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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 Engine tested · Source checked · 5/5 tests · Production surface contract 1/1 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
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 · 5/5 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
5 property · Production surface contract 1/1 · 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; 164 CURRENT) @ 2026-09-17T23:04:35.003Z
Semantic contract
PASS

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 · 5/5 tests · Production surface contract 1/1 · 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: Pipe entrance, Sudden expansion, Minor loss, Flow rate, Pipe tee .

h Pipe entrance › h Sudden expansion › K Minor loss › Q Flow rate › h Pipe tee ›
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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.