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

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

General

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

Solve 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. General mode, with Pw or Dh.	—	input / output
`Pw`	Wetted perimeter in m. Alias P. General mode.	—	input / output
`R`	Hydraulic radius A/P_w in m. Alternative to A+Pw. D_h=4R. Not a Manning n solve.	—	input / output
`Dh`	Hydraulic diameter in m. Inverts Pw or A in general mode.	—	input / output
`D`	Inside diameter in m. Circular full-pipe mode. D_h=D.	—	input / output
`a`	Internal width in m. Closed rectangular duct.	—	input / output
`b`	Internal height in m. Closed rectangular duct.	—	input / output
`D_o`	Annulus outer diameter in m.	—	input / output
`D_i`	Annulus inner diameter in m. Must be smaller than D_o.	—	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

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 15/15 calculation tests · golden 2/2 · boundary 8/8 · property 5/5
Engine tested: Yes
Source checked: Yes
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)

Production attestation: 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; 163 CURRENT) @ 2026-09-17T06:27:56.932Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T06:27:56.176Z
Last production check: 2026-09-17T06:27:56.176Z
Public / cache: PASS
Origin: PASS

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 3/3.

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

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

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"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.