Verified calculation capability

Drowned sluice Calculation Capability

Swamee 1992 drowned undershot sluice: Q=C_d a b √(2g y1) with C_d from y1, a, and y2. Not free-flow sluice, not Villemonte H1+H2, not tank orifice, not Manning n, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.drowned_sluice · 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 = θ · 0.611 [(y1 − a)/(y1 + 15 a)]^{0.072}
Drowned factor: θ = (y1 − y2)^{0.7} / {0.32 [0.81 y2 (y2/a)^{0.72} − y1]^{0.7} + (y1 − a)^{0.7}}

Solve modes: flow · opening

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`a`	Gate opening in m. Required for flow. Alternatives: a_m, opening, gate_opening. Not orifice A.	—	input / output
`b`	Gate width in m. Required. Alternatives: b_m, width, gate_width. Not weir L, not side-weir B.	—	input / output
`y1`	Upstream depth in m. Required. Alternatives: y_1, upstream_depth. Not weir H or H1.	—	input / output
`y2`	Downstream depth in m. Required. Alternatives: y_2, downstream_depth. Drowned when y1 < 0.81 y2 (y2/a)^{0.72}.	—	input / output
`Q`	Volume flow in m³/s. Required for opening. Alternatives: flow, Q_m3_s.	—	input / output
`Cd`	—	—	output
`theta`	—	—	output
`g`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Drowned undershot sluice; y2 required
SI g=9.80665 unless given
Swamee 1992 θ and (y1+15a) form; C_d is reported
Drowned when y1 < 0.81 y2 (y2/a)^{0.72}
Not free-flow sluice, not Villemonte weir, not orifice, not Manning, not Q=Av

Not supported

free-flow sluice without y2
Villemonte H1+H2
tank orifice
Manning n
Q=Av

Example

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

a=0.2 b=1 y1=1 y2=0.8 → Q≈0.13961

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: 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; 164 CURRENT) @ 2026-09-18T13:56:15.885Z
Semantic contract: PASS
Evidence attested at: 2026-09-18T13:56:15.080Z
Last production check: 2026-09-18T13:56:15.080Z
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. Production surface contract 1/1.

Tool id: drowned-sluice
Engine: drowned-sluice
REST: POST /api/v1/calc/drowned-sluice
MCP: execute_calculation with capability_id: "physics.fluid.drowned_sluice"
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 — J. Irrig. Drain. Eng. 118(1), 1992
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.drowned_sluice"}}}'

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