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 Engine tested · Source checked · 17/17 tests · Production surface contract 3/3 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
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 · 17/17 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 80000-4 — Mechanics — Energy, length, speed
Chow, V.T. Open-Channel Hydraulics — Specific energy
Sources
Evidence: 2 golden · 10 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) @ 2026-09-17T09:03:11.906Z
Semantic contract: PASS

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

Enter y

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

Enter v

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

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.

y=1 m, v=2 m/s

Default g=9.80665 m/s²

E = 1 + 4 / (2 × 9.80665)

E ≈ 1.20394 m

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

Engine tested 17/17 tests · Production surface contract 3/3
Named expert review Not performed
Calculation version 1.0.0

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 → 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 3/3 · 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: Froude number, Hydraulic jump, Manning formula, Chezy formula .

}

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 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.