Verified calculation capability

Trapezoidal normal depth Calculation Capability

Trapezoid uniform-flow yn from SI Manning with A=(b+z y)y and P=b+2 y √(1+z²). Not rectangular yn, not trapezoid yc, not Manning A,R, not Chezy C, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.trapezoid_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 + z y) y
Wetted perimeter: P = b + 2 y √(1+z²)

Solve modes: depth · discharge

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`b`	Bottom 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
`z`	Side slope run/rise (z>0). Required. Alternatives: z_side, side_slope, m. z=0 is rectangular /calc/physics/normal-depth. Do not send a bank angle.	—	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
`T`	temperature	—	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

Trapezoid uniform flow: Q=(1/n) A R^{2/3} S^{1/2}; A=(b+z yn) yn; P=b+2 yn √(1+z²); SI k=1; z>0 is run/rise; yn is unknown in depth mode
yn/b∈[0.01, 10]; n∈[0.008, 0.15]; S∈[1e-6, 0.1]; z∈(0, 10]; geometry is b and z, not A and R
Not rectangular yn; not trapezoid yc; not Manning Q with given A,R; not Chezy C; not Q=Av

Not supported

rectangular yn
trapezoid yc
Manning A
R
Chezy C
Q=Av
z=0
US k=1.486

Example

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

Q=2.30256 b=2 z=1 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: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T21:41:56.329Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T21:41:55.460Z
Last production check: 2026-09-18T21:41:55.460Z
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. Production surface contract 1/1.

Tool id: trapezoidal-normal-depth
Engine: trapezoidal-normal-depth
REST: POST /api/v1/calc/trapezoidal-normal-depth
MCP: execute_calculation with capability_id: "physics.fluid.trapezoid_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 a trapezoidal section

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.trapezoid_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.