Q=Av, not Darcy f, not compressible ε
Units
  • SI; D1, D2 in m; Q in m³/s; Δp in Pa; ρ in kg/m³; Re_D dimensionless
Boundary conditions
  • missing D1, D2/beta, Re_D, Δp, Q, or ρ when required → MISSING_REQUIRED_INPUT
  • D1 < 50 mm, β outside [0.30,0.80], or Re_D outside [7e4,1e7] → VALUE_OUT_OF_RANGE
  • C_d given, orifice d+D, A or v, Darcy f, μ, tank H, Cv/Kv, K, ε, kind → MIXED_INPUT_ENCODING
  • mode=Cd or unknown mode → INVALID_MODE
Example
D1=0.1 D2=0.05 Re_D=1e6 dP=10000 rho=1000 → C≈0.97656 Q≈0.008856
Validation cases

3 published on this page · 6/6 tests · Production surface contract 6/6 · View evidence

  • D1=0.1 D2=0.05 Re_D=1e6 dP=10000 rho=1000 → C≈0.97656 Q≈0.008856
  • D1=0.1 D2=0.05 Re_D=1e6 Cd=0.98 → MIXED_INPUT_ENCODING
  • mode=Cd D1=0.1 D2=0.05 Re_D=1e6 → INVALID_MODE
Sources
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute ISO 5167-3 ISA 1932 nozzle discharge from β, Re_D, and Δp. C is computed, not supplied.

Supported and not supported

Supported — Q from D1, D2 or β, Re_D, and Δp · invert Δp · C from β and Re_D · API physics.fluid.iso_nozzle

Not supported — given venturi C_d=0.98, orifice C_d=0.61, Q=Av, Darcy f, compressible ε, long-radius nozzle, Venturi nozzle

Agent / API notes

Capability id: physics.fluid.iso_nozzle · tool id: iso-nozzle · pin 1.0.0.

{ "D1": 0.1, "D2": 0.05, "Re_D": 1000000, "dP": 10000, "rho": 1000 }

Modes: flow (default), pressure, coefficient. 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-nozzle. There is no /calc/fluid.

Other calculators in this family: Alternate Depth Calculator, Bernoulli Equation Calculator, Broad-Crested Weir Calculator, Cavitation Number Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator . Explore all Fluid Mechanics.

→ Alternate Depth Calculator Compute both rectangular depths at the same specific energy from E, Q, and width b. Runs locally. Not specific energy from y+v; not specific force M; not hydraulic jump y2; not critical depth yc as the product. › → Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser. › → Broad-Crested Weir Calculator Compute rectangular broad-crested weir discharge Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. Runs locally. Not a thin-plate weir, not Manning, not Q=Av, and not an orifice. › → Cavitation Number Calculator Compute the cavitation number σ = (p − p_v) / (½ ρ v²). Runs locally. Not NPSH, not Thoma NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²). › → Chezy Formula Calculator Compute open-channel mean velocity V = C √(R S). Runs locally. Not Manning n, not Q=Av, not Hazen–Williams, and not Darcy. › → Colebrook Friction Factor Calculator Solve the Colebrook–White equation for Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Runs locally. Not laminar 64/Re and not a Moody-chart lookup. › → Concentric Reducer Calculator Compute concentric-reducer loss h = K v₂² / (2g) with K = 0.5 (1 − A₂/A₁) referenced to the downstream speed. Runs locally. Not sudden expansion, not gradual contraction α, not vena-contracta C_c, not catalog K, and not Q=Av. › → Critical Depth Calculator Compute rectangular critical depth yc = (q²/g)^{1/3}. Runs locally. Not a Froude wrap, not specific energy, not a hydraulic jump, and not Q=Av. ›

Frequently asked questions

Key distinctions behind the calculation.

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. At β=0.5 and Re_D=10⁶ this page reports C≈0.97656, not 0.98.

Is this an orifice meter?

No. A given C_d plate is /calc/physics/orifice-discharge (default C_d=0.61). ISO 5167-2 Reader–Harris/Gallagher C from β and Re_D is /calc/physics/iso-orifice. Sending d and D here is MIXED_INPUT_ENCODING.

Is this a long-radius nozzle?

No. ISO 5167-3 long-radius C=0.9965−0.00653 β^{0.5} is /calc/physics/long-radius-nozzle. Sending kind here is MIXED_INPUT_ENCODING. At β=0.5 this page reports C≈0.97656, not 0.99188.

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.

Can I invert C_d from Q?

No. C is computed from β and Re_D. Venturi invert Cd is /calc/physics/venturi. mode=Cd is INVALID_MODE.

Where does this run?

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