CVP verified calculation capability

Hydraulic diameter Calculation Capability

Hydraulic diameter D_h=4A/P_w. Full circular pipe D_h=D, closed rectangular duct 2ab/(a+b), annulus D_o−D_i. Not Q=Av, not Manning Q, not Reynolds, not Darcy.

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

Model

General

General: D_h = 4 A / P_w
Circular: D_h = D
Rectangular duct: D_h = 2 a b / (a + b)

Modes: general · circular · rectangular · annular

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`A`	Flow area in m²	—	input / output
`Pw`	Wetted perimeter in m	—	input / output
`R`	Hydraulic radius A/P_w in m	—	input / output
`Dh`	Hydraulic diameter in m	—	input / output
`D`	Inside diameter in m	—	input / output
`a`	Internal width in m	—	input / output
`b`	Internal height in m	—	input / output
`D_o`	Annulus outer diameter in m	—	input / output
`D_i`	Annulus inner diameter in m	—	input / output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

D_h = 4 A / P_w; R = A / P_w = D_h / 4
Full circular pipe: D_h = D; closed rectangular duct: D_h = 2ab/(a+b); annulus: D_h = D_o − D_i
Not Q=Av, not Manning Q, not Reynolds, not Darcy, not a weir or orifice

Not supported

Q=Av identities
Manning discharge
Reynolds number
Darcy–Weisbach
weir
orifice
open-channel rectangular as a silent duct formula

Example

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

A=0.01 Pw=0.4 → D_h=0.1 m

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · D_h = 4A/P_w for a general section, full circular pipe, closed rectangular duct, or annulus, plus R = D_h/4, + O3 mpmath tabulated diameter.. 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 · D_h = 4A/P_w for a general section, full circular pipe, closed rectangular duct, or annulus, plus R = D_h/4, + O3 mpmath tabulated diameter.· View Manifest · CVP overview · Specification
Verified scope: D_h = 4A/P_w for a general section, full circular pipe, closed rectangular duct, or annulus, plus R = D_h/4, + O3 mpmath tabulated diameter.
Assurance: Engineering
Declared partition coverage: PASS · 7/7 declared partitions (alias, circular, shaped, radius, awkward, default, invalid-domain)
Deferred: Not Q=Av, not Manning, and not Darcy.
Calculation version: 1.0.0
Verification: 15/15 calculation tests · 2/2 legacy golden · 8/8 legacy boundary · 5/5 legacy property
Production surface contract: 5/5
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-10-28.meta-metrics-v2
Verification revision: 2026-10-28.meta-metrics-v2 · 1/1 property · digest edc8371a99ac
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: hydraulic diameter vs a separate-module identity (≤2 ULP). Not Q=Av, not Manning, and not Darcy. ≤2 ULP vs O3 applies only to the published tabulated hydraulic-diameter vectors. Not Q=Av, not Manning, and not Darcy.
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 · 7/7 CVP boundary · 7/7 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 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 5/5.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/hydraulic-diameter' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"A":0.01,"Pw":0.4},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "A": 0.01,
    "Pw": 0.4
  },
  "calculation_version": "1.0.0"
}

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

Full REST contract: REST API docs.

Tool id: hydraulic-diameter
Engine: hydraulic-diameter
REST: POST /api/v1/calc/hydraulic-diameter
MCP: execute_calculation with capability_id: "physics.fluid.hydraulic_diameter"
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

ISO 5167-1 — Measurement of fluid flow by means of pressure differential devices — Hydraulic diameter
White, F.M. Fluid Mechanics — Noncircular ducts

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.hydraulic_diameter"},"_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.hydraulic_diameter","inputs":{"A":0.01,"Pw":0.4},"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.