Sewer Overflow formula (Water Overlay): Difference between revisions

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m (Modified threshold calculation to more accurately refrelct implementation of sewer threshold (percentage of section of sewer which extends above-ground))
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The sewer overflow threshold height H<sub>o</sub> within the sewer is calculated as:
The sewer overflow threshold height H<sub>o</sub> within the sewer is calculated as:
: ''H<sub>o</sub> = ( H<sub>s</sub> - max ( 0 , B<sub>o</sub> - B<sub>a</sub> ) ) * T<sub>o</sub>
: ''H<sub>o</sub> = ( H<sub>s</sub> * T<sub>o</sub> ) + max ( 0 , B<sub>o</sub> - B<sub>a</sub> )
<!--: ''H<sub>o</sub> = H<sub>s</sub> * T<sub>o</sub>
 
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Water only flows out of the sewer if:
Water only flows out of the sewer if:
: ''h<sub>s</sub> &gt; H<sub>o</sub>'' and
: ''h<sub>s</sub> &gt; H<sub>o</sub>'' and
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* B<sub>o</sub> = The [[terrain height (Water Overlay)|surface height]] at the centerpoint of the [[sewer overflow (Water Overlay)|sewer overflow]], relative to {{datum}}.
* B<sub>o</sub> = The [[terrain height (Water Overlay)|surface height]] at the centerpoint of the [[sewer overflow (Water Overlay)|sewer overflow]], relative to {{datum}}.
* B<sub>a</sub> = The height of the sewer relative to the sewer overflow, as defined by the [[Sewer overflow attribute (Water Overlay)|SEWER_OVERFLOW]] of the [[sewer overflow (Water Overlay)|sewer overflow]].
* B<sub>a</sub> = The height of the sewer relative to {{datum}}, as defined by the [[Sewer overflow attribute (Water Overlay)|SEWER_OVERFLOW]] of the [[sewer overflow (Water Overlay)|sewer overflow]].
* B<sub>s</sub> = The assumed surface height of the sewer, relative to {{datum}}.
* B<sub>s</sub> = The assumed surface height of the sewer, relative to {{datum}}.
* w<sub>o</sub> = The [[Surface water level formula (Water Overlay)|water level]] at the [[sewer overflow (Water Overlay)|sewer overflow]]'s exit, relative to {{datum}}.
* w<sub>o</sub> = The [[Surface water level formula (Water Overlay)|water level]] at the [[sewer overflow (Water Overlay)|sewer overflow]]'s exit, relative to {{datum}}.
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: [[Sewer model (Water Overlay)|Sewer model]]
: [[Sewer model (Water Overlay)|Sewer model]]


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Latest revision as of 12:04, 14 August 2020

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 = Bo

The water level at the sewer is calculated based on that height:

ws = hs + Bs

The sewer overflow threshold height Ho within the sewer is calculated as:

Ho = ( Hs * To ) + max ( 0 , Bo - Ba )

Water only flows out of the sewer if:

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 - Ho , ws - wo)

The flow is then calculated with the SEWER_OVERFLOW_SPEED attribute of the sewer overflow and the maximum speed with which water can flow through the sewer overflow:

Δw = min( Δh, Δt * qo / As)

The amount of water added to the exit cell(s) of the sewer overflow:

Qt = Δw * As

where:

  • hs = The sewer water height.
  • Hs = The SEWER_STORAGE attribute of the sewer area, the maximum water height allowed in the sewer.
  • Δh = The amount of water that can flow out of sewer based on the threshold and the water levels inside and outside the sewer.
  • Δw = Water level change in the sewer, due to sewer overflow taking place.
  • Δt = Computational timestep.
  • As = The surface area of the sewer.

Notes

  • The sewer's surface area is computed 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.

Related

The following topics are related to this formula.

Structures and features
Sewer area
Sewer overflow
Models
Surface model
Sewer model
Water Module
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Water Module
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Tutorials
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Overview
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Theory
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Benchmarks
Models
Surface • Ground • Rain • Evaporation • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
Model formulas
Timestep • Season • Surface water level • Groundwater level
Flow formulas
Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
Hydraulic structure formulas
Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
Related
Building attributes • Hydrological features • Hydraulic structures •  Terrain attributes • Model attributes • Results • Simulation data
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