--- title: "Flat V Weir | Technical Reference" slug: "flat-v-weir" description: "Find the data, theory and guidance for modelling a Flat V weir with a triangular longitudinal profile. " tags: ["1D river modelling", "weir"] updated: 2022-09-21T16:50:10Z published: 2022-09-21T16:50:10Z canonical: "help.floodmodeller.com/flat-v-weir" stale: true --- > ## Documentation Index > Fetch the complete documentation index at: https://help.floodmodeller.com/llms.txt > Use this file to discover all available pages before exploring further. # Flat V Weir The Flat V weir is long-based weir with a triangular longitudinal profile and a transverse symmetrical V-shaped crest having small side-slopes. ## 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 *Cv* 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 long-based weir with a triangular longitudinal profile and a transverse symmetrical V-shaped crest having small side-slopes. 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)](/v1/docs/references-1#white66), [White W.R. (1968)](/v1/docs/references-1#white68), [White W.R. (1971)](/v1/docs/references-1#white71)) and documented in [BS/ISO 4377 (2002)](/v1/docs/references-1#bsiso), [Herschey R.W. (1985)](/v1/docs/references-1#herschey85) and [Bos (1989)](/v1/docs/references-1#bos89). The Flat-V 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 V-shape (typically 1:10, 1:20 or 1:40) in the plane normal to the flow direction. Research by [White W.R. (1968)](/v1/docs/references-1#white68) has provided some alternatives for a downstream sloping face of 1:2, and [Herschey R. W. (1985)](/v1/docs/references-1#herschey85) provides adjustment factors for a non-vertical 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 head-discharge 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 ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/flatvimage002.gif) where: *m* is the slope of the V (1 [vertical]:*m* [horizontal]); *Z* is a shape function dependent on the channel side-slope; its value is unity when flow is wholly within the V; when the water surface lies above the top of the V, ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/flatvimage004.gif) *Cdr* is a drowned flow reduction factor (set to one if flow is free (modular)); *He* is the total effective upstream head *(=h1+**a**v2/2g-kh*), m; *n* is the channel side slope (1 [vertical]:*n* [horizontal]); *h'* is the depth of the V (*=b/(2m)*), m; *h1* 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 *kh* 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 *Cd* and *kh* for different slopes are given in the table below. | | m=40+ | m=20 | m=10 | | --- | --- | --- | --- | | 1:5 slope, flow within V | *Cd*=0.625 *kh*=0.0004 | *Cd*=0.62 *kh*=0.0005 | *Cd*=0.615 *kh*=0.0008 | | 1:5 slope, flow out of V | *Cd*=0.63 *kh*=0.0004 | *Cd*=0.625 *kh*=0.0005 | *Cd*=0.62 *kh*=0.0008 | | 1:2 slope, flow within V | Not known | *Cd*=0.665 *kh*=0.0004 | *Cd*=0.655 *kh*=0.0006 | | 1:2 slope, flow out of V | Not known | *Cd*=0.66 *kh*=0.0004 | *Cd*=0.665 *kh*=0.0006 | Further studies by [White W.R. (1968)](/v1/docs/references-1#white68) have considered a flat-V 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 V-slope, 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 non-modular 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 ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/flatvimage006.gif)for ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/flatvimage008.gif) ![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/flatvimage010.gif)for![](https://cdn.document360.io/5074bc26-a9ef-4bf4-b1de-a5c6ce628aca/Images/Documentation/flatvimage012.gif), where *H1e* and *H2e* 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 *H1e/h'*. Bos lists the values of the modular limit ranging from 0.67 (*H1e/h'**»**0.5)* to 0.78 (*H1e/h'**»**1.5)*; Flood Modeller will interpolate for the modular limit between these two values of *H1e/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)](/v1/docs/references-1#white68). #### 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 V-slope. - For V-slopes 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 #### 1:2 downstream face slope ### 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 0r | | Equation Z=1; Cdr<1 (see above) | | Mode 3 | Free flow - out of 'V' | | Condition h1>h'; H2e/H1eh'; H2e/H1e