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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 Engine tested · Source checked · 17/17 tests · Production surface contract 3/3 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
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 · 17/17 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
  • ISO 80000-4 — Mechanics — Pressure, density, speed
  • Wylie, E.B. and Streeter, V.L. Fluid Transients — Joukowsky equation
Sources
Evidence
2 golden · 10 boundary · 5 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 163 CURRENT) @ 2026-09-17T13:12:27.589Z
Semantic contract
PASS

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 3/3 · 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: Minor loss, Darcy–Weisbach, Colebrook, Pitot tube .

K Minor loss › hf Darcy–Weisbach › f Colebrook › v Pitot tube ›
}

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.