Weir formula (Water Overlay): Difference between revisions
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Where: | Where: | ||
* h<sub>s</sub> = The height of the water column relative to the top of the weir, on the side with the highest water level. | * h<sub>s</sub> = The height of the water column relative to the top of the weir, on the side with the highest [[Surface water level formula (Water Overlay)|water level]]. | ||
* h<sub>d</sub> = The height of the water column relative to the top of the weir, on the side with the lowest water level. | * h<sub>d</sub> = The height of the water column relative to the top of the weir, on the side with the lowest [[Surface water level formula (Water Overlay)|water level]]. | ||
* w<sub>l</sub> = The water level on the left side of the weir, relative to | * w<sub>l</sub> = The water level on the left side of the weir, relative to {{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}}. | ||
* z<sub>w</sub> = The [[Weir height (Water Overlay)|WEIR_HEIGHT]] | * z<sub>w</sub> = The [[Weir height (Water Overlay)|WEIR_HEIGHT]] of the weir. | ||
* f<sub>w,d</sub> = Dutch weir factor, set to 1.7. | * f<sub>w,d</sub> = Dutch weir factor, set to 1.7. | ||
* c<sub>w</sub> = The [[Weir coefficient (Water Overlay)|WEIR_COEFFICIENT]] | * c<sub>w</sub> = The [[Weir coefficient (Water Overlay)|WEIR_COEFFICIENT]] of the weir. | ||
* w<sub>w</sub> = The [[Weir width (Water Overlay)|WEIR_WIDTH]] | * w<sub>w</sub> = The [[Weir width (Water Overlay)|WEIR_WIDTH]] of the weir. | ||
* C = The potential rate of water flow across the weir. | * C = The potential rate of water flow across the weir. | ||
* h<sub>ratio</sub> = The ratio of water heights on either side of the culvert. | * h<sub>ratio</sub> = The ratio of water heights on either side of the culvert. | ||
* C<sub>free</sub> = The potential rate of water flow across the weir, based on a free flow calculation. | * C<sub>free</sub> = The potential rate of water flow across the weir, based on a free flow calculation. | ||
* C<sub>submerged</sub> = The potential rate of water flow across the weir, based on a submerged calculation. | * C<sub>submerged</sub> = The potential rate of water flow across the weir, based on a submerged calculation. | ||
* U<sub>loss</sub> = Loss coefficient for submerged weirs | * U<sub>loss</sub> = Loss coefficient for submerged weirs, set to 0.9. | ||
* A = Flow area, based on the highest water column height relative to the top of the weir, and | * A = Flow area, based on the highest water column height relative to the top of the weir, and [[Weir width (Water Overlay)|WEIR_WIDTH]] of the weir. | ||
* g = Acceleration factor of | * g = Acceleration factor of [[Gravity (Water Overlay)|GRAVITY]], defined for the Water Overlay. | ||
* Δw = The water flow which takes place. | * Δw = The water flow which takes place. | ||
* Δt = Computational timestep. | * Δt = Computational timestep. | ||
Revision as of 08:29, 14 June 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)
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:
- hratio = hd / hs
- C = min( Csubmerged , Cfree) if hratio > 0,5
- C = Cfree otherwise
For free flow, capacity is calculated directly:
- Cfree = fw,d * cw * ww * ( hs - hd )3/2
For submerged flow, the following calculation is used:
- Csubmerged = Uloss * A * sqrt( 2 * g * ( hs - hd ) )
Finally the actual amount of water flow is calculated:
- Δw = Δt * C / Δx
Where:
- 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.
- 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.
- zw = The WEIR_HEIGHT of the weir.
- fw,d = Dutch weir factor, set to 1.7.
- cw = The WEIR_COEFFICIENT of the weir.
- ww = The WEIR_WIDTH of the weir.
- C = The potential rate of water flow across the weir.
- hratio = 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.
- Uloss = Loss coefficient for submerged weirs, set to 0.9.
- A = Flow area, based on the highest water column height relative to the top of the weir, and WEIR_WIDTH of the weir.
- g = Acceleration factor of GRAVITY, defined for the Water Overlay.
- Δw = The water flow which takes place.
- Δt = Computational timestep.
- Δx = Cell size.