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Physics calculator

Pipe Wye Calculator

Compute equal-area sharp wye loss h = K v_c² / (2g) from branch angle α in (0, 90°), dividing or combining flow, and branch or run split. Runs locally. Not a 90° tee, not catalog K, not a bend, and not Q=Av.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 6/6 tests · Production surface contract 1/1 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Equal-area sharp wye head from common-channel speed, branch angle α∈(0,90°), dividing or combining pattern, branch or run, and q=Q_path/Q_c. Invert v_c. Optional Δp from ρ.
Scope
Equal-area sharp wye: h = K v_c² / (2g); K referenced to common-channel speed; α ∈ (0, 90°); K is reported, not an input
Verification
Engine tested · 6/6 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review
Optional · Not performed
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
Sources
Evidence
6 property · Production surface contract 1/1 · Artifact integrity PASS
Production
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

Formulas

Core equations used by this calculator.

Head lossh = K v_c² / (2g)
BranchK_s = 1 + q² − 2 q cos α
Dividing runK_st = 0.4 (1 − q)²
Combining runK_st = 1 − q² − 2 q (1 − q) cos α
Pressure dropΔp = ρ K v_c² / 2
iSI. q = Q_path/Q_c in [0, 1]. v_m_s is the common-channel speed v_c, not the path speed. α is the branch angle in (0, 90°); 90° is pipe-tee. g defaults to 9.80665 m/s². Do not send query v — that is calculation_version.

How to use

1

Enter α

Branch angle alpha_deg in (0, 90). 90° is /calc/physics/pipe-tee.

2

Choose pattern

dividing (split from the common inlet) or combining (merge into the common outlet). URL field is kind.

3

Choose path

branch (angled takeoff) or run (straight through). URL field is path.

4

Enter q and v_c

q_ratio = Q_path/Q_c. v_m_s is the common-channel speed. Invert on the v tab.

Example calculations

Common configurations with formula and result.

ϟ

Dividing branch, α=45°, q=0.5, v_c=2 m/s

Half the inlet flow leaves through the 45° branch

K=1+q²−2q cos α≈0.54289, h=K v_c²/(2g)
h≈0.11072 m · K≈0.54289 · Δp≈1085.8 Pa at ρ=1000
ϟ

Dividing run, q=0.5

Same split on the straight through; Idelchik 7-20

K=0.4(1−q)²=0.1
K=0.1

Pipe Wye calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Equal-area sharp wye. K is referenced to the common-channel speed v_c and reported from α, the flow pattern, and q = Q_path/Q_c. 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. α ∈ (0, 90°). Not a 90° tee, not a catalog fitting K, not a bend.
What it calculates
Equal-area sharp wye head from common-channel speed, branch angle α∈(0,90°), dividing or combining pattern, branch or run, and q=Q_path/Q_c. Invert v_c. Optional Δp from ρ.
Inputs
  • mode?
  • kind?
  • path?
  • q_ratio
  • alpha_deg
  • v_m_s|h
  • rho?
  • g?
Outputs
  • h
  • v
  • K
  • kind
  • path
  • q
  • q_ratio
  • g
  • rho
  • dP
  • alpha_deg
  • mode
  • model
Formula
h = K v_c² / (2g); branch 1+q²−2q cos α; dividing run 0.4(1−q)²; combining run 1−q²−2q(1−q)cos α
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
Units
  • SI; v_c in m/s; h in m; q dimensionless; α in degrees; ρ in kg/m³; Δp in Pa; K dimensionless
Boundary conditions
  • missing v_m_s, h, q_ratio, or alpha_deg when required → MISSING_REQUIRED_INPUT
  • v_m_s ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
  • q_ratio > 1, α ∉ (0, 90), or K=0 on velocity invert → VALUE_OUT_OF_RANGE
  • K, rd, n_miters, θ, f, Q, A, v1/v2, ri_d, α=90° → MIXED_INPUT_ENCODING
  • flush, circular, or unknown kind/path/mode → INVALID_MODE
Example
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
Validation cases

3 published on this page · 6/6 tests · Production surface contract 1/1 · View evidence

  • 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
  • v_m_s=2 kind=dividing path=run q_ratio=0.5 alpha_deg=45 → K=0.1
  • v_m_s=2 kind=dividing path=branch q_ratio=0.5 alpha_deg=90 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Length, speed, pressure
    Supports: h is a head; v is a speed; Δp is a 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
    Supports: 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; K referenced to v_c. Not a 90° tee, not catalog K, not a bend
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute pipe-wye loss from common-channel speed, branch angle, dividing or combining flow, and the branch or run split.

Supported and not supported

Supported — h from v_c, α, kind, path, and q · invert v_c · API physics.fluid.pipe_wye

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

Agent / API notes

Capability id: physics.fluid.pipe_wye · tool id: pipe-wye · pin 1.0.0.

{ "v_m_s": 2, "kind": "dividing", "path": "branch", "q_ratio": 0.5, "alpha_deg": 45 }

Modes: head (default), pressure, velocity. Kinds: dividing (default), combining. Paths: branch (default), run. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/pipe-wye. There is no /calc/fluid.

Other calculators in this family: Pipe tee, Minor loss, Pipe bend, Pipe entrance .

h Pipe tee › K Minor loss › h Pipe bend › h Pipe entrance ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this a 90° tee?

No. The equal-area sharp 90° T is /calc/physics/pipe-tee. Sending alpha_deg=90 is MIXED_INPUT_ENCODING.

Is this minor-loss K?

No. Catalog fitting K is /calc/physics/minor-loss. Sending K is MIXED_INPUT_ENCODING. This page reports K from α, kind, path, and q.

Is this circular-arc pipe-bend?

No. Smooth R/D ≥ 1 is /calc/physics/pipe-bend. Sending rd or θ is MIXED_INPUT_ENCODING. This wye is a sharp junction with branch angle α.

Is this Q = A·v?

No. Volumetric flow is /calc/physics/flow-rate. Sending Q or A is MIXED_INPUT_ENCODING. q_ratio is the dimensionless split Q_path/Q_c.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine pipeWye wrapper.