HomeCalculatorsPhysicsFluid MechanicsWeber Number Calculator
Physics calculator

Weber Number Calculator

Compute the Weber number We = ρ v² L / σ. Runs locally. Not Reynolds, not Froude, not Manning, not Q=Av, and not capillary Ca=μv/σ.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · We = ρ v² L / σ, plus velocity, length, and σ solves, + O3 mpmath tabulated We.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
We = ρ v² L / σ, plus velocity, length, and σ solves, + O3 mpmath tabulated We.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (We, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not Reynolds, not Froude, not Manning, and not Q=Av.
Numerical scope
O2: Weber vs a separate-module identity (≤2 ULP). Not Reynolds, not Froude, not Manning, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated Weber vectors. Not Reynolds, not Froude, not Manning, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Weber number We = ρ v² L / σ. Invert v, L, or σ.
Scope
Weber We = ρ v² L / σ
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · We = ρ v² L / σ, plus velocity, length, and σ solves, + O3 mpmath tabulated We.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3
Verification revision
2026-09-26.o2-o3 · 1/1 property · digest ae08aa375e31
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 · 10/10 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 · 10/10 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.

Weber numberWe = ρ v² L / σ
Velocityv = √(We σ / (ρ L))
LengthL = We σ / (ρ v²)
Surface tensionσ = ρ v² L / We
iSI. ρ in kg/m³, v in m/s, L in m, σ in N/m. This page is not Reynolds Re=ρvL/μ, not Froude Fr=v/√(gL), not Manning, not Q=Av, and not capillary Ca=μv/σ.

How to use

1

Enter density ρ

Fluid density in kg/m³. Water is 1000.

2

Enter speed v

Characteristic speed in m/s. Invert for v on the v tab. URL field is v_m_s.

3

Enter length L

Characteristic length, often droplet diameter, in metres.

4

Enter σ

Interfacial tension in N/m. Water–air at 20 °C is about 0.0728 N/m. Invert on the σ tab.

Example calculations

Common configurations with formula and result.

ϟ

We = 1000

ρ=1000 kg/m³, v=1 m/s, L=0.072 m, σ=0.072 N/m

We = 1000 × 1² × 0.072 / 0.072
We = 1000
ϟ

Invert v

We=1000, same ρ, L, σ

v = √(We σ / (ρ L))
v = 1 m/s

Weber Number calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Weber number We = ρ v² L / σ. Inertia versus surface tension. σ is interfacial tension, not viscosity.
What it calculates
Weber number We = ρ v² L / σ. Invert v, L, or σ.
Inputs
  • mode?
  • v|We
  • L|We
  • rho
  • sigma|We
Outputs
  • We
  • v
  • L
  • rho
  • sigma
  • mode
  • model
Formula
We = ρ v² L / σ
Assumptions
  • Weber We = ρ v² L / σ
  • Inertia vs surface tension; σ is interfacial tension, not viscosity μ
  • Not Reynolds, not Froude, not Manning, not Q=Av, not capillary Ca=μv/σ
Units
  • SI; ρ in kg/m³; v in m/s; L in m; σ in N/m; We dimensionless
Boundary conditions
  • missing ρ, v, L, σ, or We when required → MISSING_REQUIRED_INPUT
  • ρ, v, L, σ, or We ≤ 0 → VALUE_MUST_BE_POSITIVE
  • Re/μ/ν, Fr/g, n, C/R/S, A/Q → MIXED_INPUT_ENCODING
  • reynolds, froude, or manning as mode → INVALID_MODE
Example
rho=1000 v=1 L=0.072 sigma=0.072 → We=1000
Validation cases

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

  • rho=1000 v=1 L=0.072 sigma=0.072 → We=1000
  • mode=velocity We=1000 rho=1000 L=0.072 sigma=0.072 → v=1
  • v=1 L=0.072 rho=1000 sigma=0.072 Re=200000 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-11 — Characteristic numbers — Weber number We
    Supports: We = ρ v² l / σ; inertia/surface-tension, not viscous Reynolds, not gravity Froude
  • ISO 80000-4 — Mechanics — Surface tension
    Supports: σ has dimension force/length; v length/time; L length; ρ mass/volume
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute the Weber number from density, speed, characteristic length, and interfacial tension.

Supported and not supported

Supported — We from ρ, v, L, σ · invert v, L, or σ · API physics.fluid.weber

Not supported — Reynolds Re/μ/ν, Froude Fr/g, Manning n, Chezy C, Q=Av, capillary Ca=μv/σ

Agent / API notes

Capability id: physics.fluid.weber · tool id: weber-number · pin 1.0.0.

{ "rho": 1000, "v": 1, "L": 0.072, "sigma": 0.072 }

Modes: We (default), velocity, length, sigma. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/weber-number. 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 Reynolds number?

No. Re = ρ v L / μ is /calc/physics/reynolds. Sending Re, μ, or ν is MIXED_INPUT_ENCODING. Density ρ is required here; viscosity is not.

Is this Froude number?

No. Fr = v / √(g L) is /calc/physics/froude-number. Sending Fr or g is MIXED_INPUT_ENCODING.

Is this capillary number?

No. Ca = μ v / σ is viscous/surface-tension. Sending μ is MIXED_INPUT_ENCODING.

Is this Q = A·v?

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

Where does this run?

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