Verified calculation capability

Sluice gate Calculation Capability

Swamee 1992 free-flow undershot sluice Q from opening a, width b, and upstream depth y1. Not tank orifice, not thin-plate weir, not a flume, not Manning, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.sluice_gate · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Discharge

Discharge: Q = C_d a b √(2 g y1)
Discharge coefficient: C_d = 0.611 [(y1 − a)/y1]^{0.072}

Solve modes: flow · opening · head

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`a`	Vertical gate opening in m. Required for flow and head. Envelope a/y1∈[0.05, 0.65] and a<y1. Alternatives: a_m, opening, gate_opening. Do not send orifice A or d.	—	input / output
`b`	Gate width in m. Required. Alternatives: b_m, width, gate_width. Do not send flume W or weir crest L.	—	input / output
`y1`	Upstream depth in m. Required for flow and opening. Alternatives: y_1, upstream_depth, y_m. Do not send weir H or flume Ha.	—	input / output
`Q`	Volume flow in m³/s. Required for opening or head invert. Alternatives: flow, Q_m3_s.	—	input / output
`g`	Gravity in m/s². Optional; default 9.80665. Alternative: g_m_s2.	—	input / output
`Cd`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Swamee 1992 free-flow undershot sluice: Q = C_d a b √(2g y1); C_d = 0.611 [(y1−a)/y1]^{0.072}; SI a, b, y1, Q; C_d is reported, not an input
Gate opening a is not orifice area A; y1 is upstream depth, not weir H; a/y1∈[0.05, 0.65]; y1 > a; free flow only
Not thin-plate weir, not tank orifice C_d A √(2gH), not a flume, not Manning n, not Q=Av, not submerged y2

Not supported

tank orifice given C_d
thin-plate weir
broad-crested weir
Parshall
cutthroat
Manning n
Q=Av
submerged y2

Example

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

a=0.2 b=1 y1=1 → Q≈0.53256

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) @ 2026-09-18T02:44:05.986Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T02:44:05.231Z
Last production check: 2026-09-18T02:44:05.231Z
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: sluice-gate
Engine: sluice-gate
REST: POST /api/v1/calc/sluice-gate
MCP: execute_calculation with capability_id: "physics.fluid.sluice_gate"
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

Swamee, P.K. — Sluice-Gate Discharge Equations — Free-flow undershot C_d
ISO 80000-4 — Mechanics — Volume flow rate

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.sluice_gate"}}}'

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