Physics calculator

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 Engine tested · Source checked · 6/6 tests · Production surface contract 1/1 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
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 · 6/6 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 80000-4 — Mechanics — Force and volume flow
Chow, V.T. Open-Channel Hydraulics — Hydraulic jump in a trapezoidal section
Sources
Evidence: 6 property · Production surface contract 1/1 · Artifact integrity PASS
Production: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T21:41:56.329Z
Semantic contract: PASS

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

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.

Read y₂

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

Example calculations

Common configurations with formula and result.

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

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

Engine tested 6/6 tests · Production surface contract 1/1
Named expert review Not performed
Calculation version 1.0.0

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 · 6/6 tests · Production surface contract 1/1 · 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: Hydraulic jump, Trapezoidal alternate depth, Specific force, Trapezoidal critical depth, Trapezoidal specific energy, Froude number .

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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. Rectangular M=Q²/(gA)+A ȳ 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.