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 Engine tested · Source checked · 5/5 tests · Production surface contract 1/1 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: ISO 5167-5 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 · 5/5 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 80000-4 — Mechanics — Length, speed, pressure
ISO 5167-5 — Measurement of fluid flow by means of pressure differential devices — Cone meters — Uncalibrated discharge coefficient
Sources
Evidence: 5 property · Production surface contract 1/1 · Artifact integrity PASS
Production: Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T10:48:34.503Z
Semantic contract: PASS

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

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.

Enter Re_D

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

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.

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

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

Engine tested 5/5 tests · Production surface contract 1/1
Named expert review Not performed
Calculation version 1.0.0

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 · 5/5 tests · Production surface contract 1/1 · 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: ISO 80000-4 — Mechanics — Length, speed, pressure
Supports: D is a length; Q is a volume flow; Δp is a pressure
ISO 5167-5 — Measurement of fluid flow by means of pressure differential devices — Cone meters — Uncalibrated discharge coefficient
Supports: C=0.82; β=√(1−(d_c/D)²); D 50–500 mm; β 0.45–0.75; Re_D 8e4–1.2e7. Not ISA 1932, not RHG orifice, not ISO 5167-4 type C, not long-radius
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: ISO 5167 nozzle, ISO 5167 Venturi, ISO 5167 long-radius, ISO 5167 orifice, Venturi meter .

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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.