CVP verified calculation capability

ISO 5167 wedge meter Calculation Capability

ISO 5167-6 uncalibrated wedge Q=C E A √(2Δp/ρ) with C=0.77−0.09β and β from circular-segment h/D. Not cone C=0.82, not ISA 1932, not RHG orifice, not ISO 5167-4 type C, not long-radius, not given C_d, not Q=Av, not Darcy.

Physics · Fluid Capability ID physics.fluid.iso_wedge version 1.0.0 CVP VERIFIED CURRENT Engineering

Model

Discharge

Discharge: Q = C E A √(2Δp / ρ)
Wedge β: β from circular-segment h/D · E = 1/√(1 − β⁴)
Uncalibrated C: C = 0.77 − 0.09 β

Modes: flow · pressure · coefficient

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`D`	Pipe inside diameter in m	—	input / output
`h`	Wedge gap in m	—	input / output
`h_over_D`	Wedge gap ratio h/D	—	input / output
`beta`	ISO wedge β from the circular-segment of h/D, not d/D and not √	—	input / output
`Re_D`	Pipe Reynolds number on D	—	input / output
`dP`	Differential pressure in Pa	—	input / output
`rho`	Density in kg/m³	—	input / output
`Q`	Volume flow in m³/s	—	input / output
`E`	—	—	output
`A1`	—	—	output
`A`	—	—	output
`C`	—	—	output
`Cd`	—	—	output
`v1`	—	—	output
`v2`	—	—	output
`model`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

ISO 5167-6 uncalibrated wedge: Q = C E A √(2Δp/ρ); C=0.77−0.09β; β from circular-segment h/D; A=(π/4) D² β²; incompressible ε=1; C is reported, not an input
Re_D∈[1e4, 9e6] is the ISO envelope; h/D∈[0.20,0.60]; β∈[0.377,0.791]; D∈[50 mm, 600 mm]; h/D=0.5 → β=√0.5
Not cone C=0.82, 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

Not supported

cone C=0.82
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

Example

One numerical check. The calculator page holds worked steps and FAQ.

D=0.1 h=0.05 Re_D=1e6 dP=10000 rho=1000 → C≈0.70636 Q≈0.014324

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q = C E A √(2Δp/ρ) with C=0.77−0.09β, β from circular-segment h/D; plus pressure and coefficient solves; + O3 mpmath tabulated discharge.. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q = C E A √(2Δp/ρ) with C=0.77−0.09β, β from circular-segment h/D; plus pressure and coefficient solves; + O3 mpmath tabulated discharge.· View Manifest · CVP overview · Specification
Verified scope: Q = C E A √(2Δp/ρ) with C=0.77−0.09β, β from circular-segment h/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)
Deferred: Not cone C=0.82, 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.
Calculation version: 1.0.0
Verification: 6/6 calculation tests · 1/1 legacy golden · 0/0 legacy boundary · 5/5 legacy property
Production surface contract: 6/6
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-27.o2-o3.v3
Verification revision: 2026-09-27.o2-o3.v3 · 1/1 property · digest 4b2daddda385
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: ISO 5167-6 uncalibrated wedge Q=C E A √(2Δp/ρ), C=0.77−0.09β, β from circular-segment h/D vs a separate-module identity (≤2 ULP). Not cone C=0.82, 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-wedge vectors. Not cone, not ISA 1932, not RHG orifice, not venturi type C, not given C_d, and not Q=Av.
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.
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
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/iso-wedge' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"D":0.1,"h":0.05,"Re_D":1000000,"dP":10000,"rho":1000},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "D": 0.1,
    "h": 0.05,
    "Re_D": 1000000,
    "dP": 10000,
    "rho": 1000
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/iso-wedge. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: iso-wedge
Engine: iso-wedge
REST: POST /api/v1/calc/iso-wedge
MCP: execute_calculation with capability_id: "physics.fluid.iso_wedge"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"physics.fluid.iso_wedge"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"physics.fluid.iso_wedge","inputs":{"D":0.1,"h":0.05,"Re_D":1000000,"dP":10000,"rho":1000},"calculation_version":"1.0.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.