Physics calculator

Concentric Reducer Calculator

Q: 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 A₂/A₁.

Q: Is this Q = A·v?

No. Volumetric flow is /calc/physics/flow-rate. Sending Q or a single A is MIXED_INPUT_ENCODING.

Q: Where does this run?

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

Compute concentric-reducer loss h = K v₂² / (2g) with K = 0.5 (1 − A₂/A₁) referenced to the downstream speed. Runs locally. Not sudden expansion, not gradual contraction α, not vena-contracta C_c, not catalog K, and not Q=Av.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · 5/5 tests · Production surface contract 1/1 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Concentric reducer head from downstream speed and area ratio A₂/A₁. Invert v₂. Optional Δp from ρ.
Scope: Concentric reducer: h = K v₂² / (2g); K = 0.5 (1 − A₂/A₁); K referenced to downstream speed; K is reported, not an input
Verification: Engine tested · 5/5 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 — Concentric reducer; K referenced to the downstream section
Sources
Evidence: 5 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 STALE (1 capability; 163 remain CURRENT) @ 2026-09-17T23:16:16.380Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

Head lossh = K v₂² / (2g)

Area-ratio KK = 0.5 (1 − A₂/A₁)

Pressure dropΔp = ρ K v₂² / 2

iSI. v_m_s is the downstream speed v₂. area_ratio is A₂/A₁, not cavitation σ and not venturi β. g defaults to 9.80665 m/s². Do not send query v — that is calculation_version.

How to use

Enter the area ratio

area_ratio = A₂/A₁ in (0, 1). REST may send A1+A2 or D1+D2 instead. Do not mix encodings.

Enter v₂

v_m_s is the downstream speed. Invert on the v tab from a known h.

Example calculations

Common configurations with formula and result.

σ=0.5, v₂=2 m/s

Downstream area is half the upstream area

K=0.5(1−0.5)=0.25, h=K v₂²/(2g)

h≈0.05099 m · K=0.25 · Δp=500 Pa at ρ=1000

Same σ via A1+A2

A1=2 m², A2=1 m²

σ=A2/A1=0.5

K=0.25

Concentric Reducer calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 5/5 tests · Production surface contract 1/1
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Concentric reducer. K is referenced to the downstream speed v₂ and reported from the area ratio σ = A₂/A₁. K = 0.5 (1 − σ). σ ∈ (0, 1). Geometry from area_ratio or A1+A2 or D1+D2. Not vena-contracta C_c, not conical α, not Borda–Carnot (v1−v2)², not a catalog fitting K.
What it calculates: Concentric reducer head from downstream speed and area ratio A₂/A₁. Invert v₂. Optional Δp from ρ.
Inputs: mode?
area_ratio|A1+A2|D1+D2
v_m_s|h
rho?
g?
Outputs: h
v
v2
K
area_ratio
g
rho
dP
mode
model
Formula: h = K v₂² / (2g); K = 0.5 (1 − A₂/A₁)
Assumptions: Concentric reducer: h = K v₂² / (2g); K = 0.5 (1 − A₂/A₁); K referenced to downstream speed; K is reported, not an input
A₂/A₁ in (0, 1); default g=9.80665 m/s²; default ρ=1000 kg/m³; incompressible; geometry from area_ratio or A1+A2 or D1+D2
Not sudden expansion (v1−v2)², not gradual contraction α, not vena-contracta C_c, not catalog minor-loss K given, not a four-way cross, not Q=Av
Units: SI; v₂ in m/s; h in m; area_ratio dimensionless; ρ in kg/m³; Δp in Pa; K dimensionless
Boundary conditions: missing v_m_s, h, or area_ratio when required → MISSING_REQUIRED_INPUT
v_m_s ≤ 0, h ≤ 0, or area_ratio ≤ 0 → VALUE_MUST_BE_POSITIVE
area_ratio ≥ 1 or K=0 on velocity invert → VALUE_OUT_OF_RANGE
mixed area_ratio with A1+A2 or D1+D2, C_c, α, v1, K given, Q, f, kind, sigma, beta → MIXED_INPUT_ENCODING
unknown mode → INVALID_MODE
Example: v_m_s=2 area_ratio=0.5 → h=K v₂²/(2g) K=0.25
Validation cases: 3 published on this page · 5/5 tests · Production surface contract 1/1 · View evidence
v_m_s=2 area_ratio=0.5 → h=K v₂²/(2g) K=0.25
v_m_s=2 A1=2 A2=1 → K=0.25
v_m_s=2 area_ratio=0.5 C_c=0.62 → 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 — Concentric reducer; K referenced to the downstream section
Supports: K=0.5(1−A₂/A₁) on v₂. Not vena-contracta C_c, not conical α, not catalog K
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute concentric-reducer loss from downstream speed and the area ratio A₂/A₁.

Supported and not supported

Supported — h from v₂ and A₂/A₁ · invert v₂ · API physics.fluid.concentric_reducer

Not supported — vena-contracta C_c, conical α, Borda–Carnot (v1−v2)², catalog minor-loss K, four-way cross, Darcy f, Q=Av, cavitation σ, venturi β

Agent / API notes

Capability id: physics.fluid.concentric_reducer · tool id: concentric-reducer · pin 1.0.0.

{ "v_m_s": 2, "area_ratio": 0.5 }

Modes: head (default), pressure, velocity. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/concentric-reducer. There is no /calc/fluid.

Other calculators in this family: Sudden contraction, Gradual contraction, Sudden expansion, Minor loss .

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Frequently asked questions

Key distinctions behind the calculation.

Is this a sudden contraction?

No. Vena-contracta sudden contraction is /calc/physics/sudden-contraction. That page takes C_c (default 0.62) and does not take A₂/A₁. Sending C_c here is MIXED_INPUT_ENCODING. At σ=0.5 this page reports K=0.25; sudden contraction still reports K≈0.376.

Is this a gradual contraction?

No. The conical confuser with wall half-angle α is /calc/physics/gradual-contraction. Sending alpha_deg is MIXED_INPUT_ENCODING.

Is this sudden expansion?

No. Borda–Carnot (v1−v2)² is /calc/physics/sudden-expansion. This page is a reducer, A₂<A₁, and uses one downstream speed.

Is this minor-loss K?