Culvert formula (Water Overlay): Difference between revisions
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* WH<sub>left</sub> = The height of the water column relative to the bottom of the culvert on the left side of the culvert. | * WH<sub>left</sub> = The height of the water column relative to the bottom of the culvert on the left side of the culvert. | ||
* WH<sub>right</sub> = The height of the water column relative to the bottom of the culvert on the right side of the culvert. | * WH<sub>right</sub> = The height of the water column relative to the bottom of the culvert on the right side of the culvert. | ||
* CH<sub>real</sub> = The | * CH<sub>real</sub> = The [[Culvert threshold (Water Overlay)|CULVERT_THRESHOLD]] of the culvert, recalculated so the culvert is not below ground on either side. | ||
* A = Flow area, based on the height of the water in the (circular) culvert. | * A = Flow area, based on the height of the water in the (circular) culvert. | ||
* G = Acceleration factor of gravity | * G = Acceleration factor of gravity | ||
* CW = The | * CW = The [[Culvert diameter (Water Overlay)|CULVERT_DIAMETER]] attribute of the culvert. <!--Unused--> | ||
* CH<sub>attr</sub> = The | * CH<sub>attr</sub> = The CULVERT_THRESHOLD attribute of the culvert. | ||
* CN = The | * CN = The [[Culvert n (Water Overlay)|CULVERT_N]] attribute of the culvert. | ||
* WL<sub>left</sub> = The water level on the left side of the culvert, relative to | * WL<sub>left</sub> = The water level on the left side of the culvert, relative to [[Datum|datum]]. | ||
* WL<sub>right</sub> = The water level on the right side of the culvert, relative to | * WL<sub>right</sub> = The water level on the right side of the culvert, relative to datum. | ||
* L = The length of the culvert, calculated as the distance between the culvert's endpoints. | * L = The length of the culvert, calculated as the distance between the culvert's endpoints. | ||
* Rh = The hydrological radius in the culvert<ref name="hydradius" />. | * Rh = The hydrological radius in the culvert<ref name="hydradius" />. | ||
Revision as of 12:46, 4 April 2019
Flow through culverts is based on an open channel flow calculation.
The actual height of the culvert is at least the height of the terrain on either end of the culvert:
- CHreal = max( CHattr , Tleft , Tright )
The height of the water column at either end of the culvert, relative to the culvert, is calculated:
- WHleft = max(0, WLleft-CHreal)
- WHright = max(0, WLright-CHreal)
The loss coefficient for the culvert is calculated:
- U = sqrt( 1.0 / ( 1.0 + 2.0 * G * CN * CN * length / (Rh ^ (4 / 3 ) ) )
The potential flow through the culvert is then calculated:
- C = U * A * sqrt( 2 * G * abs(WHleft - WHright) )
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 through the culvert.
- U = Loss coefficient for culverts.
- WHleft = The height of the water column relative to the bottom of the culvert on the left side of the culvert.
- WHright = The height of the water column relative to the bottom of the culvert on the right side of the culvert.
- CHreal = The CULVERT_THRESHOLD of the culvert, recalculated so the culvert is not below ground on either side.
- A = Flow area, based on the height of the water in the (circular) culvert.
- G = Acceleration factor of gravity
- CW = The CULVERT_DIAMETER attribute of the culvert.
- CHattr = The CULVERT_THRESHOLD attribute of the culvert.
- CN = The CULVERT_N attribute of the culvert.
- WLleft = The water level on the left side of the culvert, relative to datum.
- WLright = The water level on the right side of the culvert, relative to datum.
- L = The length of the culvert, calculated as the distance between the culvert's endpoints.
- Rh = The hydrological radius in the culvert[1].
See also
References
- ↑ Hydraulic Radius Equations Formulas Calculator ∙ found at: https://www.ajdesigner.com/phphydraulicradius/hydraulic_radius_equation_pipe.php ∙ (last visited 2019-02-11)