Weir flow calculation

Measurement of liquid flowrate in open channel

1. Introduction
2. Rectangular weirs : flow calculation
3. Triangular notch weirs : flow calculation

1. Introduction

Calculation of flow rate through weirs is particularly interesting in water systems engineering, for the calculation of flow of rivers, dams, sewage system...etc... that have an overflow system that takes the form of a weir.

Different weir designs are available :

  • Rectangular weir
  • Triangular notch weir

The equations below [Perry] are valid for water flow. With a different fluid, a correction due to the viscosity is required.

2. Rectangular weir : flow calculation

Rectangular weir flow

The flow capacity through a rectangular weir is given by the following formula, which applies to sharp edged rectangular weirs :


Rectangular weir flowrate calculation formula

With :

Q = volume flow rate (m3/s)
L = crest length (m)
h0 = weir head (m)
g = gravity acceleration = 9.81 m.s-2

In case h0 > L, a modification of the calculation formula must be considered :


Narrow Rectangular weir flowrate calculation formula

3. Triangular notch weir : flow calculation

Triangular notch weir flow

The flowrate that can be achieved through a triangular notch weir (also called V notch weir), sharp edged, is calculated with the following equation :

Q=(0.31*h02.5*(2*g)0.5)/tan Φ

Triangular weir flowrate calculation formula


[Perry] Perry's Chemical Engineer's Handbook, Section 10 Transport and storage of fluids, page 10-24, McGraw-Hill, 2008