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Physics calculator

Water Hammer Calculator

Compute Joukowsky water-hammer Δp = ρ c Δv. Runs locally. Not Darcy f, not minor-loss K, and not Q=Av.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Δp = ρ c Δv (Joukowsky) with velocity and celerity solves; + O3 mpmath tabulated Δp.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Δp = ρ c Δv (Joukowsky) with velocity and celerity solves; + O3 mpmath tabulated Δp.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (pressure, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not Darcy, not minor-loss K, not Moens–Korteweg c from K/D/e/E, and not Q=Av.
Numerical scope
O2: Joukowsky Δp=ρ c Δv vs a separate-module identity (≤2 ULP). Not Darcy, not minor-loss K, not Moens–Korteweg c, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated water-hammer vectors. Not catalog K, not pipe-entrance geometry, not sudden expansion (v1−v2)², not Darcy, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Joukowsky surge pressure from density, celerity, and a sudden speed change. Invert Δv or c.
Scope
Joukowsky water hammer: Δp = ρ c Δv; h = Δp/(ρ g); default ρ=1000 kg/m³; default g=9.80665 m/s²
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Δp = ρ c Δv (Joukowsky) with velocity and celerity solves; + O3 mpmath tabulated Δp.· 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 aec02649b485
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
  • ISO 80000-4 — Mechanics — Pressure, density, speed
  • Wylie, E.B. and Streeter, V.L. Fluid Transients — Joukowsky equation
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.

Joukowsky pressureΔp = ρ c Δv
Headh = Δp / (ρ g) = c Δv / g
Speed invertΔv = Δp / (ρ c)
iSI rigid-column sudden-closure form. Give c; do not send K, L, D, e, or E. Not Darcy fL/D, not minor-loss K, not Q=Av.

How to use

1

Enter c

Wave celerity in m/s. Invert for c on the c tab. REST may send c; the query layer uses c_m_s.

2

Enter Δv

Sudden speed change in m/s. REST may send dV; the query layer uses dv_m_s.

3

Read Δp

Δp = ρ c Δv. Head h is reported. Invert Δv on the Δv tab when Δp and c are known.

Example calculations

Common configurations with formula and result.

ϟ

c=1000 m/s, Δv=1 m/s

Default ρ=1000 kg/m³

Δp = 1000 × 1000 × 1
Δp = 1 000 000 Pa
ϟ

Invert Δv

Δp = 1 000 000 Pa, c=1000 m/s

Δv = Δp / (ρ c)
Δv = 1 m/s

Water Hammer calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Joukowsky water hammer: Δp = ρ c Δv with default ρ=1000 kg/m³. c is a given celerity, not Moens–Korteweg from bulk modulus. This page computes Δp, not Darcy hf and not minor-loss K v²/(2g).
What it calculates
Joukowsky surge pressure from density, celerity, and a sudden speed change. Invert Δv or c.
Inputs
  • mode?
  • c|dP
  • dV|dP
  • rho?
  • g?
Outputs
  • dP
  • rho
  • c
  • dV
  • h
  • g
  • mode
  • model
Formula
Δp = ρ c Δv
Assumptions
  • Joukowsky water hammer: Δp = ρ c Δv; h = Δp/(ρ g); default ρ=1000 kg/m³; default g=9.80665 m/s²
  • c is the given celerity, not Moens–Korteweg from bulk modulus K, D, e, E
  • Not Darcy f, not Colebrook, not minor-loss K, not Q=Av
Units
  • SI; Δp in Pa; ρ in kg/m³; c and Δv in m/s; h in m
Boundary conditions
  • missing c, Δv, or Δp when required → MISSING_REQUIRED_INPUT
  • c, Δv, Δp, ρ, or g ≤ 0 → VALUE_MUST_BE_POSITIVE
  • f/Re, K, L/D/e/E, n, A/Q, v → MIXED_INPUT_ENCODING
  • darcy, minor, or manning as mode → INVALID_MODE
Example
ρ=1000 c=1000 dV=1 → Δp=1e6
Validation cases

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

  • c=1000 dV=1 → Δp=1e6
  • mode=velocity dP=1e6 c=1000 → dV=1
  • c=1000 dV=1 f=0.02 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Pressure, density, speed
    Supports: Δp is a pressure; ρ is a density; c and Δv are speeds
  • Wylie, E.B. and Streeter, V.L. Fluid Transients — Joukowsky equation
    Supports: Δp = ρ c Δv for a rapid velocity change in a liquid-filled pipe
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute Joukowsky water hammer.

Supported and not supported

Supported — Δp from ρ, c, and Δv · invert Δv · invert c · API physics.fluid.water_hammer

Not supported — Darcy hf=fLv²/(2gD), minor-loss K, Moens–Korteweg elastic c, Q=Av

Agent / API notes

Capability id: physics.fluid.water_hammer · tool id: water-hammer · pin 1.0.0.

{ "c": 1000, "dV": 1 }

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

Calculator URL stays /calc/physics/water-hammer. 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 Darcy–Weisbach?

No. Steady hf = f L v²/(2gD) is /calc/physics/darcy-weisbach. Sending f, Re, or L is MIXED_INPUT_ENCODING.

Is this a minor-loss K?

No. Fitting loss h_m = K v²/(2g) is /calc/physics/minor-loss. Sending K is MIXED_INPUT_ENCODING.

Do I enter bulk modulus or wall thickness?

No. This page takes celerity c. Elastic-wave c from K, D, e, E is not wrapped here.

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 waterHammer wrapper.