Sewer Overflow formula (Water Overlay): Difference between revisions

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Water only flows out of the sewer iff:
Water only flows out of the sewer iff:
: ''h<sub>s</sub> &gt H<sub>o</sub> and
: ''h<sub>s</sub> &gt; H<sub>o</sub> and
: ''h<sub>s</sub> + B<sub>s</sub>  &gt w<sub>o</sub>
: ''h<sub>s</sub> + B<sub>s</sub>  &gt; w<sub>o</sub>


The amount that can overflow relies on both the sewer overflow itself as well as the sewer overflow threshold:
The amount that can overflow relies on both the water level at the sewer overflow itself as well as the sewer overflow threshold and the stored sewer water:
: Δh = min ( h<sub>s</sub> - H<sub>s</sub> , w<sub>s</sub> - w<sub>o</sub>)


The flow is then calculated with the [[SEWER_OVERFLOW_SPEED_(Water Overlay)| SEWER_OVERFLOW_SPEED]] attribute of the sewer overflow.
The flow is then calculated with the [[SEWER_OVERFLOW_SPEED_(Water Overlay)| SEWER_OVERFLOW_SPEED]] attribute of the sewer overflow.
:  Δh = min ( h<sub>s</sub> - H<sub>s</sub> , w<sub>s</sub> - w<sub>o</sub>)
:  Δw = min( Δh, Δt * q<sub>o</sub> / A<sub>s</sub>)
:  Δw = min( max( 0 , h<sub>s</sub> ),  Δt * v<sub>o</sub>


: ''C<sub>threshold</sub> = max( 0 , h<sub>s</sub> - H<sub>s</sub> * T<sub>s</sub> )''
where:
: ''C<sub>height</sub> = max( 0, T<sub>sewer</sub> + H>sub>o</sub> + h<sub>sewer</sub> - T<sub>overflow</sub> )''
: ''C = min ( C<sub>threshold</sub>, C<sub>height</sub> )''


Actual overflow is then calculated:
* B<sub>o</sub> = The height of the terrain at the centerpoint of the sewer overflow, relative to {{datum}}.
: ''Δw = min( 0 , C * Σ<sub>sewer</sub> , Δt * SOS )''
* B<sub>s</sub> = The assumed surface height of the sewer, relative to {{datum}}.


where:
* h<sub>s</sub> = The height of the water column in the sewer.
* h<sub>s</sub> = The height of the water column in the sewer.
* H<sub>S</sub> = The [[Sewer storage (Water Overlay)|SEWER_STORAGE]] attribute of the sewer area, the maximum water height allowed in the sewer.
* H<sub>S</sub> = The [[Sewer storage (Water Overlay)|SEWER_STORAGE]] attribute of the sewer area, the maximum water height allowed in the sewer.
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* Δt = Computational timestep.
* Δt = Computational timestep.


* C = The amount of water that can overflow out of the sewer
* A<sub>s</sub> = The surface area of the sewer.
* C<sub>threshold</sub> = The amount of water that could overflow, based on the sewer overflow threshold.
* C<sub>height</sub> = The amount of water that could overflow, based on the properties of the sewer overflow.


* Σ<sub>sewer</sub> = The surface area of the sewer.
* T<sub>sewer</sub> = The average height of the terrain where the sewer is present, relative to {{datum}}.
* T<sub>overflow</sub> = The height of the terrain at the centerpoint of the sewer overflow, relative to {{datum}}.


* H<sub>o<sub> = The surface height of the sewer, determined by [[Sewer overflow (Water Overlay)|SEWER_OVERFLOW]] attribute of the sewer overflow.
* H<sub>o<sub> = The surface height of the sewer, determined by [[Sewer overflow (Water Overlay)|SEWER_OVERFLOW]] attribute of the sewer overflow.
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==Notes==
==Notes==
* The sewers area is counted as the amount of sewered grid cells times the size of a grid cell.
* The sewer's height relative to {{datum}} is not defined in the Sewer itself. It is relative to the sewer overflow and determined by the SEWER_OVERFLOW attribute of the overflow.
* The sewer's height relative to {{datum}} is not defined in the Sewer itself. It is relative to the sewer overflow and determined by the SEWER_OVERFLOW attribute of the overflow.


==See also==
==See also==

Revision as of 12:28, 15 April 2019

Sewer overflow model.png
Sewer overflow model2.png

Overflow from the sewer is calculated for the entirety of the sewer, and the single attached sewer overflow.

The sewer base height is located at the height indicated by the sewer overflow:

Bs = Bso

The sewer overflow height is calculated as:

Ho = Hs * To

The water level at the sewer is then:

ws = hs + Bs

Water only flows out of the sewer iff:

hs > Ho and
hs + Bs > wo

The amount that can overflow relies on both the water level at the sewer overflow itself as well as the sewer overflow threshold and the stored sewer water:

Δh = min ( hs - Hs , ws - wo)

The flow is then calculated with the SEWER_OVERFLOW_SPEED attribute of the sewer overflow.

Δw = min( Δh, Δt * qo / As)

where:

  • Bo = The height of the terrain at the centerpoint of the sewer overflow, relative to datum.
  • Bs = The assumed surface height of the sewer, relative to datum.
  • hs = The height of the water column in the sewer.
  • HS = The SEWER_STORAGE attribute of the sewer area, the maximum water height allowed in the sewer.
  • Δw = The amount of sewer overflow which takes place.
  • Δt = Computational timestep.
  • As = The surface area of the sewer.


Notes

  • The sewers area is counted as the amount of sewered grid cells times the size of a grid cell.
  • The sewer's height relative to datum is not defined in the Sewer itself. It is relative to the sewer overflow and determined by the SEWER_OVERFLOW attribute of the overflow.


See also

Template:WaterOverlay nav

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