Physics calculator

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.

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: Rectangular critical depth from unit discharge. Invert q. REST accepts Q and b as q=Q/b.
Scope: Rectangular critical depth: yc = (q²/g)^{1/3}; q = Q/b; 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 — Length, speed, acceleration
Chow, V.T. Open-Channel Hydraulics — Critical flow
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.

Critical depthyc = (q² / g)^{1/3}

Unit discharge invertq = √(g yc³)

From dischargeq = Q / b

iSI rectangular prismatic channel. vc = √(g yc) is reported. Fr=1 is the definition of critical flow, not a Froude-number wrap. Not specific energy E, not a hydraulic jump, not Manning, not Q=Av.

How to use

Enter q

Unit discharge in m²/s. REST may send q or Q+b; the query layer uses q_m2_s.

Read yc

yc = (q²/g)^{1/3}. Invert q on the q tab when yc is known.

Optional g

Gravity defaults to 9.80665 m/s².

Example calculations

Common configurations with formula and result.

q=1 m²/s

Default g=9.80665 m/s²

yc = (1 / 9.80665)^{1/3}

yc ≈ 0.46719 m

Invert q

yc ≈ 0.46719 m

q = √(g yc³)

q = 1 m²/s

Critical Depth 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: Rectangular critical depth: yc = (q²/g)^{1/3} with q = Q/b and default g=9.80665 m/s². This page computes yc, not Fr = v/√(gL) and not E = y+v²/(2g).
What it calculates: Rectangular critical depth from unit discharge. Invert q. REST accepts Q and b as q=Q/b.
Inputs: mode?
q|yc
Q?
b?
g?
Outputs: yc
q
g
vc
mode
model
Formula: yc = (q² / g)^{1/3}
Assumptions: Rectangular critical depth: yc = (q²/g)^{1/3}; q = Q/b; default g=9.80665 m/s²
Critical speed vc = √(g yc) is reported, not an input; Fr=1 is the definition, not a Froude wrap
Not a Froude wrap, not specific energy E, not a hydraulic jump, not Manning, not Q=Av
Units: SI; yc in m; q in m²/s; Q in m³/s; b in m; g in m/s²
Boundary conditions: missing q or yc when required → MISSING_REQUIRED_INPUT
q, yc, Q, b, or g ≤ 0 → VALUE_MUST_BE_POSITIVE
Fr/L, E/y, y1/y2, n, A, v → MIXED_INPUT_ENCODING
froude, energy, or jump as mode → INVALID_MODE
Example: q=1 → yc=(1/g)^{1/3}
Validation cases: 3 published on this page · 17/17 tests · Production surface contract 3/3 · View evidence
q=1 → yc=(1/9.80665)^{1/3}
mode=unit_discharge yc=(1/g)^{1/3} → q=1
q=1 Fr=1 → MIXED_INPUT_ENCODING
Sources: ISO 80000-4 — Mechanics — Length, speed, acceleration
Supports: yc is a length; q is discharge per width; g is acceleration
Chow, V.T. Open-Channel Hydraulics — Critical flow
Supports: yc = (q²/g)^{1/3} for a rectangular channel at Fr=1
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute rectangular critical depth.

Supported and not supported

Supported — yc from q or Q+b · invert q · API physics.fluid.critical_depth

Not supported — Froude-only Fr=v/√(gL), specific energy E=y+v²/(2g), hydraulic jump sequent depths, Manning n, Q=Av

Agent / API notes

Capability id: physics.fluid.critical_depth · tool id: critical-depth · pin 1.0.0.

{ "q": 1 }

Modes: depth (default), unit_discharge. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/critical-depth. There is no /calc/fluid.

Other calculators in this family: Specific energy, Froude number, Hydraulic jump, Manning formula .

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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 yc. Sending Fr or L is MIXED_INPUT_ENCODING.

Is this specific energy?

No. E = y + v²/(2g) is /calc/physics/specific-energy. Sending E or y 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 Q = A·v?

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

Where does this run?

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