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

Open calculator REST API MCP Evidence Evidence JSON Review policy

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))

Solve modes: flow · length

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`B`	Channel width in m. Required. Alternatives: B_m, channel_width. Do not send sluice/broad-crested b.	—	input / output
`L`	Along-channel weir length in m. Required for flow. Alternatives: L_m, weir_length.	—	input / output
`y1`	Upstream depth in m. Required. Alternatives: y_1, upstream_depth, y_m. Do not send weir H or flume Ha.	—	input / output
`p`	Sill height in m. Required. Envelope p/y1∈[0.1, 0.9]. Alternatives: p_m, sill, sill_height. Do not send ogee P or Hd.	—	input / output
`Q1`	Approach discharge in m³/s. Required unless v1 is given. Alternatives: Q_1, approach, inflow, Q_in. Optional v1 as Q1=v1·B·y1.	—	input / output
`Q`	Lateral overflow in m³/s. Required for length invert. Alternatives: flow, Q_m3_s, Q_w.	—	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

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: 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: 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

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.side_weir"}}}'

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