Sewer Overflow formula (Water Overlay): Difference between revisions

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:

B_s = B_o

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

w_s = h_s + B_s

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

H_o = ( H_s * T_o ) + max ( 0 , B_o - B_a )

Water only flows out of the sewer if:

h_s > H_o and

h_s + B_s > w_o

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_s - H_o , w_s - w_o)

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 * q_o / A_s)

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

Q_t = Δw * A_s

where:

B_o = The surface height at the centerpoint of the sewer overflow, relative to datum.
B_a = The height of the sewer relative to datum, as defined by the SEWER_OVERFLOW of the sewer overflow.
B_s = The assumed surface height of the sewer, relative to datum.
w_o = The water level at the sewer overflow's exit, relative to datum.
w_s = The water level in the sewer, relative to datum.
H_o = The height of the sewer overflow threshold in the sewer.

h_s = The sewer water height.
H_s = 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.

A_s = The surface area of the sewer.

q_o = The SEWER_OVERFLOW_SPEED attribute of the sewer overflow.
T_o = The SEWER_OVERFLOW_THRESHOLD, the threshold factor indicating the fraction of the sewer's storage height that is blocked by the sewer overflow's threshold.
Q_t = The amount of water which flows out of the sewer through the sewer overflow.

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.

@@ Line 1: / Line 1: @@
-<!--Needs the sewer overflow threshold-->
+<!--[[File:Sewer_overflow_model.png|right|500px]]
-Overflow from the sewer is calculated for the entirety of the sewer, and the single attached sewer overflow.
+[[File:Sewer_overflow_model2.png|right|500px]]-->
+Overflow from the [[sewer model (Water Overlay)|sewer]] is calculated for the entirety of the sewer, and the single attached [[sewer overflow (Water Overlay)|sewer overflow]].
-The amount that can overflow relies on both the sewer overflow itself as well as the sewer overflow threshold:
+The sewer base height is located at the height indicated by the sewer overflow:
-: ''C<sub>threshold</sub> = max( 0 , WH<sub>sewer</sub> - SS * SOT )''
+: ''B<sub>s</sub> = B<sub>o</sub><!-- + B<sub>a</sub>-->
-: ''C<sub>height</sub> = max( 0, T<sub>sewer</sub> + SO + WH<sub>sewer</sub> - T<sub>overflow</sub> )''
-: ''C = min ( C<sub>threshold</sub>, C<sub>height</sub> )''
-Actual overflow is then calculated:
+The water level at the sewer is calculated based on that height:
-: ''Δw = min( 0 , C * Σ<sub>sewer</sub> , Δt * SOS )''
+: ''w<sub>s</sub> = h<sub>s</sub> + B<sub>s</sub>
+The sewer overflow threshold height H<sub>o</sub> within the sewer is calculated as:
+: ''H<sub>o</sub> = ( H<sub>s</sub> * T<sub>o</sub> ) + max ( 0 , B<sub>o</sub> - B<sub>a</sub> )
+Water only flows out of the sewer if:
+: ''h<sub>s</sub> &gt; H<sub>o</sub>'' and
+: ''h<sub>s</sub> + B<sub>s</sub>  &gt; w<sub>o</sub>
+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>o</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 and the maximum speed with which water can flow through the sewer overflow:
+:  ''Δw = min( Δh,  Δt * q<sub>o</sub> / A<sub>s</sub>)
+The amount of water added to the exit cell(s) of the sewer overflow:
+: ''Q<sub>t</sub> = Δw * A<sub>s</sub>
 where:
-* Δw = The amount of sewer overflow which takes place.
+* 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 {{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}}.
+* 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>s</sub> = The water level in the sewer, relative to {{datum}}.
+* H<sub>o</sub> = The height of the sewer overflow threshold in the sewer.
+* h<sub>s</sub> = The sewer water height.
+* H<sub>s</sub> = The [[Sewer storage (Water Overlay)|SEWER_STORAGE]] attribute of the [[Sewer area (Water Overlay)|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.
-* 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.
+* q<sub>o</sub> = The [[Sewer overflow speed (Water Overlay)|SEWER_OVERFLOW_SPEED]] attribute of the [[sewer overflow (Water Overlay)|sewer overflow]].
+* T<sub>o</sub> = The [[Sewer overflow threshold model attribute (Water Overlay)|SEWER_OVERFLOW_THRESHOLD]], the threshold factor indicating the fraction of the sewer's storage height that is blocked by the sewer overflow's threshold.
+* Q<sub>t</sub> = The amount of water which flows out of the sewer through the [[sewer overflow (Water Overlay)|sewer overflow]].
-* Σ<sub>sewer</sub> = The surface area of the sewer.
+==Notes==
-* WH<sub>sewer</sub> = The height of the water column in the sewer.
+* The sewer's surface area is computed as the amount of sewered grid cells times the size of a grid cell.
-* T<sub>sewer</sub> = The average height of the terrain where the sewer is present, relative to {{datum}}.
+* The sewer's height relative to {{datum}} is not defined in the sewer itself. It is relative to the [[sewer overflow (Water Overlay)|sewer overflow]] and determined by the [[Sewer overflow attribute (Water Overlay)|SEWER_OVERFLOW]] attribute of the overflow.
-* T<sub>overflow</sub> = The height of the terrain at the centerpoint of the sewer overflow, relative to {{datum}}.
-* SO = The [[Sewer overflow (Water Overlay)|SEWER_OVERFLOW]] attribute of the sewer overflow.
-* SOS = The [[Sewer overflow speed (Water Overlay)|SEWER_OVERFLOW_SPEED]] attribute of the sewer overflow.
-* SS = The [[Sewer storage (Water Overlay)|SEWER_STORAGE]] attribute of the sewer area.
-* SOT = The [[Sewer overflow threshold model attribute (Water Overlay)|SEWER_OVERFLOW_THRESHOLD]].
-==See also==
+==Related==
-* [[Sewer model (Water Overlay)|Sewer]]
+The following topics are related to this formula.
+; Structures and features
+: [[Sewer area (Water Overlay)|Sewer area]]
+: [[Sewer overflow (Water Overlay)|Sewer overflow]]
+; Models
+: [[Surface model (Water Overlay)|Surface model]]
+: [[Sewer model (Water Overlay)|Sewer model]]
-{{Template:WaterOverlay_nav}}
+{{WaterOverlay formula nav}}

Sewer Overflow formula (Water Overlay): Difference between revisions

Latest revision as of 12:04, 14 August 2020

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