 21 Sep 2022
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Weir
 Updated on 21 Sep 2022
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Data
Field in Data Entry Form  Description  Name in Datafile 

Discharge coefficient  Coefficient of discharge  C_{d} 
Velocity Coefficient  Coefficient of approach velocity  C_{v} 
Breadth of Crest  Breadth of weir at control section (normal to the flow direction) (m)  b 
Elevation of Crest  Elevation of weir crest (m Above Datum)  z_{c} 
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 C_{v }or discharge coefficient C_{d} 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
y_{1} ³y_{2} (forward flow) h_{1} = h_{u}
y_{1} < y_{2} (reverse flow) h_{1} = h_{d}
h_{1} = y_{1}  z_{c}
h_{2} = y_{2}  z_{c}
h_{u} = upstream head
h_{d} = downstream head
Figure 1: Weir Parameters
Mode 0  Dry Crest
Condition  y_{1} < z_{c} y_{2}_{ }< z_{c} 
Equation  Q = 0 
Mode 1  Free Flow (positive sense)
Condition  y_{1}_{ }> z_{c} h_{1}_{ }> h_{2} h_{2} / h1 ³ m where: m is the modular limit  
Equation 

Figure 2: Weir (Free Flow)
Mode 2  Free Flow (negative sense)
Condition  y_{2} > z_{c} h_{2} > h_{1} h_{1} / h_{2}£ m  
Equation 

Mode 3  Drowned Flow (Positive Sense)
Condition  y_{1} > z_{c} h_{1} ³ h_{2} h_{2} / h_{1} > m  
Equation 

Mode 4  Drowned Flow (Negative Sense)
Condition  y_{2}_{ }> z_{c} h_{2} ³ h_{1} h_{1} / h_{2} > m  
Equation 

General
The Weir adopts a more simplified approach to modelling weirs than that adopted in the round nosed or sharpcrested weirs.
A weir with a triangular control section can be modelled by choosing a discharge coefficient according to:

where: q is the angle at the base of the control section. 
For a parabolic control section, the discharge coefficient should be amended to:

where: f is the focal distance in metres of the parabolic control section. 
For nonrectangular 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  C_{d}, C_{v}, b, z_{c}, m
Example
WEIR
UNIT021 UNIT022
2.000
1.100 0.900 10.000 1.000 0.900