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Physics calculator

Specific Energy Calculator

Compute open-channel specific energy E = y + v²/(2g). Runs locally. Not a Froude wrap, not a hydraulic jump, 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 · E = y + v²/(2g) with depth and velocity solves; + O3 mpmath tabulated E.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
E = y + v²/(2g) with depth and velocity solves; + O3 mpmath tabulated E.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (energy, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not alternate depth, not specific force M, not Froude, and not Q=Av.
Numerical scope
O2: E=y+v²/(2g) vs a separate-module identity (≤2 ULP). Not alternate depth, not specific force, not Froude, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated specific-energy vectors. Not alternate depth, not specific force, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Open-channel specific energy from depth and speed. Invert y or v.
Scope
Open-channel specific energy: E = y + v² / (2g); default g=9.80665 m/s²
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · E = y + v²/(2g) with depth and velocity solves; + O3 mpmath tabulated E.· 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 fd0952668b24
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 — Energy, length, speed
  • Chow, V.T. Open-Channel Hydraulics — Specific energy
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.

Specific energyE = y + v² / (2g)
Depth inverty = E − v² / (2g)
Speed invertv = √(2g(E − y))
iSI rectangular prismatic channel with hydrostatic pressure and α=1. Require E > y. Not Fr = v/√(gL), not a hydraulic jump, not Manning, not Q=Av.

How to use

1

Enter y

Flow depth in metres. Invert for y on the y tab.

2

Enter v

Mean speed in m/s. REST may send v; the query layer uses v_m_s.

3

Read E

E = y + v²/(2g). Invert v on the v tab when E and y are known.

Example calculations

Common configurations with formula and result.

ϟ

y=1 m, v=2 m/s

Default g=9.80665 m/s²

E = 1 + 4 / (2 × 9.80665)
E ≈ 1.20394 m
ϟ

Invert v

E ≈ 1.20394 m, y=1 m

v = √(2g(E − y))
v = 2 m/s

Specific Energy calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Open-channel specific energy: E = y + v²/(2g) with default g=9.80665 m/s². Invert depth or speed. This page computes E, not Fr = v/√(gL).
What it calculates
Open-channel specific energy from depth and speed. Invert y or v.
Inputs
  • mode?
  • y|E
  • v|E
  • g?
Outputs
  • E
  • y
  • v
  • g
  • mode
  • model
Formula
E = y + v² / (2g)
Assumptions
  • Open-channel specific energy: E = y + v² / (2g); default g=9.80665 m/s²
  • Invert y = E − v²/(2g) and v = √(2g(E−y)); require E > y
  • Not a Froude wrap, not a hydraulic jump, not Manning, not Q=Av
Units
  • SI; E and y in m; v in m/s; g in m/s²
Boundary conditions
  • missing y, v, or E when required → MISSING_REQUIRED_INPUT
  • E ≤ y or E ≤ v²/(2g) → VALUE_OUT_OF_RANGE
  • y, v, E, or g ≤ 0 → VALUE_MUST_BE_POSITIVE
  • Fr/L, y1/y2, n, A/Q, M → MIXED_INPUT_ENCODING
  • froude, jump, or manning as mode → INVALID_MODE
Example
y=1 v=2 → E=1+2/g
Validation cases

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

  • y=1 v=2 → E=1+2/9.80665
  • mode=velocity E=1+2/g y=1 → v=2
  • y=1 v=2 Fr=0.64 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Energy, length, speed
    Supports: E and y are lengths; v is speed; g is acceleration
  • Chow, V.T. Open-Channel Hydraulics — Specific energy
    Supports: E = y + v²/(2g) for a rectangular channel with hydrostatic pressure
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute open-channel specific energy.

Supported and not supported

Supported — E from y and v · invert y · invert v · API physics.fluid.specific_energy

Not supported — Froude-only Fr=v/√(gL), hydraulic jump sequent depths, Manning n, Q=Av

Agent / API notes

Capability id: physics.fluid.specific_energy · tool id: specific-energy · pin 1.0.0.

{ "y": 1, "v": 2 }

Modes: energy (default), depth, velocity. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/specific-energy. 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 the Froude number?

No. Fr = v / √(g L) is /calc/physics/froude-number. This page returns E. Sending Fr or L is MIXED_INPUT_ENCODING.

Is this specific force?

No. M = Q²/(gA) + A ȳ is /calc/physics/specific-force. This page takes y and v and rejects Q. Sending M is MIXED_INPUT_ENCODING.

Is this alternate depth?

No. Both y from E, Q, and b are /calc/physics/alternate-depth. Sending Q or b is MIXED_INPUT_ENCODING.

Is this a hydraulic jump?

No. Sequent depths are /calc/physics/hydraulic-jump. Sending y1 or y2 is MIXED_INPUT_ENCODING.

Is this Manning?

No. Uniform open-channel Q from n is /calc/physics/manning-formula. Sending n is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from area and velocity is /calc/physics/flow-rate. Sending A or Q is MIXED_INPUT_ENCODING.

Where does this run?

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