CVP verified calculation capability

Pump power Calculation Capability

Pump hydraulic and shaft power P_h=ρgQH, P=P_h/η, plus affinity Q∝ND, H∝N²D², P∝N³D³. Not an orifice, not a weir, not Q=Av, not Darcy, not NPSH.

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

Model

Hydraulic

Hydraulic: P_h = ρ g Q H
Shaft: P = P_h / η
Affinity: Q ∝ N D · H ∝ N² D² · P ∝ N³ D³

Modes: power · affinity

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`Q`	Volume flow in m³/s	—	input / output
`H`	Pump head in m	—	input / output
`dP`	Pressure rise in Pa	—	input / output
`P`	Shaft power in W	—	input / output
`eta`	Overall pump efficiency	—	input / output
`rho`	Density in kg/m³	—	input / output
`g`	Gravity in m/s²	—	input / output
`Q1`	Known flow in m³/s	—	input / output
`H1`	Known head in m	—	input / output
`P1`	Known shaft power in W	—	input / output
`N1`	Known rotational speed	—	input / output
`N2`	Scaled rotational speed	—	input / output
`D1`	Known impeller diameter	—	input / output
`D2`	Scaled impeller diameter	—	input / output
`P_h`	—	—	output
`Q2`	—	—	output
`H2`	—	—	output
`P2`	—	—	output
`n_ratio`	—	—	output
`D_ratio`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Incompressible pump; P_h = ρ g Q H; P = P_h/η; default ρ=1000 kg/m³; η in (0, 1]
Affinity: Q∝N D, H∝N² D², P∝N³ D³; geometrically similar; same fluid
Not orifice, not weir, not Q=Av, not Darcy, not NPSH, not a catalog curve

Not supported

orifice discharge
weir overflow
Q=Av identities
Darcy–Weisbach
NPSH
manufacturer curves
viscous corrections

Example

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

Q=0.05 H=20 eta=0.75 → P=ρgQH/η

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Pump hydraulic/shaft power P_h=ρgQH, P=P_h/η, plus affinity laws, + O3 mpmath tabulated P.. 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 · Pump hydraulic/shaft power P_h=ρgQH, P=P_h/η, plus affinity laws, + O3 mpmath tabulated P.· View Manifest · CVP overview · Specification
Verified scope: Pump hydraulic/shaft power P_h=ρgQH, P=P_h/η, plus affinity laws, + O3 mpmath tabulated P.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (power, affinity, alias, awkward, invalid-domain)
Deferred: Not orifice, not weir, not Manning, not Darcy, and not NPSH.
Calculation version: 1.0.0
Verification: 16/16 calculation tests · 1/1 legacy golden · 10/10 legacy boundary · 5/5 legacy property
Production surface contract: 5/5
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 ce18e1b48677
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: pump power/affinity vs a separate-module identity (≤2 ULP). Not orifice, not weir, not Manning, not Darcy, and not NPSH. ≤2 ULP vs O3 applies only to the published tabulated pump vectors. Not orifice, not weir, not Manning, not Darcy, and not NPSH.
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 · 9/9 CVP boundary · 10/10 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 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 5/5.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/pump-power' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"Q":0.05,"H":20,"eta":0.75},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "Q": 0.05,
    "H": 20,
    "eta": 0.75
  },
  "calculation_version": "1.0.0"
}

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

Full REST contract: REST API docs.

Tool id: pump-power
Engine: pump-power
REST: POST /api/v1/calc/pump-power
MCP: execute_calculation with capability_id: "physics.fluid.pump"
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 9906 — Rotodynamic pumps — Hydraulic performance acceptance tests — Pump power and efficiency definitions
Stepanoff, A.J. Centrifugal and Axial Flow Pumps — Affinity laws

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.pump"},"_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.pump","inputs":{"Q":0.05,"H":20,"eta":0.75},"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.