CVP verified calculation capability

Normal depth Calculation Capability

Rectangular uniform-flow yn from SI Manning with A=b yn and R=b yn/(b+2 yn). Not Manning A,R; not critical depth yc; not specific energy E; not Chezy C; not Q=Av.

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

Model

Manning

Manning: Q = (1/n) A R^{2/3} S^{1/2}
Area: A = b yn
Hydraulic radius: R = b yn / (b + 2 yn)

Modes: depth · discharge

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`b`	Rectangular surface width in m	—	input / output
`n`	SI Manning n	—	input / output
`S`	Bed slope	—	input / output
`Q`	Volume flow in m³/s	—	input / output
`yn`	Normal depth in m	—	input / output
`A`	—	—	output
`P`	—	—	output
`R`	—	—	output
`v`	—	—	output
`k`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Rectangular uniform flow: Q=(1/n) A R^{2/3} S^{1/2}; A=b yn; R=b yn/(b+2 yn); SI k=1; yn is unknown in depth mode
yn/b∈[0.01, 10]; n∈[0.008, 0.15]; S∈[1e-6, 0.1]; geometry is b, not A and R
Not Manning Q with given A,R; not critical depth yc=(q²/g)^{1/3}; not specific energy E; not Chezy C; not Q=Av

Not supported

Manning A
R
critical depth yc
specific energy E
Chezy C
Q=Av
trapezoid z
US k=1.486

Example

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

Q=1.32807 b=2 n=0.03 S=0.001 → yn=1.0000

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Rectangular SI Manning yn invert with A=b y and P=b+2y; + O3 mpmath tabulated yn.. 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 · Rectangular SI Manning yn invert with A=b y and P=b+2y; + O3 mpmath tabulated yn.· View Manifest · CVP overview · Specification
Verified scope: Rectangular SI Manning yn invert with A=b y and P=b+2y; + O3 mpmath tabulated yn.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (depth, solve, alias, awkward, invalid-domain)
Deferred: Not trapezoid yn, not yc, not Manning A,R, not Chezy, and not Q=Av.
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 2026-09-26.o2-o3.cov
Verification revision: 2026-09-26.o2-o3.cov · 1/1 property · digest 020fed1bdedd
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: rectangular SI Manning yn invert A=b y, P=b+2y vs a separate-module identity (≤2 ULP). Not trapezoid yn, not yc, not Manning A,R, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated normal-depth vectors. Not trapezoid yn, not yc, and not Manning A,R.
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: 5/5 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/normal-depth' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"Q":1.3280733965528158,"b":2,"n":0.03,"S":0.001},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "Q": 1.3280733965528158,
    "b": 2,
    "n": 0.03,
    "S": 0.001
  },
  "calculation_version": "1.0.0"
}

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

Full REST contract: REST API docs.

Tool id: normal-depth
Engine: normal-depth
REST: POST /api/v1/calc/normal-depth
MCP: execute_calculation with capability_id: "physics.fluid.normal_depth"
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 radius
Chow, V.T. Open-Channel Hydraulics — Normal depth in uniform flow

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.normal_depth"},"_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.normal_depth","inputs":{"Q":1.3280733965528158,"b":2,"n":0.03,"S":0.001},"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.