CVP verified calculation capability

Net positive suction head Calculation Capability

NPSH available: open tank (p_atm−p_v)/ρg + z − hf, or suction flange (p_s−p_v)/ρg + v_s²/2g + z_s. Optional NPSHr margin. Not pump power, not orifice, not weir, not Q=Av, not Darcy.

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

Model

Flange

Flange: NPSHa = (p_s − p_v)/(ρ g) + v_s²/(2g) + z_s
Open tank: NPSHa = (p_atm − p_v)/(ρ g) + z − hf
Margin: margin = NPSHa − NPSHr

Modes: available · margin

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`p_v`	Liquid vapor pressure in Pa absolute	—	input / output
`p`	Absolute pressure at the suction flange in Pa	s	input / output
`v`	Suction-flange velocity in m/s	s	input / output
`z`	Elevation of the flange tap relative to the pump datum in m	s	input / output
`z`	Liquid-surface elevation above the pump datum in m	—	input / output
`hf`	Suction-line head loss in m	—	input / output
`p_atm`	Absolute surface pressure in Pa	—	input / output
`NPSHr`	Required NPSH in m from the manufacturer	—	input / output
`rho`	Density in kg/m³	—	input / output
`g`	Gravity in m/s²	—	input / output
`NPSHa`	—	—	output
`margin`	—	—	output
`cavitation`	—	—	output
`kind`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

NPSHa = (p_s − p_v)/(ρ g) + v_s²/(2g) + z_s; pressures absolute; SI
Open tank: p_s=p_atm (default 101325 Pa), z_s=z−hf, v_s=0; hf is an input
Not pump power, not orifice, not weir, not Q=Av, not Darcy, not a catalog NPSHr curve, not steam p_v(T)

Not supported

pump power or affinity
orifice discharge
weir overflow
Q=Av identities
Darcy–Weisbach (hf is an input)
steam p_v(T)
manufacturer catalog curves

Example

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

p_v=2339 z=2 hf=0.5 → NPSHa=(101325−2339)/(1000·9.80665)+2−0.5

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Open-tank and flange NPSHa, optional margin vs NPSHr, + O3 mpmath tabulated NPSHa.. 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 · Open-tank and flange NPSHa, optional margin vs NPSHr, + O3 mpmath tabulated NPSHa.· View Manifest · CVP overview · Specification
Verified scope: Open-tank and flange NPSHa, optional margin vs NPSHr, + O3 mpmath tabulated NPSHa.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (open_tank, flange, margin, awkward, invalid-domain)
Deferred: Not pump power, not orifice C_d, not Darcy f, and not Manning n.
Calculation version: 1.0.0
Verification: 14/14 calculation tests · 2/2 legacy golden · 7/7 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 6800deb08ffc
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: NPSHa vs a separate-module identity (≤2 ULP). Not pump power, not orifice C_d, not Darcy f, and not Manning n. ≤2 ULP vs O3 applies only to the published tabulated NPSH vectors. Not pump power, not orifice C_d, not Darcy f, and not Manning n.
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 · 7/7 CVP boundary · 9/9 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/npsh' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"p_v":2339,"z":2,"hf":0.5},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "p_v": 2339,
    "z": 2,
    "hf": 0.5
  },
  "calculation_version": "1.0.0"
}

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

Full REST contract: REST API docs.

Tool id: npsh
Engine: npsh
REST: POST /api/v1/calc/npsh
MCP: execute_calculation with capability_id: "physics.fluid.npsh"
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

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.npsh"},"_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.npsh","inputs":{"p_v":2339,"z":2,"hf":0.5},"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.