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 Engine tested · Source checked · 5/5 tests · Production surface contract 1/1 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
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 · 5/5 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review: Optional · Not performed
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: 5 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Production: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T02:44:05.986Z
Semantic contract: PASS

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

Enter channel width B

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

Enter weir length L

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

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.

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

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

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

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 · 5/5 tests · Production surface contract 1/1 · 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: Thin-plate weir, Ogee spillway, Sluice gate, Manning formula, Flow rate .

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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.