CVP verified calculation capability

Trapezoidal hydraulic jump Calculation Capability

Trapezoid sequent depths from M=Q²/(gA)+A ȳ on A=(b+z y)y. Not rectangular Bélanger, not trapezoid alternate E-pair, not trapezoid yc, not trapezoid yn, not Manning n, not Q=Av.

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

Model

Specific force

Specific force: M = Q²/(g A) + A ȳ
Section: A = (b + z y) y
Centroid: ȳ = y (3b + 2 z y) / [6 (b + z y)]

Modes: sequent · upstream · energy

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`b`	Bottom width in m	—	input / output
`z`	Side slope run/rise	—	input / output
`Q`	Volume flow in m³/s	—	input / output
`y1`	Upstream depth in m	—	input / output
`y2`	Downstream sequent depth in m	—	input / output
`g`	Gravity in m/s²	—	input / output
`Fr1`	—	—	output
`Fr2`	—	—	output
`v1`	—	—	output
`v2`	—	—	output
`dE`	—	—	output
`E1`	—	—	output
`E2`	—	—	output
`M`	—	—	output
`yc`	—	—	output
`A1`	—	—	output
`A2`	—	—	output
`T1`	—	—	output
`T2`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Trapezoid hydraulic jump: sequent depths from M=Q²/(gA)+A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; z>0 is run/rise; Fr₁>1
Unknown is y2 (sequent) or y1 (upstream invert) or ΔE (energy); Fr is reported not an input; not Bélanger y2/y1=(√(1+8Fr₁²)−1)/2
Not rectangular sequent depths; not trapezoid alternate E-pair; not trapezoid yc; not trapezoid yn; not Manning n; not Q=Av

Not supported

rectangular Bélanger y₂/y₁=(√(1+8 Fr₁²)−1)/2
trapezoid alternate E-pair
trapezoid yc
trapezoid yn
Manning n
Q=Av
z=0

Example

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

y1=0.25 Q=2 b=2 z=1 → y2≈0.68128

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Trapezoid sequent depths from equal specific force M; + O3 mpmath tabulated y2.. 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 · Trapezoid sequent depths from equal specific force M; + O3 mpmath tabulated y2.· View Manifest · CVP overview · Specification
Verified scope: Trapezoid sequent depths from equal specific force M; + O3 mpmath tabulated y2.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (sequent, alias, awkward, fast, invalid-domain)
Deferred: Not rectangular jump, not alternate E-pair, not upstream invert in this pack, and not Q=Av.
Calculation version: 1.0.0
Verification: 7/7 calculation tests · 1/1 legacy golden · 0/0 legacy boundary · 6/6 legacy property
Production surface contract: 6/6
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3
Verification revision: 2026-09-26.o2-o3 · 1/1 property · digest e099b6d80395
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: trapezoid sequent depths from equal M=Q²/(gA)+A ȳ vs a separate-module identity (≤2 ULP). Not rectangular jump, not alternate E-pair, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated trapezoid-hydraulic-jump vectors. Not rectangular jump, not alternate E-pair, and not M alone.
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: 4/4 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/trapezoidal-hydraulic-jump' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"y1":0.25,"Q":2,"b":2,"z":1},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "y1": 0.25,
    "Q": 2,
    "b": 2,
    "z": 1
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/trapezoidal-hydraulic-jump. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: trapezoidal-hydraulic-jump
Engine: trapezoidal-hydraulic-jump
REST: POST /api/v1/calc/trapezoidal-hydraulic-jump
MCP: execute_calculation with capability_id: "physics.fluid.trapezoid_hydraulic_jump"
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 — Force and volume flow
Chow, V.T. Open-Channel Hydraulics — Hydraulic jump in a trapezoidal section

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.trapezoid_hydraulic_jump"},"_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.trapezoid_hydraulic_jump","inputs":{"y1":0.25,"Q":2,"b":2,"z":1},"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.