Culvert formula (Water Overlay): Difference between revisions
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Where: | Where: | ||
* D = The [[Culvert diameter (Water Overlay)|CULVERT_DIAMETER]] attribute of the culvert. | * D = The [[Culvert diameter (Water Overlay)|CULVERT_DIAMETER]] attribute of the culvert. | ||
* T<sub>c</sub> = The [[Culvert threshold (Water Overlay)|CULVERT_THRESHOLD]] attribute of the culvert. | * T<sub>c</sub> = The [[Culvert threshold (Water Overlay)|CULVERT_THRESHOLD]] attribute of the culvert. | ||
* B<sub>c</sub> = The surface height of the base of the culvert. | * B<sub>c</sub> = The [[Terrain height (Water Overlay)|surface height]] of the base of the culvert. | ||
* w<sub>left</sub> = The water level on the left side of the culvert, relative to | * w<sub>left</sub> = The [[Surface water level formula (Water Overlay)|water level]] on the left side of the culvert, relative to {{datum}}. | ||
* w<sub>right</sub> = The water level on the right side of the culvert, relative to datum. | * w<sub>right</sub> = The Surface water level formula (Water Overlay)|water level]] on the right side of the culvert, relative to {{datum}}. | ||
* R<sub>h</sub> = The hydraulic radius in the culvert<ref name="hydradius"/>. | * R<sub>h</sub> = The hydraulic radius in the culvert<ref name="hydradius"/>. | ||
* K = Flow area, based on the height of the water in the (circular) culvert. | * K = Flow area, based on the height of the water in the (circular) culvert. | ||
* g = Acceleration factor of | * g = Acceleration factor of [[Gravity (Water Overlay)|GRAVITY]], defined for the Water Overlay. | ||
* 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. | ||
* U = Loss coefficient for culverts. | * U = Loss coefficient for culverts. | ||
Revision as of 08:24, 14 June 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 and the provided threshold height:
- Bc = max( Tc , Bl , Br )
The radius of the culvert:
- r = D / 2.
The height of the water column at either end of the culvert, relative to the culvert, is calculated:
- wl = max(0, wl - Bc)
- wr = max(0, wr - Bc)
Flow depth d is:
- d = max ( 0 , min ( D , max ( wl , wr ) - Bc ) ) )
The loss coefficient for the culvert is calculated:
- U = sqrt( 1 / ( 1 + 2 * g * n2 * length / Rh4/3 ) )
The hydraulic radius Rh is calculated using the formula's in the image on the right.
The potential flow through the culvert is then calculated:
- C = U * K * sqrt( 2 * g * abs( wl - wr ) )
Finally the actual amount of water flow is calculated:
- Δf = Δt * C / Δx
Where:
- D = The CULVERT_DIAMETER attribute of the culvert.
- Tc = The CULVERT_THRESHOLD attribute of the culvert.
- Bc = The surface height of the base of the culvert.
- wleft = The water level on the left side of the culvert, relative to datum.
- wright = The Surface water level formula (Water Overlay)|water level]] on the right side of the culvert, relative to datum.
- Rh = The hydraulic radius in the culvert[1].
- K = Flow area, based on the height of the water in the (circular) culvert.
- g = Acceleration factor of GRAVITY, defined for the Water Overlay.
- L = The length of the culvert, calculated as the distance between the culvert's endpoints.
- U = Loss coefficient for culverts.
- n = The CULVERT_N attribute of the culvert.
- C = The potential rate of water flow through the culvert.
- Δf = The water flow which takes place.
- Δt = Computational timestep.
- Δx = Cell size.
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)