HomeCalculatorsPhysicsFluid MechanicsISO 5167 Cone Meter Calculator
Physics calculator

ISO 5167 Cone Meter Calculator

Compute ISO 5167-5 uncalibrated cone-meter discharge. β=√(1−(d_c/D)²). Runs locally. Not ISA 1932, not RHG orifice, not ISO 5167-4 type C, not long-radius, not given C_d.

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 A √(2Δp/ρ) with C=0.82, β=√(1−(d_c/D)²); plus pressure and coefficient solves; + O3 mpmath tabulated discharge.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Q = C E A √(2Δp/ρ) with C=0.82, β=√(1−(d_c/D)²); 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 ISA 1932, not RHG orifice, not ISO 5167-4 type C, not long-radius, not given C_d, not Q=Av, not Darcy, not compressible ε.
Numerical scope
O2: ISO 5167-5 uncalibrated cone Q=C E A √(2Δp/ρ), C=0.82, β=√(1−(d_c/D)²) vs a separate-module identity (≤2 ULP). Not ISA 1932, not RHG orifice, not ISO 5167-4 type C, not long-radius, not given C_d, not Q=Av, and not Darcy. ≤2 ULP vs O3 applies only to the published tabulated ISO-cone vectors. Not ISA 1932, not RHG orifice, not venturi type C, not long-radius, not given C_d, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
ISO 5167-5 uncalibrated cone-meter discharge from D, d_c or cone β, Re_D, and Δp. Invert Δp. Report C=0.82.
Scope
ISO 5167-5 uncalibrated cone: Q = C E A √(2Δp/ρ); C=0.82; β=√(1−(d_c/D)²); A=(π/4) D² β²; 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 A √(2Δp/ρ) with C=0.82, β=√(1−(d_c/D)²); 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.v2
Verification revision
2026-09-27.o2-o3.v2 · 1/1 property · digest d50806cc17cf
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 A √(2Δp / ρ)
Cone ββ = √(1 − (d_c/D)²) · E = 1/√(1 − β⁴)
Uncalibrated CC = 0.82
iSI. Incompressible ε=1. C is reported; do not send C_d. Do not send query v — that is calculation_version. Re_D bounds the envelope; it does not interpolate C. A is the annulus (π/4)D²β², not (π/4)d_c².

How to use

1

Enter D and d_c

Pipe ID D and cone beta-edge diameter d_c. REST may send D+beta instead of d_c. Cone β is √(1−(d_c/D)²), not d_c/D and not orifice d+D.

2

Enter Re_D

Pipe Reynolds number on D. Required as the ISO envelope. Do not send ρ, μ, and v to wrap Reynolds.

3

Enter Δp and ρ

Inlet-to-annulus differential pressure. Invert on the Δp tab. Read C on the C tab without Δp.

Example calculations

Common configurations with formula and result.

ϟ

D=0.1 m, d_c=0.08 m, Re_D=10⁶, 10 kPa

β=√(1−0.64)=0.6, Δp=10 kPa, ρ=1000 kg/m³

C=0.82, Q=C E A √(2Δp/ρ)
C=0.82 · Q≈0.011114 m³/s
ϟ

Same β via D+beta

D=0.1 m, beta=0.6

d_c=D √(1−β²)
d_c=0.08 m · same Q

ISO 5167 Cone Meter calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
ISO 5167-5 uncalibrated cone meter. Incompressible Q = C E A √(2Δp/ρ) with E=1/√(1−β⁴) and annular A=(π/4) D² β². C=0.82. β=√(1−(d_c/D)²). Re_D is the ISO envelope, not a term in C. β∈[0.45,0.75], D∈[50 mm, 500 mm], Re_D∈[8e4, 1.2e7]. Not ISA 1932 C(β,Re), not an RHG orifice plate, not ISO 5167-4 type C, not long-radius C(β).
What it calculates
ISO 5167-5 uncalibrated cone-meter discharge from D, d_c or cone β, Re_D, and Δp. Invert Δp. Report C=0.82.
Inputs
  • mode?
  • D
  • d_c|beta
  • Re_D
  • dP?
  • rho?
  • Q?
Outputs
  • Q?
  • D
  • d_c
  • beta
  • E
  • A1
  • A
  • C
  • Cd
  • Re_D
  • v1?
  • v2?
  • rho?
  • dP?
  • mode
  • model
Formula
Q = C E A √(2Δp/ρ); C = 0.82; β = √(1 − (d_c/D)²); A = (π/4) D² β²
Assumptions
  • ISO 5167-5 uncalibrated cone: Q = C E A √(2Δp/ρ); C=0.82; β=√(1−(d_c/D)²); A=(π/4) D² β²; incompressible ε=1; C is reported, not an input
  • Re_D∈[8e4, 1.2e7] is the ISO envelope; β∈[0.45,0.75]; D∈[50 mm, 500 mm]; relative uncertainty of uncalibrated C is 5%
  • Not ISA 1932 C(β,Re), not RHG orifice, not ISO 5167-4 type C, not long-radius C(β), not given C_d, not Q=Av, not Darcy f, not compressible ε
Units
  • SI; D, d_c in m; Q in m³/s; Δp in Pa; ρ in kg/m³; Re_D dimensionless
Boundary conditions
  • missing D, d_c/beta, Re_D, Δp, Q, or ρ when required → MISSING_REQUIRED_INPUT
  • D outside [50 mm, 500 mm], β outside [0.45,0.75], or Re_D outside [8e4, 1.2e7] → VALUE_OUT_OF_RANGE
  • C_d given, orifice d+D, nozzle D1+D2, tank H, A or v, Darcy f, μ, Cv/Kv, K, ε, tapping, kind=isa1932 or kind=machined → MIXED_INPUT_ENCODING
  • mode=Cd or unknown mode → INVALID_MODE
Example
D=0.1 d_c=0.08 Re_D=1e6 dP=10000 rho=1000 → C=0.82 Q≈0.011114
Validation cases

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

  • D=0.1 d_c=0.08 Re_D=1e6 dP=10000 rho=1000 → C=0.82 Q≈0.011114
  • D=0.1 d_c=0.08 Re_D=1e6 Cd=0.98 → MIXED_INPUT_ENCODING
  • D1=0.1 D2=0.08 Re_D=1e6 dP=10000 rho=1000 → MIXED_INPUT_ENCODING
  • mode=Cd D=0.1 d_c=0.08 Re_D=1e6 → INVALID_MODE
Sources
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute ISO 5167-5 uncalibrated cone-meter discharge from D, d_c, Re_D, and Δp. C is 0.82, not supplied.

Supported and not supported

Supported — Q from D, d_c or cone β, Re_D, and Δp · invert Δp · C=0.82 · API physics.fluid.iso_cone

Not supported — ISA 1932 C(β,Re), RHG orifice, ISO 5167-4 type C, long-radius C(β), given C_d, Q=Av, Darcy f, compressible ε

Agent / API notes

Capability id: physics.fluid.iso_cone · tool id: iso-cone · pin 1.0.0.

{ "D": 0.1, "d_c": 0.08, "Re_D": 1000000, "dP": 10000, "rho": 1000 }

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 cone β the same as orifice β=d/D?

No. ISO 5167-5 β=√(1−(d_c/D)²). A larger cone lowers β. Orifice, nozzle, and Venturi use β=d/D. Sending orifice d+D or nozzle D1+D2 is MIXED_INPUT_ENCODING.

Can I send a given C_d=0.98?

No. Uncalibrated C=0.82 is reported. A given C_d is /calc/physics/venturi or /calc/physics/orifice-discharge. Sending C_d here is MIXED_INPUT_ENCODING.

Is this an ISA 1932 nozzle or long-radius nozzle?

No. ISA 1932 is /calc/physics/iso-nozzle (C from β and Re_D). Long-radius is /calc/physics/long-radius-nozzle (C=0.9965−0.00653 β^{0.5}). Sending kind=isa1932 or kind=long-radius here is MIXED_INPUT_ENCODING.

Is this an ISO 5167-4 Venturi tube?

No. Machined/rough/as-cast type C is /calc/physics/iso-venturi (machined C=0.995). Sending kind=machined here is MIXED_INPUT_ENCODING.

Does C change with Re_D?

No. Uncalibrated C is 0.82. Re_D must lie in [8e4, 1.2e7] or the engine returns VALUE_OUT_OF_RANGE.

Is the throat area (π/4)d_c²?

No. ISO 5167-1 equivalent d=D·β, so A=(π/4) D² β² is the annulus, not the cone disk.

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 isoCone wrapper.