 21 Sep 2022
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Flat V Weir
 Updated on 21 Sep 2022
 6 Minutes to read

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The Flat V weir is longbased weir with a triangular longitudinal profile and a transverse symmetrical Vshaped crest having small sideslopes.
Data
Field in Data Entry Form  Description  Name  Default  Constraints 

Upstream  Upstream node label  Label1 


Downstream  Downstream node label  Label2    Max. 12 characters, no internal or leading spaces 
Upstream Remote Node  Upstream remote node label (used if upstream node is not a channel section)  Label3 


Downstream Remote Node  Downstream remote node label (used if downstream node is not a channel section)  Label4    Max. 12 characters, no internal or leading spaces 
Elevation of Crest  elevation of crest at the vertex of 'V' (m above datum).  Zc    >9999.99 
Breadth of Crest  breadth of weir crest (at the top of 'V'(m)  b  0  >0 
‘V’ Slope  'V' slope (horizontal distance/vertical distance)  m    >0; warning if <10. 
Side Slope  channel side slope (horizontal distance/vertical distance)  n  0  ³0 
Upstream Height  weir crest height above upstream bed (m)  p1  0  >0 
Downstream Height  weir crest height above downstream bed (m)  p2  0  >0 
Modular Limit  Calculation Method = Variable: value will be calculated internally; else (if FIXED) enter the value to be used for modular limit (will be calculated if r=0 in the data file)  r  0  0 £ r < 1 
Calibration Coefficient  calibration coefficient, to adjust C_{v} value, for instance.  Cc  1  ³0 
Downstream Slope Flag  Flag to switch between 1:5 and 1:2 for d/s face  ds_fslope  5  2 or 5 only; integer 
Coriolis Coefficient  Coriolis energy coefficient  alpha  1.2  > 0 
Elevation of Bank Top  Elevation of channel bank top / limit of extent of sloping channel walls (m AD)  zbank    Higher than the top of the 'V' 
Theory and Guidance
Introduction
The Flat V weir is longbased weir with a triangular longitudinal profile and a transverse symmetrical Vshaped crest having small sideslopes. It is a common structure in waterways in the UK and elsewhere. It conforms to BSI and ISO standards.
The hydraulics of the Flat V weir are well understood, following research by White at the Hydraulics Research Station (White W.R. (1966), White W.R. (1968), White W.R. (1971)) and documented in BS/ISO 4377 (2002), Herschey R.W. (1985) and Bos (1989).
The FlatV weir resembles a Crump weir in section (in direction of flow, i.e. 1:2 upstream face; 1:5 downstream face), and has a mildly sloping Vshape (typically 1:10, 1:20 or 1:40) in the plane normal to the flow direction. Research by White W.R. (1968) has provided some alternatives for a downstream sloping face of 1:2, and Herschey R. W. (1985) provides adjustment factors for a nonvertical walled approach channel, although neither of these form part of either of the aforementioned Standard.
Connectivity
The unit is connected as per other weir units, although remote nodes are available from which to calculate areas, and hence the velocity in the approach and downstream channels. If the weir unit is not connected, directly or remotely, to a channel section (from which areas can be obtained), the area is calculated using the dimensions of the weir unit (breadth × depth above bed [given by p values]).
It is noted that the headdischarge relationship may be very sensitive to changes in velocity, particular at high velocity flows, so the choice of an appropriate section is important.
General equations of flow
The general form of the discharge relationship can be given as
where:
m is the slope of the V (1 [vertical]:m [horizontal]);
Z is a shape function dependent on the channel sideslope; its value is unity when flow is wholly within the V; when the water surface lies above the top of the V,
C_{dr} is a drowned flow reduction factor (set to one if flow is free (modular));
H_{e} is the total effective upstream head (=h_{1}+av^{2}/2gk_{h}), m;
n is the channel side slope (1 [vertical]:n [horizontal]);
h^{'} is the depth of the V (=b/(2m)), m;
h_{1} is the upstream gauged head, m above crest;
b is the breadth of the weir crest (at the top of the V), m;
v is the upstream velocity, ms^{1};
a is the coriolis energy coefficient, and
k_{h} is the head adjustment factor due to water properties, m.
Two alternative methods are described in the BS/ISO standard to calculate discharge; one based on total head, the other based on gauged head using a coefficient of approach velocity factor. The former method is used in Flood Modeller.
Tables for values of C_{d} and k_{h} for different slopes are given in the table below.
m=40+  m=20  m=10  

1:5 slope, flow within V  C_{d}=0.625 k_{h}=0.0004  C_{d}=0.62 k_{h}=0.0005  C_{d}=0.615 k_{h}=0.0008 
1:5 slope, flow out of V  C_{d}=0.63 k_{h}=0.0004  C_{d}=0.625 k_{h}=0.0005  C_{d}=0.62 k_{h}=0.0008 
1:2 slope, flow within V  Not known  C_{d}=0.665 k_{h}=0.0004  C_{d}=0.655 k_{h}=0.0006 
1:2 slope, flow out of V  Not known  C_{d}=0.66 k_{h}=0.0004  C_{d}=0.665 k_{h}=0.0006 
Further studies by White W.R. (1968) have considered a flatV weir with a downstream face slope of 1:2, although this does not form part of the BS/ISO standard. Furthermore, no data exists for the 1:40 Vslope, the regions of applicability are more restricted and the drowned flow conditions are much more complex and harder to quantify
Drowned Flow
The BS/ISO standard provides drowning reduction factors for nonmodular flow, based on downstream tappings, in the absence of crest tappings. Although less accurate than the crest tapping method, downstream tappings are those available within Flood Modeller. For the 1:5 downstream face slope, the drowning function is given as
for
for,
where H_{1e} and H_{2e} are the effective upstream and downstream heads, respectively.
This implies a modular limit of approximately 0.73, although this quantity is in reality a function of H_{1e}/h'. Bos lists the values of the modular limit ranging from 0.67 (H_{1e}/h'»0.5) to 0.78 (H_{1e}/h'»1.5); Flood Modeller will interpolate for the modular limit between these two values of H_{1e}/h', and use the given values as lower and upper bounds of modular limit outside of them.
For the 1:2 downstream face slope, the modular limit values are generally lower, and more complex. The values for modular limit and drowning function are derived from Figures 21 and 22, respectively, in White W.R. (1968).
Reverse Flow
For reverse flow, the same equations apply, with the nodes reversed. It is noted, however, that in the case of the 1:5 downstream face slope, this is not ideal, since the geometry of the weir with respect to the direction of flow will have changed.
Notes
 Cross slopes of less than 1:10 are undesirable, and validated results are not provided for these.
 The 1:2 downstream face slope is not part of the BS/ISO Standard, and the flow equations for this structure are less well understood; no data is provided in the literature for such with a 1:40 Vslope.
 For Vslopes other than 1:10, 1:20 or 1:40, parameters are either interpolated or taken from those relating to the nearest published value.
 Unit state: The drowned flow reduction factor is output in the unit state.
Limits of applicability
1:5 downstream face slope
 The ratio h'/p_{1} should not exceed 2.5
 The ratio H_{1e}/p_{2} should not exceed 2.5 for the when flow is within the V.
 The ratio H_{1e}/p_{2} should not exceed 8.2 (1:20 and 1:40 Vslopes) or 4.2 (1:10 Vslope) when flow is out of the V.
 For further limits of applicability, the user is referred to the BS/ISO Standard.
1:2 downstream face slope
 The ratio h'/p_{1} should not exceed 1.6 (1:20 Vslope) or 1.5 (1:10 Vslope).
 The ratio H_{1e}/p_{2} should not exceed 1.6 (1:20 Vslope) or 1.5 (1:10 Vslope), when flow is within the V.
 The ratio H_{1e}/p_{2} should not exceed 3.2 (1:20 Vslope) or 2.7 (1:10 Vslope), when flow is out of the V.
 The out of V ratio H_{1e}/h' should not exceed 2 (1:20 Vslope) or 1.8 (1:10 Vslope).
Modes of flow
Mode number  Description 
Mode 0  Dry Crest 
Condition h1<0; h2<0  
Equation Q=0  
Mode 1  Free flow  within 'V' 
Condition 0<h1<h'; H2e/H1e<r  
Equation Z=1; Cdr=1  
Mode 2
 Drowned flow  within 'V' 
Condition 0<h1<h'; H2e/H1e>r  
Equation Z=1; Cdr<1 (see above)  
Mode 3  Free flow  out of 'V' 
Condition h1>h'; H2e/H1e<r  
Equation Z<1; Cdr=1 (see above)  
Mode 4  Drowned flow  out of 'V' (Z<1, Cdr<1) 
Condition h1>h'; H2e/H1e<r  
Equation Z<1; Cdr<1 (see above) 
Reverse flow modes:
These are the same conditions and equations as the forward flow modes, with the nodes reversed; mode number = forward flow mode + 4, i.e.:
Mode 5  Free reverse flow  within 'V'
Mode 6  Drowned reverse flow  within 'V'
Mode 7  Free reverse flow  out of 'V'
Mode 8  Drowned reverse flow  out of 'V'
Note
To prevent flow from extending into an indefinitely increasing (with respect to depth) width of channel, it is recommended to apply the Elevation of Bank Top field if the channel side slopes are nonvertical. Above this level, flow will be contained with vertical walls, and not and indefinite continuation of the side slope.
Datafile Format
Line 1  Keyword 'FLATV WEIR' [comment]. NB Only first four characters read.
Line 2  Label1, Label2, Label3, Label4
Line 3  Cc, b, zc, r, m, n, ds_fslope, alpha, zbank
Line 4  p1, p2
Example
FLATV WEIR
UNIT076 UNIT076 UNIT077 UNIT078
1.0 0.0 0.0 0.0 0.0 5 1.2
0.000 0.000