CVP verified calculation capability

Specific force Calculation Capability

Rectangular M=Q²/(gA)+A ȳ with ȳ=y/2. Not hydraulic jump y2, not specific energy E, not Froude as the product, not Manning n, not Q=Av, not critical slope Sc.

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

Model

Specific force

Specific force: M = Q²/(gA) + A y/2
Section: A = b y
Critical: Mc = (3/2) b yc²

Modes: force · depth

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`b`	Rectangular surface width in m	—	input / output
`Q`	Volume flow in m³/s	—	input / output
`y`	Flow depth in m	—	input / output
`M`	Specific force in m²	—	input / output
`g`	Gravity in m/s²	—	input / output
`branch`	Depth invert branch: omit or subcritical	—	input
`y_alt`	—	—	output
`yc`	—	—	output
`Mc`	—	—	output
`ybar`	—	—	output
`A`	—	—	output
`v`	—	—	output
`Fr`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Rectangular specific force: M = Q²/(gA) + A ȳ with A=b y and ȳ=y/2; SI; default g=9.80665; M is m²
Unknown is M (force mode) or y (depth invert, subcritical y>yc by default); conjugate y_alt is reported; Fr is reported not an input
Not hydraulic jump y2 from Fr₁>1; not specific energy E=y+v²/(2g); not Froude as the product; not Manning n; not Q=Av; not critical slope Sc

Not supported

hydraulic jump y2 from Fr₁>1
specific energy E
Froude as the product
Manning n
Q=Av
critical slope Sc
trapezoid z (that is /calc/physics/trapezoidal-specific-force)

Example

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

Q=2 b=2 y=1 → M≈1.20394

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Rectangular M = Q²/(gA) + A y/2 with depth invert; + O3 mpmath tabulated M.. 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 · Rectangular M = Q²/(gA) + A y/2 with depth invert; + O3 mpmath tabulated M.· View Manifest · CVP overview · Specification
Verified scope: Rectangular M = Q²/(gA) + A y/2 with depth invert; + O3 mpmath tabulated M.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (force, solve, alias, awkward, invalid-domain)
Deferred: Not jump y2, not specific energy E, not Froude as the product, not trapezoid M, and 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 f373c0b162f6
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: rectangular M=Q²/(gA)+A y/2 vs a separate-module identity (≤2 ULP). Not jump y2, not specific energy E, not Froude as the product, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated specific-force vectors. Not jump y2, not E, and not trapezoid M.
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 · 2/2 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/specific-force' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"Q":2,"b":2,"y":1},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "Q": 2,
    "b": 2,
    "y": 1
  },
  "calculation_version": "1.0.0"
}

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

Full REST contract: REST API docs.

Tool id: specific-force
Engine: specific-force
REST: POST /api/v1/calc/specific-force
MCP: execute_calculation with capability_id: "physics.fluid.specific_force"
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

ISO 80000-4 — Mechanics — Volume flow rate and force
Chow, V.T. Open-Channel Hydraulics — Specific force and sequent depths

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.specific_force"},"_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.specific_force","inputs":{"Q":2,"b":2,"y":1},"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.