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 Engine tested · Source checked · 5/5 tests · Production surface contract 2/2 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
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 · 5/5 tests · Production surface contract 2/2 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 80000-4 — Mechanics — Volume flow rate and force
Chow, V.T. Open-Channel Hydraulics — Specific force in a trapezoidal section
Sources
Evidence: 5 property · Production surface contract 2/2 · Artifact integrity PASS
Production: Embedded snapshot: Capability production binding: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · Evidence changed after the last successful production attestation. Re-attestation required. · Public/cache ✓ · Origin ✓
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. 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

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.

Read M

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

Example calculations

Common configurations with formula and result.

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

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

Engine tested 5/5 tests · Production surface contract 2/2
Named expert review Not performed
Calculation version 1.0.0

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 · 5/5 tests · Production surface contract 2/2 · 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: Specific force, Trapezoidal hydraulic jump, Trapezoidal specific energy, Trapezoidal alternate depth, Trapezoidal critical depth, Froude number .

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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.