• 21 Sep 2022
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# Round Nosed Broad Crested Weir

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Article summary

This is a general purpose unit for modelling a broad crested weir with a rectangular throat. It is also possible to model weirs with a parabolic or triangular control section by amending the input coefficients.

## Data

Field in Data Entry Form

Description

Name in Datafile

Coefficient of Velocity

Coefficient of approach velocity

Cv

Length of Weir

Length of the weir crest in the direction of flow (m)

L

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

b

Elevation of Weir

zc

Modular Limit

If FIXED, modular limit value used (for example 0.8); if VARIABLE (or m=0) then Flood Modeller will calculate the modular limit.

m

Upstream Crest Height

Height of crest above bed of upstream channel (m)

p1

Downstream Crest Height

Height of crest above bed of downstream channel (m)

p2

Upstream Label

Upstream Label

label 1

Downstream Label

Downstream Label

label 2

## Theory and Guidance

This unit models a round nosed broad crested weir in free or drowned mode with forward or reverse flow.

Round-nosed broad-crested weirs are often used as measuring structures.
The theoretical equations in free mode, where the downstream water level has no effect on the flow over the structure, are based on the assumption that the weir crest length in the direction of flow is sufficiently long for supercritical flow to develop on the crest.

Drowned flow, where the downstream level does affect the flow across the crest, commences when the ratio of downstream to upstream head over the crest exceeds the modular limit.

The modular limit is defined by an empirical relationship, as is the discharge coefficient. The modular limit can be determined from fig. 7.9 in Ackers P. et al (1978) (originally as fig. 11 in Harrison (1967)). It is taken to be the mean of the sloping back face and vertical back face curves.

Reverse flow is modelled assuming the same coefficients prevail.

The radius of curvature at the leading edge of the weir is set to be 0.1 metres.

### Equations

y1 ³ y2 (forward flow) h1 = hu, etc

y1 < y2 (reverse flow) h1 = hd, etc

h1 = y1 - zc

h2 = y2 - zc

#### Mode 0 - Dry Crest

Condition

y1< zc

y2 < zc

Equation

 Q = 0 (1)

Figure 1: Round Nosed Broad Crested Weir parameters

#### Mode 3 - Free Flow

Condition

y1 > zc

h2 / h1 £ m

where:

m is the modular limit

Equation

 Q = Cd Cv (2/3)1.5 Ö g b h11.5 (2)

where:

Cd = [ 1 - d (L - r ) / b ] [ 1 - (d / 2h1) (L - r) ]1.5

d = function of the boundary layer thickness which is set constant at 0.01

g = gravitational acceleration (m/s2)

Figure 2: Round Nosed Broad Crested Weir (free flow)

#### Mode 4 - Drowned Flow

Condition

y1 > zc

h2 / h1 > m

Equation

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

where:

Cd = [ 1 - d (L - r ) / b ] [ 1 - (d / 2h1) (L - r) ]1.5

d = function of the boundary layer thickness which is set constant at 0.01

g = gravitational acceleration (m/s2)

Figure 3: Round Nosed Broad Crested Weir (drowned flow)

### General

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 l, b, r, or zc .

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.

There are no formulae for drowned flow mode in the hydraulics literature. The equation here is based on the Bernoulli Equation with Cd as for free mode and assuming a smooth transition for free to drowned mode at the modular limit.

## Datafile Format

Line 1 - keyword `RNWEIR' [comment]

Line 2 - label 1, label 2

Line 3 - Cv, L, b, Zc, m

Line 4 - p1, p2

### Example

``````RNWEIR   Canoe Ramp
UNIT019     UNIT020
0.900     1.000    10.000     1.000     0.800
1.000     2.000``````