CVP 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 CVP VERIFIED CURRENT Engineering

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}}

Modes: flow · opening

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`a`	Gate opening in m	—	input / output
`b`	Gate width in m	—	input / output
`y1`	Upstream depth in m	—	input / output
`y2`	Downstream depth in m	—	input / output
`Q`	Volume flow in 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

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Swamee 1992 drowned undershot sluice Q=C_d a b √(2g y1) with θ from y1,y2,a, + O3 mpmath tabulated Q.. 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 · Swamee 1992 drowned undershot sluice Q=C_d a b √(2g y1) with θ from y1,y2,a, + O3 mpmath tabulated Q.· View Manifest · CVP overview · Specification
Verified scope: Swamee 1992 drowned undershot sluice Q=C_d a b √(2g y1) with θ from y1,y2,a, + O3 mpmath tabulated Q.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (flow, alias, awkward, deep, invalid-domain)
Deferred: Not free-flow sluice without y2, not Villemonte H1/H2, not orifice Cd/A, not Manning, not Q=Av.
Calculation version: 1.0.0
Verification: 6/6 calculation tests · 1/1 legacy golden · 0/0 legacy boundary · 5/5 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 23e051cc2209
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: Swamee drowned undershot sluice vs a separate-module identity (≤2 ULP). Not free-flow sluice without y2, not Villemonte H1/H2, not orifice Cd/A, not Manning, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated drowned-sluice vectors. Not free-flow without y2, not Villemonte H1/H2, not orifice, not Manning, and not Q=Av.
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 · 3/3 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/drowned-sluice' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"a":0.2,"b":1,"y1":1,"y2":0.8},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "a": 0.2,
    "b": 1,
    "y1": 1,
    "y2": 0.8
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/drowned-sluice. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

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

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.drowned_sluice"},"_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.drowned_sluice","inputs":{"a":0.2,"b":1,"y1":1,"y2":0.8},"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.