Verified calculation capability

Hydraulic jump Calculation Capability

Rectangular sequent depths y2/y1=(√(1+8Fr₁²)−1)/2. Fr₁>1. Not a Froude wrap, not Manning, not a weir, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.hydraulic_jump · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Sequent depth

Sequent depth: y₂/y₁ = (√(1+8 Fr₁²) − 1)/2
Energy loss: ΔE = (y₂ − y₁)³ / (4 y₁ y₂)
Downstream Froude: Fr₂ = Fr₁ / (y₂/y₁)^{3/2}

Solve modes: sequent · upstream · energy

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`y1`	Upstream depth in m. Required except upstream invert.	—	input / output
`y2`	Downstream sequent depth in m. Required for upstream and energy.	—	input / output
`Fr`	Upstream Froude number Fr₁ > 1. Alternative: Fr1. Do not send with v.	—	input
`v`	Upstream speed in m/s. Alternative: v_m_s. Do not send with Fr.	—	input
`v`	Upstream speed in m/s (query). REST may send v.	m/s	input
`g`	Gravity in m/s². Default 9.80665.	—	input / output
`Fr1`	—	—	output
`Fr2`	—	—	output
`v1`	—	—	output
`v2`	—	—	output
`dE`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Rectangular hydraulic jump: y2/y1 = (√(1+8 Fr₁²) − 1)/2; Fr₁ > 1
ΔE = (y2 − y1)³ / (4 y1 y2); Fr₂ = Fr₁ / (y2/y1)^{3/2}
Not a Froude wrap, not Manning, not Chezy, not a weir, not Q=Av

Not supported

Froude-only Fr=v/√(gL)
Manning n
Chezy C
weir Q(H)
Q=Av

Example

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

y1=1 Fr=2 → y2=(√33−1)/2

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: 17/17 calculation tests · golden 2/2 · boundary 10/10 · 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; 163 CURRENT) @ 2026-09-17T09:03:11.906Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T09:03:11.074Z
Last production check: 2026-09-17T09:03:11.074Z
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. Reference Calculation Standard — Production surface contract 3/3.

Tool id: hydraulic-jump
Engine: hydraulic-jump
REST: POST /api/v1/calc/hydraulic-jump
MCP: execute_calculation with capability_id: "physics.fluid.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 80000-11 — Characteristic numbers — Froude number Fr
Chow, V.T. Open-Channel Hydraulics — Hydraulic jump

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.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.