 21 Sep 2022
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Round Nosed Broad Crested Weir
 Updated on 21 Sep 2022
 3 Minutes to read
 Print
 DarkLight
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  C_{v} 
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)  z_{c} 
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)  p_{1} 
Downstream Crest Height  Height of crest above bed of downstream channel (m)  _{p}_{2} 
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.
Roundnosed broadcrested 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
y_{1} ³ y_{2} (forward flow) h_{1} = h_{u}, etc
y_{1} < y_{2} (reverse flow) h_{1} = h_{d}, etc
h_{1} = y_{1}  z_{c}
h_{2} = y_{2}  z_{c}
h_{u} = upstream head
h_{d} = downstream head
Mode 0  Dry Crest
Condition  y_{1}< z_{c} y_{2}_{ }< z_{c}  
Equation 

Mode 3  Free Flow
Condition  y_{1} > z_{c} h_{2}_{ }/ h_{1} £ m where: m is the modular limit  
Equation 
where: C_{d} = [ 1  d (L  r ) / b ] [ 1  (d / 2h_{1}) (L  r) ]^{1.5} d = function of the boundary layer thickness which is set constant at 0.01 g = gravitational acceleration (m/s^{2}) 
Mode 4  Drowned Flow
Condition  y_{1} > z_{c} h_{2} / h_{1} > m  
Equation 
where: C_{d} = [ 1  d (L  r ) / b ] [ 1  (d / 2h_{1}) (L  r) ]^{1.5} d = function of the boundary layer thickness which is set constant at 0.01 g = gravitational acceleration (m/s^{2}) 
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 z_{c} .
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 sharpcrested weir.
There are no formulae for drowned flow mode in the hydraulics literature. The equation here is based on the Bernoulli Equation with C_{d} 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  C_{v}, L, b, Z_{c}, m
Line 4  p_{1}, p_{2}
Example
RNWEIR Canoe Ramp
UNIT019 UNIT020
0.900 1.000 10.000 1.000 0.800
1.000 2.000