Verified calculation capability

Hazen–Williams Calculation Capability

SI Hazen–Williams circular water-pipe head loss hf=10.67 L Q^{1.852}/(C^{1.852} D^{4.87}). Invert Q, D, or C. Not Darcy, not Colebrook, not Manning, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.hazen_williams · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Head loss

Head loss: hf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87})
Friction slope: S = hf / L

Solve modes: head loss · flow · diameter · C

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`C`	Hazen–Williams coefficient. Empirical; typical water-pipe 80–150.	—	input / output
`L`	Pipe length in m.	—	input / output
`Q`	Volume flow in m³/s. Required except flow invert. Not v from Q=Av.	—	input / output
`D`	Inside diameter in m. Circular full flow. Required except diameter invert.	—	input / output
`hf`	Head loss in m. Required for flow, diameter, and C invert. Alternative: S. Do not send with head_loss.	—	input / output
`S`	Friction slope hf/L. Alternative to hf on invert modes. Do not send both.	—	input / output
`k`	SI constant. Omit or 10.67. US customary is INVALID_MODE.	—	input / output
`v`	velocity	—	output
`A`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

SI Hazen–Williams k=10.67
Circular full-flow water pipe
Empirical C; not Darcy f, not Colebrook, not Manning n
Not Q=Av identities
Not US customary gpm/in

Not supported

Darcy–Weisbach f
Colebrook
Manning
Q=Av identities
US customary gpm/in
non-circular sections
compressible flow

Example

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

C=120 L=100 Q=0.02 D=0.2 → hf=10.67 L Q^{1.852}/(C^{1.852} D^{4.87})

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: 17/17 calculation tests · golden 2/2 · boundary 10/10 · 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 4/4.

Tool id: hazen-williams
Engine: hazen-williams
REST: POST /api/v1/calc/hazen-williams
MCP: execute_calculation with capability_id: "physics.fluid.hazen_williams"
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 80000-4 — Mechanics — Volume flow rate and hydraulic head
Williams, G.S. and Hazen, A. Hydraulic Tables — Empirical pipe formula

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.hazen_williams"}}}'

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