Verified calculation capability

Ogee spillway Calculation Capability

USBR high-overflow ogee Q from crest L, head H, and design head Hd. Not thin-plate weir, not broad-crested weir, not sluice, not Manning, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.ogee_spillway · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Discharge

Discharge: Q_cfs = C L_ft H_ft^{3/2}
Coefficient: C = 3.98 (H / Hd)^{0.12}

Solve modes: flow · head

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`L`	Crest length in m. Required. Alternatives: L_m, crest, crest_length. Do not send broad-crested b.	—	input / output
`H`	Upstream head above the crest in m. Required for flow. Envelope H/Hd∈[0.2, 1.33]. Alternatives: head, H_m. Do not send flume Ha or sluice y1.	—	input / output
`Hd`	Design head in m. Required. Alternatives: H_d, Hd_m, design_head. Thin-plate weirs have no Hd.	—	input / output
`Q`	Volume flow in m³/s. Required for head invert. Alternatives: flow, Q_m3_s.	—	input / output
`P`	Optional spillway height in m. Envelope P/Hd≥1.7. Alternatives: P_m, height, spillway_height.	—	input / output
`C`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

USBR high-overflow ogee: Q_cfs = C L_ft H_ft^{3/2}; C = 3.98 (H/Hd)^{0.12}; SI L, H, Hd, Q; C is reported, not an input
H/Hd∈[0.2, 1.33]; optional P with P/Hd≥1.7; vertical upstream face; free overflow
Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not broad-crested (2/3)^{3/2} b √g H^{3/2}, not sluice, not Manning n, not Q=Av, not Francis 3.33

Not supported

thin-plate weir given C_d
broad-crested weir
sluice
Manning n
Q=Av
Francis 3.33
drowned spillway

Example

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

L=1 H=1 Hd=1 → Q≈2.19731

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: ogee-spillway
Engine: ogee-spillway
REST: POST /api/v1/calc/ogee-spillway
MCP: execute_calculation with capability_id: "physics.fluid.ogee_spillway"
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

USBR — Design of Small Dams — High overflow ogee, vertical upstream face
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.ogee_spillway"}}}'

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