Verified calculation capability

Pipe wye Calculation Capability

Equal-area sharp wye h=K v_c²/(2g) from α∈(0,90°), dividing/combining, and branch/run split. Not a 90° tee, not catalog K, not circular-arc, not Q=Av. · Physics · Fluid

Capability ID physics.fluid.pipe_wye · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Head loss

Head loss: h = K v_c² / (2g)
Branch: K_s = 1 + q² − 2 q cos α
Dividing run: K_st = 0.4 (1 − q)²
Combining run: K_st = 1 − q² − 2 q (1 − q) cos α
Pressure drop: Δp = ρ K v_c² / 2

Solve modes: head · pressure · velocity

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`kind`	Flow pattern. dividing (default, split from the common inlet) or combining (merge into the common outlet). Alternative: pattern.	—	input / output
`path`	Leg. branch (default, angled takeoff) or run (straight through). Alternative: leg.	—	input / output
`q_ratio`	Q_path / Q_c. Required. Alternatives: q, flow_ratio. Not Q=Av.	—	input / output
`alpha_deg`	Branch angle in degrees, exclusive (0, 90). Required. 90° is pipe-tee. Alternatives: alpha, alpha_rad.	—	input / output
`alpha_rad`	Branch angle in radians. Alternative to alpha_deg. Do not send both.	—	input
`v`	Common-channel speed v_c in m/s. Required except velocity invert. Alternative: speed. Do not send query v (that is calculation_version).	m/s	input
`speed`	Common-channel speed in m/s (REST alias of v_m_s).	—	input
`h`	Head loss in m. Required for velocity invert. Alternatives: hm, h_m.	—	input / output
`h`	Head loss in m (query/UI). REST may send h.	m	input
`rho`	Density in kg/m³. Optional; default 1000.	—	input / output
`g`	Gravity in m/s². Optional; default 9.80665.	—	input / output
`v`	velocity	—	output
`K`	—	—	output
`q`	—	—	output
`dP`	—	—	output
`model`	—	—	output

Assumptions / Validity

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

Assumptions

Equal-area sharp wye: h = K v_c² / (2g); K referenced to common-channel speed; α ∈ (0, 90°); K is reported, not an input
Branch K=1+q²−2q cos α. Dividing run K=0.4(1−q)². Combining run K=1−q²−2q(1−q)cos α. q=Q_path/Q_c in [0,1]; default g=9.80665 m/s²; default ρ=1000 kg/m³
Not a 90° tee, not catalog minor-loss K given, not circular-arc R/D, not mitered n, not pipe-entrance geometry, not pipe-exit K=1, not Q=Av

Not supported

90° tee
catalog minor-loss K
circular-arc R/D
mitered n
pipe-entrance geometry
pipe-exit K=1
Darcy f
Q=Av

Example

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

v_m_s=2 kind=dividing path=branch q_ratio=0.5 alpha_deg=45 → h=K v_c²/(2g) K=1+q²−2q cos α

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: 6/6 calculation tests · golden 0/0 · boundary 0/0 · property 6/6
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; 164 CURRENT) @ 2026-09-17T23:04:35.003Z
Semantic contract: PASS
Evidence attested at: 2026-09-17T23:04:34.157Z
Last production check: 2026-09-17T23:04:34.157Z
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. Production surface contract 1/1.

Tool id: pipe-wye
Engine: pipe-wye
REST: POST /api/v1/calc/pipe-wye
MCP: execute_calculation with capability_id: "physics.fluid.pipe_wye"
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 — Length, speed, pressure
Idelchik — Handbook of Hydraulic Resistance — Diagrams 7-21 / 7-29 (dividing branch) and 7-1 (combining); 7-20 No.1 dividing run; equal-area wye

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.pipe_wye"}}}'

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