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Physics calculator

Venturi Meter Calculator

Compute incompressible venturi flow Q = C_d A2 √(2Δp/(ρ(1−β⁴))) with β = D2/D1. Default C_d = 0.98. Runs locally. Not an orifice plate, not Q=Av, not Darcy, and not valve Cv/Kv.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q = Cd E A2 sqrt(2 Δp/ρ), E = 1/sqrt(1−β^4), default Cd = 0.98, plus pressure, throat, and Cd solves, + O3 mpmath tabulated discharge.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Q = Cd E A2 sqrt(2 Δp/ρ), E = 1/sqrt(1−β^4), default Cd = 0.98, plus pressure, throat, and Cd solves, + O3 mpmath tabulated discharge.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, solve, given-cd, awkward, invalid-domain) · Matrix
Deferred
Not an orifice wrap, not Q=Av, and not Darcy.
Numerical scope
O2: venturi meter vs a separate-module identity (≤2 ULP). Not an orifice wrap, not Q=Av, and not Darcy. ≤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 venturi-tube discharge from D1, D2, and Δp or same-fluid Δh. Invert Δp, D2, or C_d. Reports Q_ideal at C_d=1.
Scope
Incompressible venturi tube; SI; default C_d=0.98; C_d in (0, 1]
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Q = Cd E A2 sqrt(2 Δp/ρ), E = 1/sqrt(1−β^4), default Cd = 0.98, plus pressure, throat, and Cd solves, + O3 mpmath tabulated discharge.· 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 a4f2e3873621
Legacy regression
17/17 tests · Production surface contract 6/6
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 · 6/6 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.

DischargeQ = C_d A2 √(2Δp / (ρ (1 − β⁴)))
Approachβ = D2/D1 · E = 1/√(1 − β⁴)
ManometerΔp = ρ g Δh (same fluid)
iSI. Default C_d = 0.98. C_d must be in (0, 1]. Throat D2 must be smaller than inlet D1. This page is not a sharp-edged orifice plate, not Q=Av, not Darcy–Weisbach, and not valve Cv/Kv.

How to use

1

Enter inlet D1 and throat D2

This is a converging–throat tube, not an orifice plate. Do not send orifice d or pipe D.

2

Enter Δp and ρ, or same-fluid Δh

Δp is inlet-to-throat differential pressure. Same-fluid manometer Δh is an alternative. Do not send tank head H.

3

Optional C_d

Leave blank for 0.98. C_d must be in (0, 1]. Invert for Δp, D2, or C_d on the other tabs.

4

Read Q and Q_ideal

Q is C_d-corrected. Q_ideal is the Bernoulli identity at C_d=1. Also reports v1 and v2.

Example calculations

Common configurations with formula and result.

ϟ

β = 0.5, 10 kPa

D1=0.1 m, D2=0.05 m, Δp=10 kPa, ρ=1000 kg/m³, default C_d=0.98

Q = 0.98 E (π D2²/4) √(2Δp/ρ)
Q≈0.008887 m³/s
ϟ

Same-fluid Δh

Same geometry, Δh=Δp/(ρ g)

Q = 0.98 E A2 √(2 g Δh)
same Q

Venturi Meter calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Q = C_d A2 √(2Δp / (ρ (1 − β⁴))), β = D2/D1. Optional same-fluid Δh with Δp = ρ g Δh. Default C_d = 0.98. Ideal Bernoulli Q_ideal uses C_d = 1.
What it calculates
Incompressible venturi-tube discharge from D1, D2, and Δp or same-fluid Δh. Invert Δp, D2, or C_d. Reports Q_ideal at C_d=1.
Inputs
  • mode?
  • D1
  • D2?
  • dP|dH
  • rho?
  • Q?
  • Cd?
  • g?
Outputs
  • Q
  • Q_ideal
  • D1
  • D2
  • beta
  • E
  • A1
  • A2
  • v1
  • v2
  • Cd
  • dP?
  • dH
Formula
Q = C_d A2 √(2Δp/(ρ(1−β⁴)))
Assumptions
  • Incompressible venturi tube; SI; default C_d=0.98; C_d in (0, 1]
  • Q=C_d A2 √(2Δp/(ρ(1−β⁴))), β=D2/D1; Q_ideal uses C_d=1
  • Optional same-fluid manometer Δh with Δp=ρ g Δh; not tank H
  • Not an orifice plate, not Q=Av, not Darcy, not minor-loss K, not valve Cv/Kv
Units
  • SI; D1, D2, Δh in m; Q in m³/s; Δp in Pa; ρ in kg/m³
Boundary conditions
  • missing D1, D2, Δp/Δh, Q, or ρ when required → MISSING_REQUIRED_INPUT
  • D1, D2, Δp, Δh, Q, ρ, or C_d ≤ 0 → VALUE_MUST_BE_POSITIVE
  • D2 ≥ D1 or inverted C_d > 1 → VALUE_OUT_OF_RANGE
  • orifice d or D, tank H, A, v, Cv/Kv, K, f, n, C, Q with flow → MIXED_INPUT_ENCODING
  • orifice, tank, weir, darcy, or Cv as mode → INVALID_MODE
Example
D1=0.1 D2=0.05 dP=10000 rho=1000 → Q=0.98 E A2 √(2Δp/ρ)
Validation cases

3 published on this page · 17/17 tests · Production surface contract 6/6 · View evidence

  • D1=0.1 D2=0.05 dP=10000 rho=1000 → Q≈0.008887
  • mode=pressure D1=0.1 D2=0.05 Q≈0.008887 rho=1000 → dP=10000
  • mode=orifice D1=0.1 D2=0.05 dP=10000 rho=1000 → INVALID_MODE
Sources
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute incompressible venturi-tube discharge Q = C_d A2 √(2Δp/(ρ(1−β⁴))).

Supported and not supported

Supported — Q from D1, D2, and Δp or same-fluid Δh · invert Δp, D2, or C_d · Q_ideal at C_d=1 · API physics.fluid.venturi

Not supported — orifice plate, Q=Av identities, Darcy–Weisbach, minor-loss K, valve Cv/Kv, compressible ISO ε(Re), ISO 5167-4 C(Re)

Agent / API notes

Capability id: physics.fluid.venturi · tool id: venturi · pin 1.0.0.

{ "D1": 0.1, "D2": 0.05, "dP": 10000, "rho": 1000 }

Manometer: { "D1": 0.1, "D2": 0.05, "dH": 1.0197, "rho": 1000 }. Optional "Cd". Modes: flow (default), pressure, throat, Cd. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/venturi. 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 an orifice meter?

No. A sharp-edged orifice plate is /calc/physics/orifice-discharge (default C_d=0.61, orifice d and pipe D). This page is a venturi tube with inlet D1, throat D2, and default C_d=0.98. Sending orifice d or pipe D is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. Sending A or v is MIXED_INPUT_ENCODING. Give D1 and D2.

Is this valve Cv or Kv?

No. Valve flow coefficients are out of scope. Sending Cv or Kv is MIXED_INPUT_ENCODING.

Does this solve ISO 5167-4 C(Re)?

No. You supply C_d or use 0.98. Compressible expansion factor ε and the ISO 5167-4 C(Re) correlation are out of scope.

Where does this run?

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