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Weirs Flow Rate

Reference data and engineering information about weirs flow rate for fluid mechanics applications.

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Overview

Engineering reference data for Weirs Flow Rate in fluid mechanics.

Key Formulas

Reynolds Number

Re=ρvDμRe = \frac{\rho v D}{\mu}

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

P+12ρv2+ρgh=constP + \frac{1}{2}\rho v^2 + \rho g h = \text{const}

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

A1v1=A2v2A_1 v_1 = A_2 v_2

Conservation of mass for incompressible flow.

Darcy-Weisbach

ΔP=fLDρv22\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}

Pressure drop due to friction in a pipe.

Variables

Symbol Description Unit
ReRe Reynolds number —
ρ\rho Fluid density kg/m³
vv Flow velocity m/s
DD Characteristic dimension m
μ\mu Dynamic viscosity Pa·s
PP Pressure Pa
ff Darcy friction factor —

Weir Types

Weirs are classified based on their crest geometry and flow characteristics. Common types include:

  • Rectangular Weirs: Feature a rectangular notch. Flow rate is primarily a function of head (h) and notch width (b).
  • Triangular (V-Notch) Weirs: Feature a V-shaped notch, defined by its angle (θ). They are highly accurate for low-flow measurements.
  • Broad-Crested Weirs: Have a wide, flat crest. They are commonly found in natural channels and dam spillways and require calibration for accurate measurement.
  • Compound Weirs: Combine different weir shapes (e.g., a V-notch with a rectangular section) to measure a wider range of flow rates.

Measurement Methods

The primary level measurement techniques used with weirs are:

  • Ultrasonic Level Transmitters: Mounted above the flow without contact. They can output linear flow signals (e.g., 4-20 mA or digital pulses).
  • Pressure Transmitters: Used for sharp-crested weirs or specific points on broad-crested weirs. They output a linear level signal, requiring flow calculation in the transmitter or control system.

Standards and Specifications

Accurate flow measurement requires installation consistent with established standards. Key references include specifications from ASTM and ISO for sharp-crested weirs. Broad-crested weir installations must be calibrated to meet accuracy requirements.

References