CVP verified calculation capability

Cutthroat flume Calculation Capability

Skogerboe cutthroat free-flow Q from throat W, independent length L_f, and gage Ha. Not Parshall, not thin-plate weir, not broad-crested weir, not Manning, not Q=Av, not orifice.

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

Model

Skogerboe free flow

Skogerboe free flow: Q_cfs = C Ha_ft^n
Coefficient: C = 3.50 W_ft^{1.025} (L_f / 3 ft)^{0.020}
Exponent: n = 1.56 (L_f / 3 ft)^{0.026}

Modes: flow · head

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`W`	Throat width in m	—	input / output
`L_f`	Independent flume length in m	—	input / output
`Ha`	Specified-gage upstream head in m	—	input / output
`Q`	Volume flow in m³/s	—	input / output
`n`	—	—	output
`C`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Skogerboe cutthroat free flow: Q_cfs = C Ha_ft^n; C=3.50 W_ft^{1.025} (L_f/3 ft)^{0.020}; n=1.56 (L_f/3 ft)^{0.026}; SI W, L_f, Ha, Q; C and n are reported, not inputs
No diverging section; L_f is independent flume length, not weir crest L; W < L_f; L_f∈[0.4572 m, 2.7432 m]; W∈[0.0508 m, 1.8288 m]; Ha∈[0.03048 m, 1.2192 m]
Not Parshall 4 W_ft Ha^{1.522 W^{0.026}}, not thin-plate weir, not broad-crested (2/3)^{3/2} √g, not Manning n, not Q=Av, not orifice, not submerged Hb

Not supported

Parshall (no independent L_f)
thin-plate weir
broad-crested weir
Manning n
Q=Av
orifice
submerged Hb/Ha

Example

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

L_f=0.9144 W=0.3048 Ha=0.3048 → Q≈0.09911

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Skogerboe 3-ft cutthroat free flow Q_cfs=C Ha_ft^n with independent L_f, + 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 · Skogerboe 3-ft cutthroat free flow Q_cfs=C Ha_ft^n with independent L_f, + O3 mpmath tabulated Q.· View Manifest · CVP overview · Specification
Verified scope: Skogerboe 3-ft cutthroat free flow Q_cfs=C Ha_ft^n with independent L_f, + O3 mpmath tabulated Q.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (flow, alias, awkward, wide, invalid-domain)
Deferred: Not submerged Hb, not Parshall (no free L_f), not thin-plate/broad crest, not Manning, not orifice.
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-o3.1
Verification revision: 2026-09-26.o2-o3.1 · 1/1 property · digest 9af5e6db77de
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: Skogerboe cutthroat free flow vs a separate-module identity (≤2 ULP). Not Parshall, not weir H/L, not Manning n input, and not submerged Hb. ≤2 ULP vs O3 applies only to the published tabulated cutthroat vectors. Not Parshall, not weir H/L, not Manning n input, and not submerged Hb.
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/cutthroat-flume' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"W":0.3048,"L_f":0.9144000000000001,"Ha":0.3048},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "W": 0.3048,
    "L_f": 0.9144000000000001,
    "Ha": 0.3048
  },
  "calculation_version": "1.0.0"
}

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

Full REST contract: REST API docs.

Tool id: cutthroat-flume
Engine: cutthroat-flume
REST: POST /api/v1/calc/cutthroat-flume
MCP: execute_calculation with capability_id: "physics.fluid.cutthroat_flume"
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

Skogerboe, G.V.; Hyatt, M.L.; England, J.D.; Johnson, J.R. — Design and Calibration of Submerged Open Channel Flow Measurement Structures, Part 3: Cutthroat Flumes — 3-ft family free-flow rating
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.cutthroat_flume"},"_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.cutthroat_flume","inputs":{"W":0.3048,"L_f":0.9144000000000001,"Ha":0.3048},"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.