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

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Hydraulic

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

Solve 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. Power mode. With H computes P; with P computes H.	—	input / output
`H`	Pump head in m. Power mode. Alternative: dP. Do not send both.	—	input / output
`dP`	Pressure rise in Pa. Power-mode alternative to H. Do not send both.	—	input / output
`P`	Shaft power in W. Inverts H or Q, or with Q and H solves η.	—	input / output
`eta`	Overall pump efficiency. Default 1. Must be in (0, 1]. Not used in affinity.	—	input / output
`rho`	Density in kg/m³. Default 1000. Power mode.	—	input / output
`g`	Gravity in m/s². Default 9.80665. Power mode.	—	input / output
`Q1`	Known flow in m³/s. Affinity.	—	input / output
`H1`	Known head in m. Affinity.	—	input / output
`P1`	Known shaft power in W. Affinity optional; scales P2∝N³D³.	—	input / output
`N1`	Known rotational speed. Same unit as N2.	—	input / output
`N2`	Scaled rotational speed. Give with N1.	—	input / output
`D1`	Known impeller diameter. Same unit as D2.	—	input / output
`D2`	Scaled impeller diameter. Give with D1.	—	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

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: 16/16 calculation tests · golden 1/1 · boundary 10/10 · 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: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 163 CURRENT) @ 2026-09-17T03:09:03.307Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T03:09:02.494Z
Last production check: 2026-09-17T03:09:02.494Z
Public / cache: PASS
Origin: PASS

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 3/3.

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

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.pump"}}}'

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