CVP verified calculation capability
Korteweg–Hall c=√[(K/ρ)/(1+(K D)/(E e))]. Not Joukowsky Δp, not Darcy f, not minor-loss K, not Q=Av.
Physics · Fluid Capability ID physics.fluid.wave_celerity version 1.0.0 CVP VERIFIED CURRENT Engineering
Korteweg–Hall celerity
c = √[(K/ρ) / (1 + (K D)/(E e))]K = c² / (1/ρ − c² D/(E e))E = K D / (e (K/(ρ c²) − 1))Modes: celerity · bulk · youngs
Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
K | Fluid bulk modulus in Pa | — | input / output |
K_bulk | Fluid bulk modulus in Pa | — | input |
D | Inner diameter in m | — | input / output |
e | Wall thickness in m | — | input / output |
e | Wall thickness in m | m | input |
E | Wall Young’s modulus in Pa | — | input / output |
c | Wave celerity in m/s | — | input / output |
c | Wave celerity in m/s | m/s | input |
rho | Density in kg/m³ | — | input / output |
model | — | — | output |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
Not supported
One numerical check. The calculator page holds worked steps and FAQ.
K=2.2e9 D=1 e=0.01 E=2e11 → c≈1023.53
CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · c = √[(K/ρ)/(1+(K D)/(E e))] (Korteweg–Hall) with bulk and Young's solves; + O3 mpmath tabulated c.. 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.
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/wave-celerity' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"K":2200000000,"D":1,"e":0.01,"E":200000000000},"calculation_version":"1.0.0"}'{
"inputs": {
"K": 2200000000,
"D": 1,
"e": 0.01,
"E": 200000000000
},
"calculation_version": "1.0.0"
}POST /api/v1/calc/wave-celerity. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
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
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.wave_celerity"},"_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.wave_celerity","inputs":{"K":2200000000,"D":1,"e":0.01,"E":200000000000},"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.