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Physics calculator

Sudden Contraction Calculator

Compute vena-contracta sudden-contraction loss h = (1/C_c − 1)² v2² / (2g). Default C_c=0.62. Runs locally. Not sudden expansion, not minor-loss K as an input, not an orifice, and not Q=Av.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 18/18 tests · Production surface contract 3/3 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Vena-contracta sudden-contraction head from v2 and C_c. Invert v2 or C_c. Optional Δp from ρ.
Scope
Vena-contracta sudden contraction: h = (1/C_c − 1)² v2² / (2g); default C_c=0.62; K = (1/C_c − 1)² is reported, not an input
Verification
Engine tested · 18/18 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
2 golden · 11 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.

Head lossh = (1/C_c − 1)² v2² / (2g)
Loss coefficientK = (1/C_c − 1)²
Vena-contracta speedv_c = v2 / C_c
Pressure dropΔp = ρ K v2² / 2
iSI. Default C_c=0.62 (sharp-edged from a large reservoir). g defaults to 9.80665 m/s². C_c is in (0, 1). This page is not sudden expansion (v1−v2)², not minor-loss K given, not orifice C_d, and not Q=Av.

How to use

1

Enter v₂

Downstream mean speed in the smaller pipe, in m/s. URL field is v2_m_s.

2

Enter C_c

Vena-contracta coefficient. Default 0.62. Invert on the C_c tab. Not orifice C_d.

3

Read h

h = (1/C_c − 1)² v2² / (2g). Optional ρ reports Δp. Invert v₂ on the v₂ tab.

Example calculations

Common configurations with formula and result.

ϟ

C_c=0.62, v2=1 m/s

Sharp-edged from a reservoir

h = (1/0.62 − 1)² / (2 g)
h≈0.01915 m · K≈0.37565 · Δp≈187.8 Pa at ρ=1000
ϟ

Invert v₂

h≈0.01915 m, C_c=0.62

v2 = √(2 g h) · C_c / (1 − C_c)
v2 = 1 m/s

Sudden Contraction calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Vena-contracta sudden contraction: h = (1/C_c − 1)² v2² / (2g). Default C_c=0.62. Reported K = (1/C_c − 1)² is not an input. Not Borda–Carnot expansion.
What it calculates
Vena-contracta sudden-contraction head from v2 and C_c. Invert v2 or C_c. Optional Δp from ρ.
Inputs
  • mode?
  • v2|h
  • C_c?
  • rho?
  • g?
Outputs
  • h
  • v2
  • C_c
  • K
  • v_c
  • g
  • rho
  • dP
  • mode
  • model
Formula
h = (1/C_c − 1)² v2² / (2g)
Assumptions
  • Vena-contracta sudden contraction: h = (1/C_c − 1)² v2² / (2g); default C_c=0.62; K = (1/C_c − 1)² is reported, not an input
  • Default g=9.80665 m/s²; default ρ=1000 kg/m³ for Δp = ρ K v2² / 2; incompressible; C_c in (0, 1)
  • Not sudden expansion (v1−v2)², not minor-loss K given, not Darcy f, not orifice C_d, not Q=Av
Units
  • SI; v in m/s; h in m; ρ in kg/m³; Δp in Pa; C_c and K dimensionless
Boundary conditions
  • missing v2, h, or C_c when required → MISSING_REQUIRED_INPUT
  • v2 ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
  • C_c ≥ 1 → VALUE_OUT_OF_RANGE
  • v1, K, f/Re, Q, C_d → MIXED_INPUT_ENCODING
  • expansion, minor, darcy, or orifice as mode → INVALID_MODE
Example
C_c=0.62 v2=1 → h=(1/0.62−1)²/(2g) K=(1/0.62−1)²
Validation cases

3 published on this page · 18/18 tests · Production surface contract 3/3 · View evidence

  • v2=1 → h=(1/0.62−1)²/(2g) K=(1/0.62−1)²
  • mode=pressure v2=1 → dP=1000·K/2
  • v2=1 K=0.37565 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Length, speed, pressure
    Supports: h is a head; v is a speed; Δp is a pressure
  • Borda–Carnot equation — Sudden contraction / vena contracta
    Supports: Loss from vena contracta to A2 is (v_c−v2)²/(2g) with v_c=v2/C_c; typical sharp-edged C_c≈0.62
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute vena-contracta sudden-contraction loss from downstream speed and C_c.

Supported and not supported

Supported — h from v2, C_c · invert v2 · invert C_c · API physics.fluid.sudden_contraction

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

Agent / API notes

Capability id: physics.fluid.sudden_contraction · tool id: sudden-contraction · pin 1.0.0.

{ "v2": 1 }

C_c defaults to 0.62 when omitted. Modes: head (default), pressure, velocity, coefficient. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/sudden-contraction. There is no /calc/fluid.

Other calculators in this family: Sudden expansion, Minor loss, Orifice discharge, Flow rate .

h Sudden expansion › K Minor loss › Q Orifice discharge › Q Flow rate ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this sudden expansion?

No. Borda–Carnot (v1−v2)²/(2g) is /calc/physics/sudden-expansion. Sending v1 is MIXED_INPUT_ENCODING.

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/C_c−1)².

Is this an orifice?

No. Orifice C_d and tank √(2gH) are /calc/physics/orifice-discharge. C_c is the vena-contracta area ratio, not C_d. Sending C_d is MIXED_INPUT_ENCODING.

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 suddenContraction wrapper.