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Physics calculator

Pipe Period Calculator

Compute the water-hammer pipe period T = 2L/c. Runs locally. Not Joukowsky Δp, not Korteweg–Hall c from K/D/e/E, and not Darcy f.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · T = 2L/c with length and celerity solves; + O3 mpmath tabulated period.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
T = 2L/c with length and celerity solves; + O3 mpmath tabulated period.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (period, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not Joukowsky Δp, not Korteweg–Hall c from K/D/e/E, not Darcy, and not Q=Av.
Numerical scope
O2: pipe period T=2L/c vs a separate-module identity (≤2 ULP). Not Joukowsky Δp, not Korteweg–Hall c, not Darcy, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated pipe-period 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
Acoustic round-trip pipe period T=2L/c from length and celerity. Invert L or c.
Scope
Pipe period T = 2L/c; c is a given celerity, not Korteweg–Hall from K, D, e, E
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · T = 2L/c with length and celerity solves; + O3 mpmath tabulated period.· 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 b0f02e6d70af
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 — Length, time, speed
  • Wylie, E.B. and Streeter, V.L. Fluid Transients — Pipe period 2L/a
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.

PeriodT = 2L / c
Length invertL = c T / 2
Celerity invertc = 2L / T
iSI. Sudden-closure Joukowsky applies when valve time t < T. Give c; do not send K, D, e, E, Δp, or Δv.

How to use

1

Enter L

Pipe length in m. Invert for L on the L tab.

2

Enter c

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

3

Read T

T = 2L/c. REST may send T; the query layer uses T_s.

Example calculations

Common configurations with formula and result.

ϟ

L=1000 m, c=1000 m/s

Round-trip time

T = 2 × 1000 / 1000
T = 2 s
ϟ

Invert L

T=2 s, c=1000 m/s

L = c T / 2
L = 1000 m

Pipe Period calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Pipe period T = 2L/c is the acoustic round-trip time in a liquid-filled line. c is a given celerity. This page computes T, not Joukowsky Δp=ρcΔv and not Korteweg–Hall c from bulk modulus.
What it calculates
Acoustic round-trip pipe period T=2L/c from length and celerity. Invert L or c.
Inputs
  • mode?
  • L|T
  • c|T
Outputs
  • T
  • L
  • c
  • mode
  • model
Formula
T = 2L / c
Assumptions
  • Pipe period T = 2L/c; c is a given celerity, not Korteweg–Hall from K, D, e, E
  • Sudden-closure Joukowsky applies when valve time t < T; this page computes T, not Δp
  • Not Joukowsky Δp=ρcΔv, not Darcy f, not minor-loss K, not Q=Av
Units
  • SI; T in s; L in m; c in m/s
Boundary conditions
  • missing L, c, or T when required → MISSING_REQUIRED_INPUT
  • L, c, or T ≤ 0 → VALUE_MUST_BE_POSITIVE
  • dP/dV/ρ, K/D/e/E, f/Re, n, A/Q, v → MIXED_INPUT_ENCODING
  • joukowsky, hall, or darcy as mode → INVALID_MODE
Example
L=1000 c=1000 → T=2
Validation cases

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

  • L=1000 c=1000 → T=2
  • mode=length T=2 c=1000 → L=1000
  • L=1000 c=1000 dP=1e6 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Length, time, speed
    Supports: L is a length; T is a time; c is a speed
  • Wylie, E.B. and Streeter, V.L. Fluid Transients — Pipe period 2L/a
    Supports: T=2L/c is the round-trip time that distinguishes sudden from gradual closure
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute the pipe period T=2L/c.

Supported and not supported

Supported — T from L and c · invert L · invert c · API physics.fluid.pipe_period

Not supported — Joukowsky Δp=ρcΔv, Korteweg–Hall c from K/D/e/E, Darcy hf, Q=Av

Agent / API notes

Capability id: physics.fluid.pipe_period · tool id: pipe-period · pin 1.0.0.

{ "L": 1000, "c": 1000 }

Modes: period (default), length, celerity. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/pipe-period. 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 Joukowsky water hammer?

No. Surge pressure Δp=ρcΔv is /calc/physics/water-hammer. Sending Δp, Δv, or ρ is MIXED_INPUT_ENCODING.

Do I enter bulk modulus or wall thickness?

No. Give celerity c. Elastic-wave c from K, D, e, E is /calc/physics/wave-celerity.

Is T the valve closure time?

T is the pipe period 2L/c. Closure is sudden when the valve time is shorter than T. This page does not integrate a closure schedule.

Is this Darcy–Weisbach?

No. Steady hf=fLv²/(2gD) is /calc/physics/darcy-weisbach. Sending f, Re, or K is MIXED_INPUT_ENCODING.

Where does this run?

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