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

Open calculator REST API MCP Evidence Evidence JSON Review policy

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)

Solve 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. Required. Alternatives: width, b_m, channel_width. Do not send Manning A or R. Do not send side-weir B.	—	input / output
`n`	SI Manning n. Required. Envelope [0.008, 0.15].	—	input / output
`S`	Bed slope (dimensionless). Required. Envelope [1e-6, 0.1]. Alternatives: slope, S0, Sf.	—	input / output
`Q`	Volume flow in m³/s. Required for depth. Alternatives: flow, Q_m3_s.	—	input / output
`yn`	Normal depth in m. Required for discharge. Alternatives: y_n, depth, y_m, y. Do not send yc or y1.	—	input / output
`A`	—	—	output
`P`	—	—	output
`R`	—	—	output
`v`	velocity	—	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

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: 5/5 calculation tests · golden 0/0 · boundary 0/0 · 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; 164 CURRENT) @ 2026-09-18T13:56:15.885Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T13:56:15.080Z
Last production check: 2026-09-18T13:56:15.080Z
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. Production surface contract 1/1.

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

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.normal_depth"}}}'

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