Weir formula (Water Overlay): Difference between revisions
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The height of the water at each end of the weir, relative to the weir, is calculated: | The height of the water at each end of the weir, relative to the weir, is calculated: | ||
: ''h<sub>s</sub> = max(0, max( w<sub>l</sub>, w<sub>r</sub> ) - | : ''h<sub>s</sub> = max(0, max( w<sub>l</sub>, w<sub>r</sub> ) - z<sub>w</sub>)'' | ||
: ''h<sub>d</sub> = max(0, min( w<sub>l</sub>, w<sub>r</sub> ) - | : ''h<sub>d</sub> = max(0, min( w<sub>l</sub>, w<sub>r</sub> ) - z<sub>w</sub>)'' | ||
For free flow, capacity is calculated directly: | For free flow, capacity is calculated directly: | ||
: ''C<sub>free</sub> = | : ''C<sub>free</sub> = f<sub>w,d</sub> * c<sub>w</sub> * WW * ( h<sub>s</sub> - h<sub>d</sub> )<sup>3/2</sup>'' | ||
For submerged flow, a culvert-like calculation is used: | For submerged flow, a culvert-like calculation is used: | ||
: ''C<sub>submerged</sub> = U * A * sqrt( 2 * | : ''C<sub>submerged</sub> = U * A * sqrt( 2 * g * ( h<sub>s</sub> - h<sub>d</sub> ) )'' | ||
Based on the relative water heights, the weir is judged to have either a submerged flow or a free flow, based on the following ratio: | Based on the relative water heights, the weir is judged to have either a submerged flow or a free flow, based on the following ratio: | ||
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* U = Loss coefficient for submerged weirs (0,9). | * U = Loss coefficient for submerged weirs (0,9). | ||
* A = Flow area, based on the highest water column height relative to the top of the weir, and the weir width, defined by the [[Weir width (Water Overlay)|WEIR_WIDTH]] attribute of the weir | * A = Flow area, based on the highest water column height relative to the top of the weir, and the weir width, defined by the [[Weir width (Water Overlay)|WEIR_WIDTH]] attribute of the weir | ||
* | * g = Acceleration factor of gravity | ||
* | * f<sub>w,d</sub> = Dutch weir factor, set to 1.7<!--<ref name="duflowfactor" />.--> | ||
* | * c<sub>w</sub> = The [[Weir coefficient (Water Overlay)|WEIR_COEFFICIENT]] attribute of the weir. | ||
* | * z<sub>w</sub> = The [[Weir height (Water Overlay)|WEIR_HEIGHT]] attribute of the weir. | ||
* w<sub>w</sub> = The [[Weir width (Water Overlay)|WEIR_WIDTH]] attribute of the weir. | |||
* w<sub>l</sub> = The water level on the left side of the weir, relative to [[Datum|datum]]. | * w<sub>l</sub> = The water level on the left side of the weir, relative to [[Datum|datum]]. | ||
* w<sub>r</sub> = The water level on the right side of the weir, relative to datum. | * w<sub>r</sub> = The water level on the right side of the weir, relative to datum. | ||
Revision as of 09:59, 15 April 2019
Flow across weirs is calculated differently for free flow and submerged flow.
The height of the water at each end of the weir, relative to the weir, is calculated:
- hs = max(0, max( wl, wr ) - zw)
- hd = max(0, min( wl, wr ) - zw)
For free flow, capacity is calculated directly:
- Cfree = fw,d * cw * WW * ( hs - hd )3/2
For submerged flow, a culvert-like calculation is used:
- Csubmerged = U * A * sqrt( 2 * g * ( hs - hd ) )
Based on the relative water heights, the weir is judged to have either a submerged flow or a free flow, based on the following ratio:
- WHrelative = hd : hs
- C = min( Csubmerged , Cfree) if WHrelative > 0,5
- C = Cfree otherwise
Finally the actual amount of water flow is calculated:
- Δw = Δt * C / cell
Where:
- Δw = The water flow which takes place.
- Δt = Computational timestep.
- cell = Cell size.
- C = The potential rate of water flow across the weir.
- WHrelative = The ratio of water heights on either side of the culvert.
- Cfree = The potential rate of water flow across the weir, based on a free flow calculation.
- Csubmerged = The potential rate of water flow across the weir, based on a submerged calculation.
- hs = The height of the water column relative to the top of the weir, on the side with the highest water level.
- hd = The height of the water column relative to the top of the weir, on the side with the lowest water level.
- U = Loss coefficient for submerged weirs (0,9).
- A = Flow area, based on the highest water column height relative to the top of the weir, and the weir width, defined by the WEIR_WIDTH attribute of the weir
- g = Acceleration factor of gravity
- fw,d = Dutch weir factor, set to 1.7
- cw = The WEIR_COEFFICIENT attribute of the weir.
- zw = The WEIR_HEIGHT attribute of the weir.
- ww = The WEIR_WIDTH attribute of the weir.
- wl = The water level on the left side of the weir, relative to datum.
- wr = The water level on the right side of the weir, relative to datum.