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Physics calculator

Pipe Exit Calculator

Compute pipe-exit loss h = K v² / (2g) with K=1 into a large reservoir. Runs locally. Not catalog K, not inlet geometry, not sudden expansion (v1−v2)², 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 · h = K v² / (2g) with K = 1, plus pressure and velocity solves, + O3 mpmath tabulated head.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
h = K v² / (2g) with K = 1, plus pressure and velocity solves, + O3 mpmath tabulated head.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (head, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not catalog K given, not pipe-entrance geometry, not sudden expansion (v1−v2)², not Darcy, and not Q=Av.
Numerical scope
O2: pipe exit K=1 vs a separate-module identity (≤2 ULP). Not catalog K, not pipe-entrance geometry, not sudden expansion (v1−v2)², not Darcy, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated pipe-exit 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
Pipe-exit head from mean speed into a large reservoir (K=1). Invert v. Optional Δp from ρ.
Scope
Pipe exit into a large reservoir: h = K v² / (2g) with K=1; kinetic energy is dissipated; K is reported, not an input
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · h = K v² / (2g) with K = 1, plus pressure and velocity solves, + O3 mpmath tabulated head.· 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 bfc3ef0c8dc1
Legacy regression
6/6 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 · 1/1 CVP boundary · 2/2 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract · Manifest
Sources
Sources
Evidence
1 legacy golden · legacy regression suite · 4/4 oracle-backed golden · 2/2 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.

Head lossh = K v² / (2g)
Exit coefficientK = 1
Pressure dropΔp = ρ K v² / 2
Speed invertv = √(2 g h / K)
iSI. K is 1 for every outlet shape into a large reservoir. g defaults to 9.80665 m/s². Do not send query v — that is calculation_version; use v_m_s.

How to use

1

Enter v

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

2

Read h

h = v² / (2g). Optional ρ reports Δp.

Example calculations

Common configurations with formula and result.

ϟ

v=2 m/s

Discharge from a pipe into a large reservoir

K=1, h=K v²/(2g)
h≈0.20394 m · K=1 · Δp=2000 Pa at ρ=1000
ϟ

Invert v

h≈0.20394 m

v = √(2 g h / K)
v = 2 m/s

Pipe Exit calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Pipe discharge into a large reservoir: h = K v² / (2g) with K=1 because kinetic energy is dissipated. K is reported, not an input. Exit geometry does not change K. Not a catalog fitting K, not inlet geometry, and not two-station sudden expansion.
What it calculates
Pipe-exit head from mean speed into a large reservoir (K=1). Invert v. Optional Δp from ρ.
Inputs
  • mode?
  • v_m_s|h
  • rho?
  • g?
Outputs
  • h
  • v
  • K
  • g
  • rho
  • dP
  • mode
  • model
Formula
h = K v² / (2g); K=1
Assumptions
  • Pipe exit into a large reservoir: h = K v² / (2g) with K=1; kinetic energy is dissipated; K is reported, not an input
  • Default g=9.80665 m/s²; default ρ=1000 kg/m³; incompressible; one mean speed in the pipe; exit geometry does not change K
  • Not catalog minor-loss K given, not pipe-entrance flush/reentrant/rounded, not sudden expansion (v1−v2)², not Darcy f, not Q=Av
Units
  • SI; v in m/s; h in m; ρ in kg/m³; Δp in Pa; K dimensionless
Boundary conditions
  • missing v_m_s or h when required → MISSING_REQUIRED_INPUT
  • v_m_s ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
  • K, k, kind, ri_d, rd, n_miters, θ, f, Q, C_d, v1/v2 → MIXED_INPUT_ENCODING
  • flush, reentrant, rounded, circular, or unknown mode → INVALID_MODE
Example
v_m_s=2 → h=K v²/(2g) K=1
Validation cases

3 published on this page · 6/6 tests · Production surface contract 5/5 · View evidence

  • v_m_s=2 → h=K v²/(2g) K=1
  • mode=pressure v_m_s=2 → dP=2000 K v²/2
  • v_m_s=2 K=1 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Length, speed, pressure
    Supports: h is a head; v is a speed; Δp is a pressure
  • White — Fluid Mechanics — Exit loss coefficient
    Supports: Pipe into a large reservoir: K=1 for every exit geometry because kinetic energy is dissipated. Not a catalog K input and not inlet geometry
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute pipe-exit loss from mean speed into a large reservoir.

Supported and not supported

Supported — h from v with K=1 · invert v · API physics.fluid.pipe_exit

Not supported — catalog minor-loss K, pipe-entrance geometry, sudden expansion (v1−v2)², Darcy f, Q=Av

Agent / API notes

Capability id: physics.fluid.pipe_exit · tool id: pipe-exit · pin 1.0.0.

{ "v_m_s": 2 }

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

Calculator URL stays /calc/physics/pipe-exit. 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 minor-loss K?

No. Catalog fitting K is /calc/physics/minor-loss. Sending K is MIXED_INPUT_ENCODING. This page reports K=1.

Is this pipe-entrance?

No. Inlet geometry (flush, reentrant, rounded) is /calc/physics/pipe-entrance. Sending kind or ri_d is MIXED_INPUT_ENCODING. Exit K is 1 for every outlet shape.

Is this sudden expansion?

No. Two-station Borda–Carnot (v1−v2)² is /calc/physics/sudden-expansion. Sending v1/v2 or A1/A2 is MIXED_INPUT_ENCODING. A2→∞ is the physical limit of that page, not this product.

Is this Darcy–Weisbach?

No. Pipe friction from a given f is /calc/physics/darcy-weisbach.

Is this Q = A·v?

No. Volumetric flow is /calc/physics/flow-rate. Sending Q or A is MIXED_INPUT_ENCODING.

Where does this run?

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