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Physics calculator

Side Weir Calculator

Compute Borghei 1999 sharp-crested rectangular side-weir discharge from channel width B, weir length L, upstream depth y1, sill p, and approach Q1. Runs locally. C_d is 0.71−0.41 Fr₁−0.22(p/y1), not an input. Not a frontal thin-plate weir, not an ogee, not a sluice, not Manning, and 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 · Borghei 1999 side weir Q=(2/3) Cd L √(2g) (y1−p)^{3/2} with Cd=0.71−0.41 Fr₁−0.22(p/y1), + O3 mpmath tabulated Q.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Borghei 1999 side weir Q=(2/3) Cd L √(2g) (y1−p)^{3/2} with Cd=0.71−0.41 Fr₁−0.22(p/y1), + O3 mpmath tabulated Q.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, alias, awkward, v1, invalid-domain) · Matrix
Deferred
Not frontal thin-plate given Cd, not ogee Hd, not sluice, not Manning, not submerged y2, not Q=Av.
Numerical scope
O2: Borghei 1999 side weir vs a separate-module identity (≤2 ULP). Not frontal thin-plate, not ogee Hd, not sluice, not Manning, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated side-weir vectors. Not frontal thin-plate, not ogee Hd, not sluice, not Manning, and not Q=Av.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Borghei 1999 sharp-crested side-weir lateral discharge or weir length. SI B, L, y1, p, Q1, Q.
Scope
Borghei 1999 sharp-crested side weir: Q=(2/3) C_d L √(2g) (y1−p)^{3/2}; C_d=0.71−0.41 Fr₁−0.22(p/y1); SI B, L, y1, p, Q1, Q; C_d is reported
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Borghei 1999 side weir Q=(2/3) Cd L √(2g) (y1−p)^{3/2} with Cd=0.71−0.41 Fr₁−0.22(p/y1), + O3 mpmath tabulated Q.· 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 a829ba1c8ed9
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
4/4 golden · 1/1 CVP boundary · 3/3 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
  • Borghei, Jalili & Ghodsian — Discharge Coefficient for Sharp-Crested Side Weir in Subcritical Flow — Journal of Hydraulic Engineering, 1999
  • ISO 80000-4 — Mechanics — Volume flow rate
Sources
Evidence
1 legacy golden · legacy regression suite · 4/4 oracle-backed golden · 3/3 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.

Lateral dischargeQ = (2/3) C_d L √(2g) (y1 − p)^{3/2}
CoefficientC_d = 0.71 − 0.41 Fr₁ − 0.22 (p / y1)
Approach FroudeFr₁ = Q1 / (B y1 √(g y1))
iSI. Envelope Fr₁∈[0.1, 0.9] and p/y1∈[0.1, 0.9]. y1 > p. Do not send query v — that is calculation_version. Approach speed is v1.

How to use

1

Enter channel width B

Rectangular approach channel in metres. This is not sluice or broad-crested b.

2

Enter weir length L

Along-channel crest. Thin-plate frontal weirs also use L, but they do not need B, p, y1, and Q1.

3

Enter y1, p, and Q1

Upstream depth, sill, and approach discharge. Head on the weir is y1−p, not an input H.

Example calculations

Common configurations with formula and result.

ϟ

Subcritical lateral overflow

B=1 m, L=2 m, y1=0.5 m, p=0.2 m, Q1=0.4 m³/s

C_d = 0.71 − 0.41 Fr₁ − 0.22 (0.2/0.5)
Q≈0.45979 m³/s
ϟ

Invert L from that Q

B=1 m, y1=0.5 m, p=0.2 m, Q1=0.4 m³/s, Q≈0.45979 m³/s

L from Q = (2/3) C_d L √(2g) H^{3/2}
L=2.0000 m

Side Weir calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Borghei 1999 sharp-crested rectangular side weir in subcritical flow. Q=(2/3) C_d L √(2g) (y1−p)^{3/2} with C_d=0.71−0.41 Fr₁−0.22(p/y1) and Fr₁=Q1/(B y1 √(g y1)). Inputs and result are SI (B, L, y1, p in m, Q and Q1 in m³/s). C_d is reported, not an input. Envelope Fr₁∈[0.1, 0.9] and p/y1∈[0.1, 0.9]. Not frontal thin-plate (2/3) C_d L √(2g) H^{3/2} with given C_d, not ogee Hd, not sluice a b √(2g y1), not Manning n, not Q=Av.
What it calculates
Borghei 1999 sharp-crested side-weir lateral discharge or weir length. SI B, L, y1, p, Q1, Q.
Inputs
  • mode?
  • B
  • y1
  • p
  • Q1 | v1
  • L | Q
Outputs
  • Q
  • Q1
  • L
  • B
  • y1
  • p
  • H
  • Fr1
  • Cd
  • g
  • mode
  • model
Formula
Q=(2/3) C_d L √(2g) (y1−p)^{3/2}; C_d=0.71−0.41 Fr₁−0.22(p/y1)
Assumptions
  • Borghei 1999 sharp-crested side weir: Q=(2/3) C_d L √(2g) (y1−p)^{3/2}; C_d=0.71−0.41 Fr₁−0.22(p/y1); SI B, L, y1, p, Q1, Q; C_d is reported
  • Rectangular channel; subcritical Fr₁∈[0.1, 0.9]; p/y1∈[0.1, 0.9]; y1>p; free lateral overflow; De Marchi-type C_d, not a given frontal C_d
  • Not thin-plate frontal weir, not ogee Hd, not sluice a b √(2g y1), not Manning n, not Q=Av, not submerged y2
Units
  • SI; B, L, y1, and p in m; Q and Q1 in m³/s
Boundary conditions
  • missing B, y1, p, Q1, L, or Q when required → MISSING_REQUIRED_INPUT
  • Cd, weir H, ogee P/Hd, sluice a/b, Manning n/R/S, Q=Av v, orifice A/d, flume Ha/L_f → MIXED_INPUT_ENCODING
  • Fr₁ outside [0.1, 0.9], p/y1 outside [0.1, 0.9], or y1≤p → VALUE_OUT_OF_RANGE
  • mode=rectangular|ogee|sluice or unknown mode → MIXED_INPUT_ENCODING or INVALID_MODE
Example
B=1 L=2 y1=0.5 p=0.2 Q1=0.4 → Q≈0.45979
Validation cases

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

  • B=1 L=2 y1=0.5 p=0.2 Q1=0.4 → Q≈0.45979 m³/s
  • L=2 y1=0.5 p=0.2 Q1=0.4 → MISSING_REQUIRED_INPUT (B)
  • B=1 L=2 y1=0.5 p=0.2 Q1=0.4 Cd=0.62 → MIXED_INPUT_ENCODING
  • kind=rectangular B=1 L=2 y1=0.5 p=0.2 Q1=0.4 → MIXED_INPUT_ENCODING
Sources
  • Borghei, Jalili & Ghodsian — Discharge Coefficient for Sharp-Crested Side Weir in Subcritical Flow — Journal of Hydraulic Engineering, 1999
    Supports: C_d = 0.71 − 0.41 Fr₁ − 0.22 (p/y1) for rectangular sharp-crested side weirs in subcritical flow
  • ISO 80000-4 — Mechanics — Volume flow rate
    Supports: Q is volume flow; B, L, y1, and p are lengths
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute Borghei 1999 sharp-crested side-weir discharge from channel width, weir length, upstream depth, sill, and approach flow.

Supported and not supported

Supported — lateral Q from B, L, y1, p, and Q1 · invert L from Q · API physics.fluid.side_weir

Not this page — frontal thin-plate weir · ogee spillway · sluice gate · Manning · Q=Av · submerged y2

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 a frontal thin-plate weir?

No. Thin-plate Q=(2/3) C_d L √(2g) H^{3/2} with given C_d is /calc/physics/weir-discharge. Sending H or Cd here is MIXED_INPUT_ENCODING. At L=2 m and H=0.3 m this page reports ≈0.45979 m³/s, not frontal C_d=0.62 ≈0.60157 m³/s.

Is this an ogee spillway?

No. USBR high-overflow ogee Q from L, H, and design head Hd is /calc/physics/ogee-spillway. Sending Hd or P here is MIXED_INPUT_ENCODING.

Is this a sluice gate?

No. A free-flow undershot sluice with Swamee C_d from a/y1 is /calc/physics/sluice-gate. Sending a or b here is MIXED_INPUT_ENCODING.

Is this the Manning formula?

No. Manning is uniform open-channel flow from n, A, R, and S at /calc/physics/manning-formula. Sending n, R, 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 v is MIXED_INPUT_ENCODING. Approach speed is the field v1.

Can I send a given C_d?

No. C_d is reported from Fr₁ and p/y1. Given C_d is the frontal thin-plate page.

Where does this run?

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