Verified calculation capability

Water hammer Calculation Capability

Joukowsky Δp=ρcΔv. Not Darcy f, not minor-loss K, not Moens–Korteweg, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.water_hammer · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Joukowsky pressure

Joukowsky pressure: Δp = ρ c Δv
Head: h = Δp / (ρ g) = c Δv / g
Speed invert: Δv = Δp / (ρ c)

Solve modes: pressure · velocity · celerity

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`c`	Wave celerity in m/s. Required except celerity invert. Alternative: c_m_s.	—	input / output
`c`	Wave celerity in m/s (query/UI). REST may send c.	m/s	input
`dV`	Sudden speed change in m/s. Required except velocity invert. Alternative: dv_m_s.	—	input / output
`dv`	Sudden speed change in m/s (query/UI). REST may send dV.	m/s	input
`dP`	Surge pressure in Pa. Required for velocity and celerity invert. Do not send with pressure mode.	—	input / output
`rho`	Density in kg/m³. Default 1000.	—	input / output
`g`	Gravity in m/s². Default 9.80665.	—	input / output
`h`	hydrogen-ion concentration	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Joukowsky water hammer: Δp = ρ c Δv; h = Δp/(ρ g); default ρ=1000 kg/m³; default g=9.80665 m/s²
c is the given celerity, not Moens–Korteweg from bulk modulus K, D, e, E
Not Darcy f, not Colebrook, not minor-loss K, not Q=Av

Not supported

Darcy hf=fLv²/(2gD)
minor-loss K
Moens–Korteweg elastic c
Q=Av

Example

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

ρ=1000 c=1000 dV=1 → Δp=1e6

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: 17/17 calculation tests · golden 2/2 · 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) @ 2026-09-17T13:12:27.589Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T13:12:26.751Z
Last production check: 2026-09-17T13:12:26.751Z
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: water-hammer
Engine: water-hammer
REST: POST /api/v1/calc/water-hammer
MCP: execute_calculation with capability_id: "physics.fluid.water_hammer"
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 — Pressure, density, speed
Wylie, E.B. and Streeter, V.L. Fluid Transients — Joukowsky equation

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.water_hammer"}}}'

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