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 | Breadth of weir at control section (normal to the flow direction) (m) | b |
Elevation of Weir | Elevation of weir crest (mAD) | 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
hu = upstream head
hd = downstream head
Mode 0 - Dry Crest
Condition | y1< zc y2 < zc | ||
Equation |
|
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 |
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 |
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