Physics calculator

Specific Force Calculator

Compute rectangular specific force M = Q²/(gA) + A ȳ with ȳ = y/2. Runs locally. Not hydraulic jump y2; not specific energy E; not Froude as the product; 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 1/1 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Rectangular specific force M from Q, b, and y. Invert y (subcritical default).
Scope: Rectangular specific force: M = Q²/(gA) + A ȳ with A=b y and ȳ=y/2; SI; default g=9.80665; M is m²
Verification: Engine tested · 5/5 tests · Production surface contract 1/1 · 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 and sequent depths
Sources
Evidence: 5 property · Production surface contract 1/1 · 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; 164 CURRENT) @ 2026-09-18T21:41:56.329Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

Specific forceM = Q²/(gA) + A y/2

SectionA = b y

CriticalMc = (3/2) b yc²

iSI rectangular prismatic channel. 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, and y

Discharge, rectangular width, and depth. Invert on the y tab when M is known.

Read M

M = Q²/(gA) + A y/2. Fr, yc, Mc, and conjugate y_alt are reported.

Example calculations

Common configurations with formula and result.

Q=2 m³/s, b=2 m, y=1 m

Rectangular channel, default g=9.80665

M = Q²/(gA) + A y/2

M ≈ 1.20394 m²

Invert y

M = 1.20394 m², same Q, b

subcritical root of M(y)

y ≈ 1.0000 m

Specific Force calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 5/5 tests · Production surface contract 1/1
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Rectangular specific force: M = Q²/(gA) + A ȳ with A = b y and ȳ = y/2. Invert depth (subcritical y>yc by default). This page computes M from Q, b, and y. Hydraulic jump sequent y2 from Fr₁>1 is a different page. Specific energy E = y + v²/(2g) is a different page.
What it calculates: Rectangular specific force M from Q, b, and y. Invert y (subcritical default).
Inputs: mode?
b
Q
y|M
g?
branch?
Outputs: M
Q
b
y
y_alt
yc
Mc
ybar
A
v
Fr
g
mode
model
Formula: M=Q²/(gA)+A y/2; A=b y
Assumptions: Rectangular specific force: M = Q²/(gA) + A ȳ with A=b y and ȳ=y/2; SI; default g=9.80665; M is m²
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 hydraulic jump y2 from Fr₁>1; not specific energy E=y+v²/(2g); not Froude as the product; not Manning n; not Q=Av; not critical slope Sc
Units: SI; y, b in m; Q in m³/s; M in m²
Boundary conditions: missing b, Q, y, or M when required → MISSING_REQUIRED_INPUT
y, Q, b, M, or g ≤ 0 → VALUE_MUST_BE_POSITIVE
A/v, y1/y2, E, Fr/L, n/C/S/R/Sc, yn/yc/q, z, H/Cd → MIXED_INPUT_ENCODING
unknown mode → INVALID_MODE
Example: Q=2 b=2 y=1 → M≈1.20394
Validation cases: 4 published on this page · 5/5 tests · Production surface contract 1/1 · View evidence
Q=2 b=2 y=1 → M ≈ 1.20394 m²
mode=depth M=1.20394 Q=2 b=2 → y ≈ 1.0000 m
Q=2 b=2 y=1 E=1.05 → MIXED_INPUT_ENCODING
Q=2 b=2 y=1 y1=1 → 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 per unit width (m²)
Chow, V.T. Open-Channel Hydraulics — Specific force and sequent depths
Supports: M = Q²/(gA) + A ȳ. Jump sequent y2 from Fr₁>1 is a different product. Specific energy E is a different product.
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute rectangular specific force M from Q, b, and depth y.

Supported and not supported

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

Not supported — hydraulic jump y2 from Fr₁>1; specific energy E; Froude as the product; Manning n; Q=Av; critical slope Sc; trapezoid z

Agent / API notes

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

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

Other calculators in this family: Hydraulic jump, Specific energy, Froude number, Critical depth, Critical slope .

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Frequently asked questions

Key distinctions behind the calculation.

Is this a hydraulic jump?

No. Sequent y2 from Fr₁>1 is /calc/physics/hydraulic-jump. That page rejects Q. Sending y1, y2, or M to the jump page is MIXED_INPUT_ENCODING.

Is this specific energy?

No. E = y + v²/(2g) is /calc/physics/specific-energy. That page rejects Q. Sending E is MIXED_INPUT_ENCODING. Golden M ≈ 1.20394 m² vs E ≈ 1.0510 m.

Is this the Froude number?

No. Fr = v / √(g L) is /calc/physics/froude-number. This page reports Fr. Sending Fr or L is MIXED_INPUT_ENCODING.

Is this Manning or Q = A·v?

No. Uniform Q from n is /calc/physics/manning-formula. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. Sending n, 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 specificForce wrapper.