Weir
• 21 Sep 2022
• Dark
Light

# Weir

• Dark
Light

Article Summary

## Data

Field in Data Entry Form

Description

Name in Datafile

Discharge coefficient

Coefficient of discharge

Cd

Velocity Coefficient

Coefficient of approach velocity

Cv

Breadth of weir at control section (normal to the flow direction) (m)

b

Elevation of Crest

Elevation of weir crest (m Above Datum)

zc

Modular Limit

Modular limit for weir

m

Exponent

Exponent of y

(e = 1.5 for rectangular control section)

(e = 2 for parabolic control section)

(e = 2.5 for triangular control section)

e

Upstream

Upstream Label (8 characters)

label 1

Downstream

Downstream Label (8 characters)

label 2

## Theory and Guidance

The Weir is a general purpose unit for modelling a broad crested weir with a rectangular throat. By amending the input coefficients, it is also possible to model weirs with a parabolic or triangular control section.

The unit models the weir in free or drowned mode with forward or reversed flow.

### Description

The Weir describes flow over a rectangular throated broad crested weir without explicitly considering the effects of boundary layer development or the dependence of approach velocity coefficient Cor discharge coefficient Cd on upstream conditions. This means that triangular and parabolic control sections can be modelled. See the General section for details of how to do this.

### Equations

y1 ³y2 (forward flow) h1 = hu

y1 < y2 (reverse flow) h1 = hd

h1 = y1 - zc

h2 = y2 - zc Figure 1: Weir Parameters

#### Mode 0 - Dry Crest

 Condition y1 < zcy2 < zc Equation Q = 0

#### Mode 1 - Free Flow (positive sense)

Condition

y1 > zc

h1 > h2

h2 / h1 ³ m

where:

m is the modular limit

Equation

 Q = Cd Cv (2/3)1.5Ög b h1e (1) Figure 2: Weir (Free Flow)

#### Mode 2 - Free Flow (negative sense)

Condition

y2 > zc

h2 > h1

h1 / h2£ m

Equation

 Q = - Cd Cv (2/3)1.5Ög b h2e (2)

#### Mode 3 - Drowned Flow (Positive Sense)

Condition

y1 > zc

h1 ³ h2

h2 / h1 > m

Equation

 Q = Cd Cv (2/3)1.5 Ög b h1 [(h1 - h2) / (1 - m)]0.5 (3) #### Mode 4 - Drowned Flow (Negative Sense)

Condition

y2 > zc

h2 ³ h1

h1 / h2 > m

Equation

 Q = Cd Cv (2/3)1.5 Ög b h2 [(h2 - h1 ) / (1 - m)]0.5 (4)

### General

The Weir adopts a more simplified approach to modelling weirs than that adopted in the round nosed or sharp-crested weirs.

A weir with a triangular control section can be modelled by choosing a discharge coefficient according to: (5)

where:

q is the angle at the base of the control section.

For a parabolic control section, the discharge coefficient should be amended to:  (6)

where:

f is the focal distance in metres of the parabolic control section.

For non-rectangular control sections the Weir Width should be set to 1 and the Approach Velocity Coefficient input as normal.

Problems can arise if the weir is not acting as a control. For example, if the upstream cross section has supercritical flow due to the bed being higher than the weir or the weir being extremely wide compared to the width of the upstream cross section.

It is not possible to carry out range checks on Weir Width or Crest Level .

Inaccuracies may be introduced if the weir crest is too short for critical flow to develop. Short crested weirs may be modelled approximately by this routine.Very short crested weirs may be better modelled with a Sharp Crested Weir.

## Datafile Format

Line 1 - keyword `WEIR' [comment]

Line 2 - label 1, label 2

Line 3 - e

Line 4 - Cd, Cv, b, zc, m

#### Example

``````WEIR
UNIT021     UNIT022
2.000
1.100     0.900    10.000     1.000     0.900``````