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Trapezoidal Hydraulic Jump Calculator

Compute trapezoid sequent depths from specific force on A=(b+z y)y. Runs locally. Not rectangular Bélanger y2/y1=(√(1+8Fr₁²)−1)/2; not trapezoid alternate E-pair; not trapezoid yc; not trapezoid yn.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Trapezoid sequent depths from equal specific force M; + O3 mpmath tabulated y2.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Trapezoid sequent depths from equal specific force M; + O3 mpmath tabulated y2.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (sequent, alias, awkward, fast, invalid-domain) · Matrix
Deferred
Not rectangular jump, not alternate E-pair, not upstream invert in this pack, and not Q=Av.
Numerical scope
O2: trapezoid sequent depths from equal M=Q²/(gA)+A ȳ vs a separate-module identity (≤2 ULP). Not rectangular jump, not alternate E-pair, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated trapezoid-hydraulic-jump vectors. Not rectangular jump, not alternate E-pair, and not M alone.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Trapezoid sequent depths from specific force given y1, Q, b, and z. Invert y1. Optional ΔE from y1 and y2.
Scope
Trapezoid hydraulic jump: sequent depths from M=Q²/(gA)+A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; z>0 is run/rise; Fr₁>1
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Trapezoid sequent depths from equal specific force M; + O3 mpmath tabulated y2.· 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 e099b6d80395
Legacy regression
7/7 tests · Production surface contract 6/6
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 · 6/6 CVP contract · Manifest
Sources
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.

Specific forceM = Q²/(g A) + A ȳ
SectionA = (b + z y) y
Centroidȳ = y (3b + 2 z y) / [6 (b + z y)]
iSI trapezoidal prismatic channel. z is run/rise, z>0. Default g=9.80665 m/s². Require Fr₁>1. Do not send query v — that is calculation_version. Mean speeds are result v1 and v2. Do not send Fr, E, M, A, yc, or yn as inputs.

How to use

1

Enter y₁, Q, b, and z

Upstream depth, discharge, bottom width, and side slope z (run/rise). z=0 is the rectangular page. Invert y₁ on the y₁ tab.

2

Read y₂

The subcritical sequent depth at the same M. ΔE, Fr, and yc are reported.

Example calculations

Common configurations with formula and result.

ϟ

y₁=0.25 m, Q=2 m³/s, b=2 m, z=1

Trapezoidal channel, default g=9.80665

M = Q²/(gA) + A ȳ
y₂ ≈ 0.68128 m
ϟ

Invert y₁

y₂ ≈ 0.68128 m, same Q, b, z

M₁ = M₂
y₁ ≈ 0.25000 m

Trapezoidal Hydraulic Jump calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Trapezoid hydraulic jump: sequent depths from M=Q²/(gA)+A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)). Fr₁>1. Rectangular Bélanger y2/y1=(√(1+8Fr₁²)−1)/2 is a different page. Trapezoid both y from E is a different page.
What it calculates
Trapezoid sequent depths from specific force given y1, Q, b, and z. Invert y1. Optional ΔE from y1 and y2.
Inputs
  • mode?
  • b
  • z
  • Q
  • y1|y2
  • g?
Outputs
  • y1
  • y2
  • Q
  • b
  • z
  • Fr1
  • Fr2
  • v1
  • v2
  • dE
  • E1
  • E2
  • M
  • yc
  • g
  • mode
  • model
Formula
M=Q²/(gA)+Aȳ; A=(b+z y)y
Assumptions
  • Trapezoid hydraulic jump: sequent depths from M=Q²/(gA)+A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; z>0 is run/rise; Fr₁>1
  • Unknown is y2 (sequent) or y1 (upstream invert) or ΔE (energy); Fr is reported not an input; not Bélanger y2/y1=(√(1+8Fr₁²)−1)/2
  • Not rectangular sequent depths; not trapezoid alternate E-pair; not trapezoid yc; not trapezoid yn; not Manning n; not Q=Av
Units
  • SI; y, b in m; Q in m³/s; z dimensionless
Boundary conditions
  • missing b, z, Q, y1, or y2 when required → MISSING_REQUIRED_INPUT
  • Fr₁ ≤ 1 or y/b outside [0.01, 20] or z>10 → VALUE_OUT_OF_RANGE
  • z=0, Fr/L, A/v, E, M, n/C/S/R/Sc, yn/yc/q, H/Cd → MIXED_INPUT_ENCODING
  • unknown mode → INVALID_MODE
Example
y1=0.25 Q=2 b=2 z=1 → y2≈0.68128
Validation cases

4 published on this page · 7/7 tests · Production surface contract 6/6 · View evidence

  • y1=0.25 Q=2 b=2 z=1 → y2 ≈ 0.68128 m
  • mode=upstream y2≈0.68128 Q=2 b=2 z=1 → y1 ≈ 0.25000 m
  • y1=0.25 Q=2 b=2 z=0 → MIXED_INPUT_ENCODING
  • y1=0.25 Q=2 b=2 z=1 Fr=2 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Force and volume flow
    Supports: M is a length² (specific force); y is a length; Q is volume flow
  • Chow, V.T. Open-Channel Hydraulics — Hydraulic jump in a trapezoidal section
    Supports: Sequent depths share specific force M=Q²/(gA)+A ȳ. Rectangular Bélanger is a different product. The E-pair is a different product.
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute trapezoid sequent depths from specific force given y₁, Q, bottom width b, and side slope z.

Supported and not supported

Supported — y₂ from y₁, Q, b, z · invert y₁ · ΔE from y₁ and y₂ · API physics.fluid.trapezoid_hydraulic_jump

Not supported — rectangular Bélanger y₂/y₁=(√(1+8 Fr₁²)−1)/2; trapezoid alternate E-pair; trapezoid yc; trapezoid yn; Manning n; Q=Av; z=0

Agent / API notes

Capability id: physics.fluid.trapezoid_hydraulic_jump · tool id: trapezoidal-hydraulic-jump · pin 1.0.0.

{ "y1": 0.25, "Q": 2, "b": 2, "z": 1 }

REST and MCP call the same trapezoidHydraulicJump wrapper as the page.

Calculator URL stays /calc/physics/trapezoidal-hydraulic-jump. 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 rectangular hydraulic jump?

No. Bélanger y₂/y₁=(√(1+8 Fr₁²)−1)/2 is /calc/physics/hydraulic-jump. This page needs z>0 and uses Q, b, z. Sending Fr here, or z to the rectangular page, is MIXED_INPUT_ENCODING. z=0 is MIXED_INPUT_ENCODING.

Is this trapezoidal alternate depth?

No. Both trapezoid y from E, Q, b, and z are /calc/physics/trapezoidal-alternate-depth. Sequent depths share M, not E. Sending E, y_sub, or mode=depths is MIXED_INPUT_ENCODING.

Is this specific force?

No. Trapezoid M=Q²/(gA)+A ȳ is /calc/physics/trapezoidal-specific-force. Rectangular ȳ=y/2 is /calc/physics/specific-force. This page reports M but the unknown is sequent y. Sending M is MIXED_INPUT_ENCODING.

Is this trapezoidal critical depth or trapezoidal normal depth?

No. Trapezoid Fr=1 from Q, b, z is /calc/physics/trapezoidal-critical-depth. Trapezoid yn from Manning is /calc/physics/trapezoidal-normal-depth. Sending yc, yn, n, or S is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. Sending A or v is MIXED_INPUT_ENCODING. Result v = Q/A is reported.

Where does this run?

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