Culvert formula (Water Overlay): Difference between revisions
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[[File:Hydraulic_radius.png|right]] | [[File:Hydraulic_radius.png|right]] | ||
Flow through culverts is based on an open channel flow calculation. | 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: | |||
: ''CH = max( TH, B<sub>l</sub> , B<sub>r</sub> )'' | |||
The | 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: | The height of the water column at either end of the culvert, relative to the culvert, is calculated: | ||
: '' | : ''w<sub>l</sub> = max(0, w<sub>l</sub>-CH<sub>real</sub>)'' | ||
: '' | : ''w<sub>r</sub> = max(0, w<sub>r</sub>-CH<sub>real</sub>)'' | ||
The loss coefficient for the culvert is calculated: | The loss coefficient for the culvert is calculated: | ||
: U = sqrt( 1.0 / ( 1.0 + 2.0 * | : U = sqrt( 1.0 / ( 1.0 + 2.0 * g * n * n * length / (Rh ^ (4 / 3 ) ) ) | ||
The potential flow through the culvert is then calculated: | The potential flow through the culvert is then calculated: | ||
: ''C = U * | : ''C = U * K * sqrt( 2 * g * abs(w<sub>l</sub> - w<sub>r</sub>) )'' | ||
Finally the actual amount of water flow is calculated: | Finally the actual amount of water flow is calculated: | ||
: '' | : ''Δf = ''Δt * C / cell'' | ||
Where: | Where: | ||
* | * Δf = The water flow which takes place. | ||
* Δt = Computational timestep. | * Δt = Computational timestep. | ||
* cell = Cell size. | * cell = Cell size. | ||
* K = Flow area, based on the height of the water in the (circular) culvert. | |||
* g = Acceleration factor of gravity | |||
* D = The [[Culvert diameter (Water Overlay)|CULVERT_DIAMETER]] attribute of the culvert. <!--Unused--> | |||
* TH = The [[Culvert threshold (Water Overlay)|CULVERT_THRESHOLD]] attribute of the culvert. | |||
* CH = The surface height of the base of the culvert. | |||
* w<sub>left</sub> = The water level on the left side of the culvert, relative to [[Datum|datum]]. | |||
* w<sub>right</sub> = The water level on the right side of the culvert, relative to datum. | |||
* Rh = The hydraulic radius in the culvert<ref name="hydradius"/>. | |||
* L = The length of the culvert, calculated as the distance between the culvert's endpoints. | |||
* U = Loss coefficient for culverts. | |||
* n = The [[Culvert n (Water Overlay)|CULVERT_N]] attribute of the culvert. | |||
* C = The potential rate of water flow through the culvert. | * C = The potential rate of water flow through the culvert. | ||
==See also== | ==See also== | ||
* [[Culvert_(Water_Overlay)|Culvert]] | * [[Culvert_(Water_Overlay)|Culvert]] | ||
Revision as of 09:24, 15 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 and the provided threshold height:
- CH = max( TH, 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-CHreal)
- wr = max(0, wr-CHreal)
The loss coefficient for the culvert is calculated:
- U = sqrt( 1.0 / ( 1.0 + 2.0 * g * n * n * length / (Rh ^ (4 / 3 ) ) )
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 / cell
Where:
- Δf = The water flow which takes place.
- Δt = Computational timestep.
- cell = Cell size.
- K = Flow area, based on the height of the water in the (circular) culvert.
- g = Acceleration factor of gravity
- D = The CULVERT_DIAMETER attribute of the culvert.
- TH = The CULVERT_THRESHOLD attribute of the culvert.
- CH = 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 water level on the right side of the culvert, relative to datum.
- Rh = The hydraulic radius in the culvert[1].
- 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.
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)