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Valve Flow Coefficient Calculator

Compute incompressible liquid valve flow from Kv or Cv. Q_m³/h = Kv √(Δp_bar/SG). Kv = 0.865 Cv. Runs locally. Not a venturi, not an orifice, not Q=Av, and not Darcy.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q_m³/h = Kv √(Δp_bar/SG), Kv = 0.865 Cv, plus pressure, Kv, and Cv solves, + O3 mpmath tabulated flow.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Q_m³/h = Kv √(Δp_bar/SG), Kv = 0.865 Cv, plus pressure, Kv, and Cv solves, + O3 mpmath tabulated flow.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, cv, solve, awkward, invalid-domain) · Matrix
Deferred
Not a venturi wrap, not an orifice, and not Q=Av.
Numerical scope
O2: valve Kv/Cv vs a separate-module identity (≤2 ULP). Not a venturi wrap, not an orifice, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated venturi vectors. Not Q=Av, not Manning, and not Darcy.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Incompressible liquid valve flow from catalog Kv or Cv. Invert Δp, Kv, or Cv. Reports Q_m³/h.
Scope
Incompressible liquid; Q_m³/h = Kv √(Δp_bar/SG); default SG=1
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q_m³/h = Kv √(Δp_bar/SG), Kv = 0.865 Cv, plus pressure, Kv, and Cv solves, + O3 mpmath tabulated flow.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3
Verification revision
2026-09-25.o2-o3 · 1/1 property · digest e7be7b65192a
Legacy regression
17/17 tests · Production surface contract 5/5
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
4/4 golden · 9/9 CVP boundary · 9/9 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract · Manifest
Sources
Sources
Evidence
2 legacy golden · 10 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 9/9 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

KvQ_m³/h = Kv √(Δp_bar / SG)
ConversionKv = 0.865 Cv
SIQ = (Kv/3600) √((Δp/10⁵) / SG)
iSI. Δp in Pa, Q in m³/s. Default SG=1 (water). Kv=0.865 Cv is frozen IEC 60534-1. This page is not a venturi, not an orifice plate, not Q=Av, and not gas/choked sizing.

How to use

1

Enter Kv or Cv

Give one catalog coefficient, not both. Kv is m³/h at 1 bar. Cv converts with Kv=0.865 Cv.

2

Enter Δp in Pa

This is the valve differential. 1 bar = 10⁵ Pa. Invert for Δp, Kv, or Cv on the other tabs.

3

Optional SG

Leave blank for water (SG=1). Or send ρ; SG=ρ/1000. Do not send both.

4

Read Q

Q is m³/s. Q_m³/h is the catalog-hour rate. This is not a venturi Q=C_d A2…

Example calculations

Common configurations with formula and result.

ϟ

Kv=10 at 1 bar

Kv=10, Δp=10⁵ Pa, SG=1

Q_m³/h = 10 √(1/1)
Q=10/3600 m³/s
ϟ

From Cv

Cv=10/0.865, same Δp

Kv=0.865 Cv
same Q

Valve Flow Coefficient calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Q_m³/h = Kv √(Δp_bar / SG). Kv = 0.865 Cv (IEC 60534-1). SI reports Q in m³/s and Δp in Pa. Default SG = 1.
What it calculates
Incompressible liquid valve flow from catalog Kv or Cv. Invert Δp, Kv, or Cv. Reports Q_m³/h.
Inputs
  • mode?
  • Kv|Cv
  • dP|Q
  • SG?
  • rho?
Outputs
  • Q
  • Q_m3_h
  • dP
  • SG
  • Kv
  • Cv
  • k
Formula
Q_m³/h = Kv √(Δp_bar/SG)
Assumptions
  • Incompressible liquid; Q_m³/h = Kv √(Δp_bar/SG); default SG=1
  • Kv = 0.865 Cv (IEC 60534-1); frozen, not a US-gpm engine
  • Not gas, not choked, not IEC 60534-2-1 xT/Y
  • Not a venturi, not an orifice, not Q=Av, not Darcy, not minor-loss K
Units
  • SI; Q in m³/s; Δp in Pa; Kv in m³/h at 1 bar; SG dimensionless
Boundary conditions
  • missing Kv/Cv, Δp, or Q when required → MISSING_REQUIRED_INPUT
  • Kv, Cv, Δp, Q, or SG ≤ 0 → VALUE_MUST_BE_POSITIVE
  • Kv and Cv, SG and ρ, D1/D2, C_d, K, A, v, or Q with flow → MIXED_INPUT_ENCODING
  • venturi, orifice, darcy, or Q=Av as mode → INVALID_MODE
Example
Kv=10 dP=1e5 → Q=10/3600
Validation cases

3 published on this page · 17/17 tests · Production surface contract 5/5 · View evidence

  • Kv=10 dP=100000 → Q=10/3600
  • Cv=10/0.865 dP=100000 → same Q
  • mode=venturi Kv=10 dP=100000 → INVALID_MODE
Sources
  • IEC 60534-1 — Industrial-process control valves — Flow capacity — Kv and the Kv–Cv relation
    Supports: Kv is m³/h of water at 1 bar; Kv = 0.865 Cv; this page is liquid incompressible only
  • ISA-75.01.01 — Flow Equations for Sizing Control Valves — Liquid sizing with Cv
    Supports: Incompressible liquid Q ∝ Cv √(ΔP/G); gas and choked corrections are out of scope here
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute incompressible liquid valve flow from catalog Kv or Cv.

Supported and not supported

Supported — Q from Kv or Cv and Δp · invert Δp, Kv, or Cv · SG or ρ · API physics.fluid.valve_cv

Not supported — venturi D1/D2, orifice C_d, Q=Av, Darcy, minor-loss K, gas/choked IEC 60534-2-1

Agent / API notes

Capability id: physics.fluid.valve_cv · tool id: valve-flow-coefficient · pin 1.0.0.

{ "Kv": 10, "dP": 100000 }

From Cv: { "Cv": 11.560693641618497, "dP": 100000 }. Optional "SG". Modes: flow (default), pressure, Kv, Cv. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/valve-flow-coefficient. There is no /calc/fluid.

Other calculators in this family: Alternate Depth Calculator, Bernoulli Equation Calculator, Broad-Crested Weir Calculator, Cavitation Number Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator . Explore all Fluid Mechanics.

→ Alternate Depth Calculator Compute both rectangular depths at the same specific energy from E, Q, and width b. Runs locally. Not specific energy from y+v; not specific force M; not hydraulic jump y2; not critical depth yc as the product. › → Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser. › → Broad-Crested Weir Calculator Compute rectangular broad-crested weir discharge Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. Runs locally. Not a thin-plate weir, not Manning, not Q=Av, and not an orifice. › → Cavitation Number Calculator Compute the cavitation number σ = (p − p_v) / (½ ρ v²). Runs locally. Not NPSH, not Thoma NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²). › → Chezy Formula Calculator Compute open-channel mean velocity V = C √(R S). Runs locally. Not Manning n, not Q=Av, not Hazen–Williams, and not Darcy. › → Colebrook Friction Factor Calculator Solve the Colebrook–White equation for Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Runs locally. Not laminar 64/Re and not a Moody-chart lookup. › → Concentric Reducer Calculator 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. › → Critical Depth Calculator Compute rectangular critical depth yc = (q²/g)^{1/3}. Runs locally. Not a Froude wrap, not specific energy, not a hydraulic jump, and not Q=Av. ›

Frequently asked questions

Key distinctions behind the calculation.

Is this a venturi meter?

No. A converging–throat Bernoulli meter is /calc/physics/venturi. Sending D1 or D2 is MIXED_INPUT_ENCODING.

Is this an orifice?

No. Tank or plate Q=C_d… is /calc/physics/orifice-discharge. Sending C_d is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from area and velocity is /calc/physics/flow-rate. Sending A or v is MIXED_INPUT_ENCODING.

Do you size gas or choked valves?

No. IEC 60534-2-1 gas expansion and choked flow (xT, Y) are out of scope.

Where does this run?

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