Notional Weir
• 21 Sep 2022
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# Notional Weir

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The Notional Weir acts as a broad crested weir with a rectangular control section for free flow only. For drowned flow, the water levels are set as identical on each side of the weir

## Data

Field in Data Entry Form

Description

Name in Datafile

Discharge Coefficient

Coefficient of discharge

Cd

Velocity Coefficient

Coefficient of approach velocity

Cv

Exponent

Exponent of y

(e = 1.5 for a rectangular control section)

(e = 2 for a parabolic control section)

(e = 2.5 for a triangular control section)

e

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

b

Elevation of Crest

Elevation of weir crest (m Above Datum)

zc

Upstream

Upstream Label

Label 1

Downstream

Downstream Label

Label 2

## Theory and Guidance

The Notional Weir acts as a broad crested weir with rectangular control section for free flow only. For drowned flow, the water levels are set as identical on each side of the weir.

The Notional Weir is extremely similar to the Weir in its simplified approach to modelling weirs, in that the effect of boundary layers and upstream dependence of the coefficients of approach velocity Cv and discharge Cd are neglected.

As with the Weir, triangular and parabolic control sections can be modelled by factoring the coefficient of discharge - see the General section below for details on how to do this.

Both forward and reverse flow can be modelled.

### Equations

y1 ³ y2 (forward flow) h1 = hu, etc

y< y2 (reverse flow) h1 = hd, etc

h1 = y1 - zc

h2 = y2 - zc

#### Mode 0 - Dry Crest

 Condition y1 ³ zcy2 ³ zc Equation Q = 0

Figure 1: Notional Weir parameters

#### Mode 1 - Free Flow (Positive Sense)

Condition

y1 > Zc

h2 £ 1.3 * hcrit

where:

 (1)

Equation

 Q = Cd Cv (2/3)1.5 Ö g b h1e (2)

Figure 2: Notional Weir (free flow)

#### Mode 2 - Free Flow (Negative Sense)

Condition

y2 > Zc

h1 £ 1.3 * hcrit

where hcrit is defined as for Mode 1

Equation

 Q = - Cd Cv (2/3)1.5 Ögb h2e (3)

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

 Condition y1 > Zch2 > 1.3 * hcritwhere hcrit is defined as for Mode 1 Equation h1 = h2

Figure 3: Notional Weir (drowned flow)

#### Mode 4 - Drowned Flow (Negative Sense)

 Condition y2 > Zch1 > 1.3 * hcritwhere hcrit is defined as for Mode 1 Equation h2 = h1

### General

Instead of an input modular limit, used in most of the Flood Modeller structures, a calculated value of

 (4)

is used to differentiate between free and drowned flows. If the downstream water elevation above the weir crest exceeds 1.3 * y crit then the flow is assumed to be drowned. Otherwise it is free.

If a non-rectangular section is employed, the results must be examined carefully as the formula to calculate the critical height is approximate in this case.

The Notional Weir can be used to model approximately regions of supercritical flow at a location which acts as a channel control at low flows but is immaterial to water levels at higher flows.

Care must be taken when a Notional Weir is attached to other structures; the model results should be closely examined to ensure the correct behaviour of the model. Results could be compared by either using a round nosed weir instead, or inserting a reach of open channel or culvert between the structures.

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. Another problem may arise when the downstream water level oscillates around the critical depth; a warning message is given in this case.

Inaccuracies may be introduced if the weir crest is too short for critical flow to develop. Short crested weirs may be modelled approximately using a Notional Weir . Very short crested weirs may be better modelled with a sharp-crested weir.

## Datafile Format

Line 1 - Keyword NOTWEIR'

Line 2 - Label 1, Label 2

Line 3 - e

Line 4 - Cd, Cv, b, zc

### Example

NOTWEIR - west drayton mill 2.022a
UNIT072     UNIT073
2.500
0.900     0.800    10.000     1.000`