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

Open calculator REST API MCP Evidence Evidence JSON Review policy

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)]

Solve 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. Required. Alternatives: width, b_m, channel_width. 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/hydraulic-jump. Do not send a bank angle.	—	input / output
`Q`	Volume flow in m³/s. Required. Alternatives: flow, Q_m3_s.	—	input / output
`y1`	Upstream depth in m. Required for sequent and energy. Alternatives: y, y_m, depth. Do not send yn or yc.	—	input / output
`y2`	Downstream sequent depth in m. Required for upstream and energy. Alternative: y_2.	—	input / output
`g`	Gravity in m/s². Optional; default 9.80665. Alternatives: g_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

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: 6/6 calculation tests · golden 0/0 · boundary 0/0 · property 6/6
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-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

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_hydraulic_jump"}}}'

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