CVP verified calculation capability

Side weir Calculation Capability

Borghei 1999 sharp-crested side weir Q from B, L, y1, p, and Q1. Not frontal thin-plate weir, not ogee, not sluice, not Manning, not Q=Av.

Physics · Fluid Capability ID physics.fluid.side_weir version 1.0.0 CVP VERIFIED CURRENT Engineering

Model

Lateral discharge

Lateral discharge: Q = (2/3) C_d L √(2g) (y1 − p)^{3/2}
Coefficient: C_d = 0.71 − 0.41 Fr₁ − 0.22 (p / y1)
Approach Froude: Fr₁ = Q1 / (B y1 √(g y1))

Modes: flow · length

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`B`	Channel width in m	—	input / output
`L`	Along-channel weir length in m	—	input / output
`y1`	Upstream depth in m	—	input / output
`p`	Sill height in m	—	input / output
`Q1`	Approach discharge in m³/s	—	input / output
`Q`	Lateral overflow in m³/s	—	input / output
`H`	—	—	output
`Fr1`	—	—	output
`Cd`	—	—	output
`g`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Borghei 1999 sharp-crested side weir: Q=(2/3) C_d L √(2g) (y1−p)^{3/2}; C_d=0.71−0.41 Fr₁−0.22(p/y1); SI B, L, y1, p, Q1, Q; C_d is reported
Rectangular channel; subcritical Fr₁∈[0.1, 0.9]; p/y1∈[0.1, 0.9]; y1>p; free lateral overflow; De Marchi-type C_d, not a given frontal C_d
Not thin-plate frontal weir, not ogee Hd, not sluice a b √(2g y1), not Manning n, not Q=Av, not submerged y2

Example

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

B=1 L=2 y1=0.5 p=0.2 Q1=0.4 → Q≈0.45979

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Borghei 1999 side weir Q=(2/3) Cd L √(2g) (y1−p)^{3/2} with Cd=0.71−0.41 Fr₁−0.22(p/y1), + 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 · Borghei 1999 side weir Q=(2/3) Cd L √(2g) (y1−p)^{3/2} with Cd=0.71−0.41 Fr₁−0.22(p/y1), + O3 mpmath tabulated Q.· View Manifest · CVP overview · Specification
Verified scope: Borghei 1999 side weir Q=(2/3) Cd L √(2g) (y1−p)^{3/2} with Cd=0.71−0.41 Fr₁−0.22(p/y1), + O3 mpmath tabulated Q.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (flow, alias, awkward, v1, invalid-domain)
Deferred: Not frontal thin-plate given Cd, not ogee Hd, not sluice, not Manning, not submerged y2, 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 a829ba1c8ed9
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: Borghei 1999 side weir vs a separate-module identity (≤2 ULP). Not frontal thin-plate, not ogee Hd, not sluice, not Manning, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated side-weir vectors. Not frontal thin-plate, not ogee Hd, not sluice, 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/side-weir' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"B":1,"L":2,"y1":0.5,"p":0.2,"Q1":0.4},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "B": 1,
    "L": 2,
    "y1": 0.5,
    "p": 0.2,
    "Q1": 0.4
  },
  "calculation_version": "1.0.0"
}

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

Full REST contract: REST API docs.

Tool id: side-weir
Engine: side-weir
REST: POST /api/v1/calc/side-weir
MCP: execute_calculation with capability_id: "physics.fluid.side_weir"
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

Borghei, Jalili & Ghodsian — Discharge Coefficient for Sharp-Crested Side Weir in Subcritical Flow — Journal of Hydraulic Engineering, 1999
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.side_weir"},"_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.side_weir","inputs":{"B":1,"L":2,"y1":0.5,"p":0.2,"Q1":0.4},"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.