HomeCalculatorsPhysicsFluid MechanicsCavitation Number Calculator
Physics calculator

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).

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · σ = (p − p_v)/(½ ρ v²) with pressure, vapor, and velocity solves; + O3 mpmath tabulated σ.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
σ = (p − p_v)/(½ ρ v²) with pressure, vapor, and velocity solves; + O3 mpmath tabulated σ.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (number, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not NPSH, not Thoma σ_Th=NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²).
Numerical scope
O2: σ=(p−p_v)/(½ ρ v²) vs a separate-module identity (≤2 ULP). Not NPSH, not Thoma, not Weber, and not Euler Eu=Δp/(ρ v²). ≤2 ULP vs O3 applies only to the published tabulated cavitation vectors. Not NPSH, not Thoma, not Weber, and not Euler.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Cavitation number σ = (p − p_v) / (½ ρ v²). Invert p, p_v, or v.
Scope
Cavitation number σ = (p − p_v) / (½ ρ v²); default ρ=1000 kg/m³; p and p_v absolute Pa
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · σ = (p − p_v)/(½ ρ v²) with pressure, vapor, and velocity solves; + O3 mpmath tabulated σ.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3.iface
Verification revision
2026-09-26.o2-o3.iface · 1/1 property · digest 8194cd4f6e6f
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 · 10/10 CVP boundary · 11/11 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 · 11/11 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.

Cavitation numberσ = (p − p_v) / (½ ρ v²)
Pressurep = p_v + σ · ½ ρ v²
Vapor pressurep_v = p − σ · ½ ρ v²
Velocityv = √(2(p − p_v) / (ρ σ))
iSI. p and p_v absolute Pa; ρ in kg/m³; v in m/s; σ dimensionless. This page is not NPSH, not Thoma σ_Th=NPSH/H, not Weber We=ρv²L/σ, and not Euler Eu=Δp/(ρ v²).

How to use

1

Enter p

Absolute reference pressure in Pa. Invert for p on the p tab.

2

Enter p_v

Absolute vapor pressure in Pa. Water at 20 °C is about 2339 Pa. Invert on the p_v tab.

3

Enter v

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

4

Read σ

σ = (p − p_v) / (½ ρ v²). Default ρ=1000 kg/m³. REST may send v; the query layer uses v_m_s.

Example calculations

Common configurations with formula and result.

ϟ

σ = 2

p=150000 Pa, p_v=50000 Pa, ρ=1000 kg/m³, v=10 m/s

σ = (150000 − 50000) / (½ × 1000 × 10²)
σ = 2
ϟ

Invert p

σ=2, p_v=50000 Pa, v=10 m/s

p = p_v + σ · ½ ρ v²
p = 150000 Pa

Cavitation Number calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Cavitation number σ = (p − p_v) / (½ ρ v²). Reference pressure minus vapor pressure, over dynamic pressure. Not NPSH head.
What it calculates
Cavitation number σ = (p − p_v) / (½ ρ v²). Invert p, p_v, or v.
Inputs
  • mode?
  • p|sigma
  • p_v|sigma
  • v|sigma
  • rho?
Outputs
  • sigma
  • p
  • p_v
  • rho
  • v
  • mode
  • model
Formula
σ = (p − p_v) / (½ ρ v²)
Assumptions
  • Cavitation number σ = (p − p_v) / (½ ρ v²); default ρ=1000 kg/m³; p and p_v absolute Pa
  • Not NPSH head, not Thoma σ_Th=NPSH/H, not Weber We=ρv²L/σ, not Euler Eu=Δp/(ρ v²)
  • Not Reynolds, not capillary Ca=μv/σ, not Q=Av
Units
  • SI; p and p_v in Pa; ρ in kg/m³; v in m/s; σ dimensionless
Boundary conditions
  • missing p, p_v, v, or σ when required → MISSING_REQUIRED_INPUT
  • p, v, ρ, or σ ≤ 0 → VALUE_MUST_BE_POSITIVE
  • p ≤ p_v → VALUE_OUT_OF_RANGE
  • NPSH/z/hf/H/g, We/L, Re/μ, Eu/Δp, A/Q → MIXED_INPUT_ENCODING
  • npsh, thoma, weber, or euler as mode → INVALID_MODE
Example
p=150000 p_v=50000 v=10 → σ=2
Validation cases

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

  • p=150000 p_v=50000 v=10 → sigma=2
  • mode=pressure sigma=2 p_v=50000 v=10 → p=150000
  • p=150000 p_v=50000 v=10 NPSH=10 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-11 — Characteristic numbers — Cavitation number
    Supports: σ = (p − p_v) / (½ ρ v²); inertia vs vapor-pressure deficit, not NPSH head
  • ISO 80000-4 — Mechanics — Pressure
    Supports: p and p_v are absolute pressures; ½ ρ v² is a dynamic pressure
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute the cavitation number from reference pressure, vapor pressure, density, and speed.

Supported and not supported

Supported — σ from p, p_v, ρ, v · invert p, p_v, or v · API physics.fluid.cavitation

Not supported — NPSH head, Thoma σ_Th=NPSH/H, Weber We, Euler Eu=Δp/(ρv²), Reynolds, capillary Ca, Q=Av

Agent / API notes

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

{ "p": 150000, "p_v": 50000, "v": 10 }

Modes: number (default), pressure, vapor, 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/cavitation-number. There is no /calc/fluid.

Other calculators in this family: Alternate Depth Calculator, Bernoulli Equation Calculator, Broad-Crested Weir Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator, Critical Slope 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. › → 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. › → Critical Slope Calculator Compute rectangular critical bed slope Sc such that yn=yc using SI Manning at y=yc. Runs locally. Not Manning A,R; not normal-depth yn; not critical-depth yc as the product; not Chezy; not Q=Av. ›

Frequently asked questions

Key distinctions behind the calculation.

Is this NPSH?

No. NPSHa is a head in metres at /calc/physics/npsh. Sending NPSH, z, hf, H, p_s, p_atm, or g is MIXED_INPUT_ENCODING.

Is this the Thoma number?

No. Thoma σ_Th = NPSH/H is a pump-similarity ratio. This page is the flow cavitation number (p−p_v)/(½ρv²).

Is this Weber number?

No. We = ρ v² L / σ with σ as N/m is /calc/physics/weber-number. Sending We, L, or σ in N/m is MIXED_INPUT_ENCODING.

Is this Euler number?

No. Eu = Δp / (ρ v²). Send p and p_v separately. A single Δp is MIXED_INPUT_ENCODING.

Where does this run?

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