Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Standards for Weir Flow Measurement

The design, construction, and operation of weirs for flow measurement are governed by detailed international and national standards. Adherence to these standards ensures accuracy, reliability, and consistency. The standards listed below are commonly referenced for thin-plate, broad-crested, and specialized weir types.

International Organization for Standardization (ISO)

*ISO 1438/1: Water flow measurement in open channels using weirs and venturi flumes - Part 1: Thin-plate weirs.
*ISO 3846: Liquid flow measurement in open channels by weirs and flumes - Rectangular broad-crested weirs.
*ISO 3847: Liquid flow measurement in open channels by weir (general).
*ISO 4360: Liquid flow measurement in open channels by weirs (triangular profile weirs).
*ISO 4362: Measurement of liquid flow in open channels - Trapezoidal profile weirs.
*ISO 4374: Liquid flow measurement in open channels - Round-nose horizontal broad-crested weirs.
*ISO 4377: Hydrometric determinations - Flow measurement in open channels using structures - Flat-V weirs.
*ISO 8333: Liquid flow measurement in open channels by weirs (V-shaped broad-crested weirs).
*ISO 9827: Measurement of liquid flow in open channels by weirs and flumes - Streamlined triangular profile weirs.

American Society for Testing and Materials (ASTM)

*ASTM D 5242: Standard Test Method for Open-Channel Flow Measurement of Water with Thin-Plate Weirs.
*ASTM D 5614: Standard Test Method for Open Channel Flow Measurement of Water with Broad-Crested Weirs.
*ASTM D 5640: Standard Guide for Selection of Weirs and Flumes for Open-Channel Flow Measurement of Water.
*ASTM D 5716: Standard Test Method for Measuring the Rate of Well Discharge by Circular Orifice Weir.

British Standards Institute (BSI)

BS 3680 P4A: Method using thin-plate weirs.
BS 3680 P4B: Triangular profile weirs.
BS 3680 P4E: Rectangular broad-crested weirs.
BS 3680 P4I: V-shaped broad-crested weirs.
BS 3680-4F: Round nose horizontal broad-crested weirs.
*BS ISO 4377: Hydrometric determinations - Flow measurement in open channels using structures - Flat-V weirs.

American Water Works Association (AWWA)

*AWWA C909 / F102: Matched-die-molded, fiberglass-reinforced plastic weir plates, scum baffles, and mounting brackets.

Other Notable Standards

DIN 19558 (Germany): Sewage treatment plants - Weir and scum baffle; arrangement, main dimensions and overflow rate.
GOST R 51657.4 (Russia): Water flow measurement in hydromelioration and water supply systems. Water discharge measurement in open channels by triangular profile weirs.
SAA AS 3778.4.x (Australia): A series covering thin-plate, rectangular broad-crested, round-nose, V-shaped, triangular profile, and Flat-V weirs.
*TAPPI TIP 0410-10: Weirs and flumes for the pulp and paper industry.

Fundamental Weir Flow Formulas

While specific discharge equations depend on the weir type and applicable standard, these general forms are foundational.

Rectangular Weir (Francis Formula)

For a rectangular weir with end contractions, the flow rate $Q$ is often estimated using a form of the Francis formula: $Q = C_d \cdot \frac{2}{3} \sqrt{2g} \left( L - 0.1nH \right) H^{3/2}$ where:

$C_d$ = Discharge coefficient (dimensionless),
$g$ = Gravitational acceleration ( $m/s^2$ or $ft/s^2$ ),
$L$ = Length of the weir crest (m or ft),
$n$ = Number of end contractions (typically 2 for a fully contracted weir),
$H$ = Head on the weir, measured upstream (m or ft).

90° V-Notch (Thomson) Weir

For a 90° triangular notch weir: $Q = C_d \cdot \frac{8}{15} \sqrt{2g} \tan\left(\frac{\theta}{2}\right) H^{5/2}$ For $\theta = 90°$ , $\tan(45°)=1$ , simplifying the equation. The exponent of $H$ ( $5/2$ ) provides high sensitivity for low-flow measurement.

References

Original Source

Source: engineeringtoolbox.com