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Physics calculator

Trapezoidal Specific Force Calculator

Compute trapezoid specific force M = Q²/(gA) + A ȳ on A=(b+z y)y. Runs locally. Not rectangular ȳ=y/2; not sequent y2; not specific energy E; not Manning; 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 · Trapezoid M = Q²/(gA) + A ȳ with A=(b+z y)y; + O3 mpmath tabulated M.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Trapezoid M = Q²/(gA) + A ȳ with A=(b+z y)y; + O3 mpmath tabulated M.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (force, alias, awkward, deep, invalid-domain) · Matrix
Deferred
Not rectangular ȳ=y/2, not depth invert, not jump y2, not E, and not Q=Av.
Numerical scope
O2: trapezoid M=Q²/(gA)+A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)) vs a separate-module identity (≤2 ULP). Not rectangular ȳ=y/2, not jump y2, not E, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated trapezoid-specific-force vectors. Not rectangular E, not yc, and not yn.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Trapezoid specific force M from Q, b, z, and y. Invert y (subcritical default).
Scope
Trapezoid specific force: M = Q²/(gA) + A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; M is m²; z>0 is run/rise
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Trapezoid M = Q²/(gA) + A ȳ with A=(b+z y)y; + O3 mpmath tabulated M.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3.cov
Verification revision
2026-09-26.o2-o3.cov · 1/1 property · digest 76935a87cec7
Legacy regression
6/6 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
5/5 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
  • ISO 80000-4 — Mechanics — Volume flow rate and force
  • Chow, V.T. Open-Channel Hydraulics — Specific force in a trapezoidal section
Sources
Evidence
1 legacy golden · legacy regression suite · 5/5 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. M is m². Depth invert defaults to the subcritical root y>yc; send branch=super for y<yc. Do not send query v — that is calculation_version. Mean speed is result v. Do not send E, y1, y2, Fr, or A as inputs.

How to use

1

Enter Q, b, z, and y

Discharge, bottom width, side slope z (run/rise), and depth. Invert on the y tab when M is known. z=0 is the rectangular page.

2

Read M

M = Q²/(gA) + A ȳ. Fr, yc, Mc, and conjugate y_alt are reported.

Example calculations

Common configurations with formula and result.

ϟ

Q=2 m³/s, b=2 m, z=1, y=1 m

Trapezoidal channel, default g=9.80665

M = Q²/(gA) + A ȳ
M ≈ 1.46930 m²
ϟ

Invert y

M = 1.46930 m², same Q, b, z

subcritical root of M(y)
y ≈ 1.0000 m

Trapezoidal Specific Force calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Trapezoid specific force: M = Q²/(gA) + A ȳ with A = (b + z y) y and ȳ = y (3b + 2 z y) / [6 (b + z y)]. Invert depth (subcritical y>yc by default). Rectangular ȳ=y/2 is a different page. Trapezoid sequent depths are a different page. Trapezoid specific energy E is a different page.
What it calculates
Trapezoid specific force M from Q, b, z, and y. Invert y (subcritical default).
Inputs
  • mode?
  • b
  • z
  • Q
  • y|M
  • g?
  • branch?
Outputs
  • M
  • Q
  • b
  • z
  • y
  • y_alt
  • yc
  • Mc
  • ybar
  • A
  • T
  • v
  • Fr
  • g
  • mode
  • model
Formula
M=Q²/(gA)+Aȳ; A=(b+z y)y
Assumptions
  • Trapezoid specific force: M = Q²/(gA) + A ȳ with A=(b+z y)y and ȳ=y(3b+2zy)/(6(b+zy)); SI; default g=9.80665; M is m²; z>0 is run/rise
  • Unknown is M (force mode) or y (depth invert, subcritical y>yc by default); conjugate y_alt is reported; Fr is reported not an input
  • Not rectangular ȳ=y/2; not trapezoid sequent y2; not trapezoid specific energy E; not Manning n; not Q=Av
Units
  • SI; y, b in m; Q in m³/s; M in m²; z dimensionless
Boundary conditions
  • missing b, z, Q, y, or M when required → MISSING_REQUIRED_INPUT
  • y, Q, b, z, M, or g ≤ 0, or y/b outside [0.01, 20], or z>10 → VALUE_OUT_OF_RANGE
  • z=0, A/v, y1/y2, E, Fr/L, n/C/S/R/Sc, yn/yc/q, H/Cd → MIXED_INPUT_ENCODING
  • unknown mode → INVALID_MODE
Example
Q=2 b=2 z=1 y=1 → M≈1.46930
Validation cases

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

  • Q=2 b=2 z=1 y=1 → M ≈ 1.46930 m²
  • mode=depth M=1.46930 Q=2 b=2 z=1 → y ≈ 1.0000 m
  • Q=2 b=2 z=0 y=1 → MIXED_INPUT_ENCODING
  • Q=2 b=2 z=1 y=1 E=1.02 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Volume flow rate and force
    Supports: Q is volume flow; specific force M is force per unit weight (m²)
  • Chow, V.T. Open-Channel Hydraulics — Specific force in a trapezoidal section
    Supports: M = Q²/(gA) + A ȳ with ȳ from the trapezoid centroid. Rectangular ȳ=y/2 is a different product. Sequent depths are a different product.
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute trapezoid specific force M from Q, bottom width b, side slope z, and depth y.

Supported and not supported

Supported — M from Q, b, z, y · invert y · API physics.fluid.trapezoid_specific_force

Not supported — rectangular ȳ=y/2; trapezoid sequent y2; trapezoid specific energy E; Manning n; Q=Av; z=0

Agent / API notes

Capability id: physics.fluid.trapezoid_specific_force · tool id: trapezoidal-specific-force · pin 1.0.0.

{ "Q": 2, "b": 2, "z": 1, "y": 1 }

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

Calculator URL stays /calc/physics/trapezoidal-specific-force. 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 specific force?

No. Rectangular M with ȳ=y/2 is /calc/physics/specific-force. This page needs z>0. Sending z to the rectangular page, or z=0 here, is MIXED_INPUT_ENCODING.

Is this a trapezoidal hydraulic jump?

No. Sequent y2 from shared M is /calc/physics/trapezoidal-hydraulic-jump. This page computes M from one depth. Sending y1, y2, or mode=sequent is MIXED_INPUT_ENCODING.

Is this trapezoidal specific energy?

No. E = y + Q²/(2g A²) is /calc/physics/trapezoidal-specific-energy. Both y from E are /calc/physics/trapezoidal-alternate-depth. Sending E is MIXED_INPUT_ENCODING.

Is this the Froude number or Manning?

No. Fr = v / √(g L) is /calc/physics/froude-number. Uniform Q from n is /calc/physics/trapezoidal-normal-depth. Sending Fr, n, A, or v is MIXED_INPUT_ENCODING. Result v = Q/A and Fr are reported.

Where does this run?

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