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Physics calculator

Pipe Entrance Calculator

Compute pipe-inlet loss h = K v² / (2g) from geometry: flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2]. Runs locally. Not catalog K, not circular-arc R/D, not mitered n, 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 flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2], plus pressure and velocity solves, + O3 mpmath tabulated head.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
h = K v² / (2g) with flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2], 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 circular-arc R/D, not mitered n, and not Q=Av.
Numerical scope
O2: geometric pipe inlet K vs a separate-module identity (≤2 ULP). Not catalog K, not circular-arc R/D, not mitered n, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated pipe-entrance vectors. Not catalog K, not circular-arc R/D, not mitered n, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Pipe-inlet head from mean speed and inlet geometry (flush, reentrant, or rounded). Invert v. Optional Δp from ρ.
Scope
Geometric pipe inlet: h = K v² / (2g); flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2]; 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 flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2], 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.bnd
Verification revision
2026-09-26.o2-o3.bnd · 1/1 property · digest e41ebe573bb8
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
  • ISO 80000-4 — Mechanics — Length, speed, pressure
  • White — Fluid Mechanics — Entrance loss coefficients
  • Swamee — rounded pipe inlet — K = 0.5 / [1 + 36 (r/D)^1.2]
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)
Flush / reentrantK_flush = 0.5, K_reentrant = 0.8
RoundedK = 0.5 / [1 + 36 (rᵢ/D)^1.2]
Pressure dropΔp = ρ K v² / 2
Speed invertv = √(2 g h / K)
iSI. kind is flush (default), reentrant, or rounded. Rounded needs ri_d = rᵢ/D in (0, 1]. g defaults to 9.80665 m/s². Do not send query v — that is calculation_version; use v_m_s.

How to use

1

Choose inlet

flush, reentrant (inward projecting), or rounded. URL field is kind.

2

Enter v

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

3

Enter rᵢ/D if rounded

Inlet fillet radius over diameter. URL field is ri_d. Not circular-arc R/D.

Example calculations

Common configurations with formula and result.

ϟ

Flush, v=2 m/s

Sharp flush inlet from a large reservoir

K=0.5, h=K v²/(2g)
h≈0.10197 m · K=0.5 · Δp=1000 Pa at ρ=1000
ϟ

Invert v

h≈0.10197 m, flush

v = √(2 g h / K)
v = 2 m/s

Pipe Entrance calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Geometric pipe inlet from a large reservoir: h = K v² / (2g). Flush K=0.5, reentrant K=0.8, rounded Swamee K=0.5/[1+36(rᵢ/D)^1.2]. K is reported, not an input. Not a catalog fitting K and not a bend.
What it calculates
Pipe-inlet head from mean speed and inlet geometry (flush, reentrant, or rounded). Invert v. Optional Δp from ρ.
Inputs
  • mode?
  • kind?
  • v_m_s|h
  • ri_d?
  • rho?
  • g?
Outputs
  • h
  • v
  • K
  • kind
  • ri_d
  • g
  • rho
  • dP
  • mode
  • model
Formula
h = K v² / (2g); flush K=0.5; reentrant K=0.8; rounded K=0.5/[1+36(rᵢ/D)^1.2]
Assumptions
  • Geometric pipe inlet: h = K v² / (2g); flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2]; K is reported, not an input
  • Require kind flush|reentrant|rounded; rounded needs 0 < rᵢ/D ≤ 1; default g=9.80665 m/s²; default ρ=1000 kg/m³; incompressible; from a large reservoir
  • Not catalog minor-loss K given, not circular-arc R/D, not mitered n, not Darcy f, not orifice C_d, not Q=Av
Units
  • SI; v in m/s; h in m; rᵢ/D dimensionless; ρ in kg/m³; Δp in Pa; K dimensionless
Boundary conditions
  • missing v_m_s, h, or ri_d when required → MISSING_REQUIRED_INPUT
  • v_m_s ≤ 0, h ≤ 0, or ri_d ≤ 0 → VALUE_MUST_BE_POSITIVE
  • ri_d > 1 → VALUE_OUT_OF_RANGE
  • K, k, rd, n_miters, θ, f, Q, C_d, v1/v2 → MIXED_INPUT_ENCODING
  • minor, circular, mitered, or unknown kind → INVALID_MODE
Example
v_m_s=2 kind=flush → h=K v²/(2g) K=0.5
Validation cases

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

  • v_m_s=2 kind=flush → h=K v²/(2g) K=0.5
  • mode=pressure v_m_s=2 kind=flush → dP=1000 K v²/2
  • v_m_s=2 kind=flush K=0.5 → 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 — Entrance loss coefficients
    Supports: Flush sharp inlet K=0.5; thin-walled reentrant / inward-projecting K=0.8. Not a catalog K input
  • Swamee — rounded pipe inlet — K = 0.5 / [1 + 36 (r/D)^1.2]
    Supports: Flush-mounted rounded entrance; r/D=0 recovers K=0.5. Not Idelchik circular-arc B1, not mitered n
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute pipe-inlet loss from mean speed and inlet geometry.

Supported and not supported

Supported — h from v and kind · rounded rᵢ/D · invert v · API physics.fluid.pipe_entrance

Not supported — catalog minor-loss K, circular-arc R/D, mitered n, Darcy f, Q=Av

Agent / API notes

Capability id: physics.fluid.pipe_entrance · tool id: pipe-entrance · pin 1.0.0.

{ "v_m_s": 2, "kind": "flush" }

Modes: head (default), pressure, velocity. Inlet kinds: flush (default), reentrant, rounded. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/pipe-entrance. 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 from inlet geometry.

Is this circular-arc pipe-bend?

No. Smooth R/D ≥ 1 is /calc/physics/pipe-bend. Sending rd is MIXED_INPUT_ENCODING. Rounded fillet is ri_d, not centerline R/D.

Is this mitered-bend?

No. Sharp segmented elbows are /calc/physics/mitered-bend. Sending n_miters is MIXED_INPUT_ENCODING.

Is this sudden contraction?

No. Two-station vena contracta with C_c is /calc/physics/sudden-contraction. This page is one speed from a large reservoir.

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.

Is this pipe-exit?

No. Discharge into a large reservoir with K=1 is /calc/physics/pipe-exit. Sending kind still reports inlet K, not exit K=1.

Where does this run?

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