Inlet formula (Water Overlay): Difference between revisions

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Inlets are hydraulic structures can pump water in and out of the project area and are connected with a water body outside the project area.__NOTOC__
[[inlet (Water Overlay)|Inlet]]s are hydraulic structures can pump water in and out of the project area and are connected with a water body outside the project area.__NOTOC__


The amount flowing in or out of inlets is calculated for the cell the inlet resides on.
The amount flowing in or out of {{Inlets}} is calculated for the cell the {{Inlet}} resides on.


'''Inlets:'''<br>
''Case 1: '''Inlet''':''<br>
When calculating inlets, first the capacities are calculated.
When calculating {{Inlets}}, first the capacities are calculated.


If a lower threshold T<sub>l</sub> is defined:
If a lower threshold <math>T_{l,t}</math> is defined:
: ''Q<sub>lth</sub> = max( 0 , T<sub>l,t</sub> - w<sub>t</sub> )''
: <math>Q_{lth} = max( 0 , T_{l,t} - w_t )</math>


If a positive Inlet q is defined:
If a positive inlet q Q<sub>t</sub> is defined:
: ''Q<sub>t</sub> = Δt * q<sub>t</sub>''
: <math>Q_t = \Delta t \cdot Q_t</math>


If a capacity Q<sub>total</sub> is defined:
If a capacity Q<sub>total</sub> is defined:
: ''Q<sub>c</sub> = Q<sub>total</sub>''- ΣQ<sub>0..t-1</sub>
: <math>Q_c = Q_{total}- \sum_{0..t-1}Q_i</math>


After calculating the capacities, the actual water inflow is calculated. If any of the terms are undefined, they are not included.
After calculating the capacities, the actual water inflow is calculated. If any of the terms are undefined, they are not included.
: ''Δw = max( 0 , min( Q<sub>lth</sub> , Q<sub>t</sub> , Q<sub>c</sub> ) ) / A''
: <math>\Delta w = \frac { max( 0 , min( Q_{lth}, Q_t , Q_c ) )}{A}</math>


'''Outlets:'''<br>
''Case 2 '''Outlets''':''<br>
When calculating outlets, first the capacities are calculated.
When calculating outlets, first the capacities are calculated.


If an upper threshold T<sub>u</sub> is defined:
If an upper threshold T<sub>u,t</sub> is defined:
: ''Q<sub>uth</sub> = min( 0 , T<sub>u</sub> - w<sub>t</sub> )''
: <math>Q_{uth} = min( 0 , T_{u,t} - w_t )</math>


If a negative Inlet q is defined:
If a negative inlet q Q<sub>t</sub> is defined:
: ''Q<sub>t</sub> = Δt * q<sub>t</sub>''
: <math>Q_t = \Delta t \cdot Q_t</math>


If a capacity Q<sub>total</sub> is defined:
If a capacity Q<sub>total</sub> is defined:
: ''Q<sub>c</sub> = -Q<sub>total</sub> - ΣQ<sub>0..t-1</sub>''
: <math>Q_c = -Q_{total} - \sum_{0..t-1}Q_i</math>


After calculating the capacities, the actual water ouflow is calculated. If any of the terms are undefined, they are not included.
After calculating the capacities, the actual water ouflow is calculated. If any of the terms are undefined, they are not included.
: ''Δw = min( 0 , max( Q<sub>uth</sub> , Q<sub>t</sub> , Q<sub>c</sub>) ) / A''
: <math>\Delta w = \frac { min( 0 , max( Q_{uth} , Q_t, Q_c) ) } {A}</math>
 
 
 
 
After the water flow (either inflow or outflow) is computed, the capacity is updated.
: ''C<sub>used</sub> (new) = C<sub>used</sub> (old) + (Δw * cell)''
 


Where:
Where:
* <math>w_t</math> = The [[Surface water level formula (Water Overlay)|water level]] on the surface relative to {{datum}}, at time t.
* <math>T_{l,t}</math> = The [[Inlet lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the {{Inlet}} at time t.
* <math>T_{u,t}</math> = The [[Inlet upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the {{Inlet}} at time t.
* <math>q_t</math> = The [[Inlet q (Water Overlay)|INLET_Q]] of the {{Inlet}} at time t.
* <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)|timestep]].
* <math>Q_{total}</math> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] of the {{Inlet}}.


* Δw = The amount of water flow which takes place.
* <math>Q_{0..n}</math> = The calculated previous amounts of flow.
* Δt = Computational timestep.
* <math>Q_{lth}</math> = The desired lower water level at the {{Inlet}}'s location, based on the [[Inlet lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the {{Inlet}}.
* cell = Cell size.
* <math>Q_{uth}</math> = The desired upper water level at the outlet's location, based on the outlet's [[Inlet upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the {{Inlet}}.
* A = area of the inlet/outlet
* <math>Q_t</math> = The amount of water inflow (or outflow when negative) possible based on the [[Inlet q (Water Overlay)|INLET_Q]] of the {{Inlet}} and timestep <math>\Delta t</math>.
* C<sub>speed</sub> = The amount of water inflow (or outflow when negative) possible based on the inlet's [[Inlet q (Water Overlay)|INLET_Q]] attribute.
* <math>Q_c</math> = The total amount of water inflow (or outflow when negative) allowed based on the total capacity of the {{Inlet}}.
* C<sub>incap</sub> = The amount of water inflow possible based on the total [[Inlet capacity (Water Overlay)|capacity]] of the inlet.
* C<sub>outcap</sub> = The amount of water outflow possible based on the total capacity of the outlet.
* C<sub>inthres</sub> = The amount of water inflow desired based on the inlet's [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] attribute.
* C<sub>outthres</sub> = The amount of water outflow desired based on the outlet's [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] attribute.


* WL<sub>surface</sub> = The water level on the surface, relative to [[Datum|datum]].
* <math>A</math> = Size of the {{Inlet}}/outlet area in m<sup>2</sup>, based on the amount of cells and cell size. Current implementation only has one cell.
* C<sub>total</sub> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] attribute of the inlet.
* <math>\Delta w</math> = The amount of water flow which takes place.
* I<sub>Q</sub> = The INLET_Q attribute of the inlet.
* T<sub>l</sub> = The LOWER_THRESHOLD attribute of the inlet.
* T<sub>u</sub> = The UPPER_THRESHOLD attribute of the inlet.


==See also==
==Related==
* [[Inlet (Water Overlay)|Inlet]]
The following topics are related to this formula.
; Structures
: [[Inlet (Water Overlay)|Inlet]]
; Models
: [[Surface model (Water Overlay)|Surface model]]


{{Template:WaterOverlay_nav}}
{{WaterOverlay formula nav}}

Latest revision as of 13:09, 5 March 2024

Inlets are hydraulic structures can pump water in and out of the project area and are connected with a water body outside the project area.

The amount flowing in or out of Inlets is calculated for the cell the Inlet resides on.

Case 1: Inlet:
When calculating Inlets, first the capacities are calculated.

If a lower threshold is defined:

If a positive inlet q Qt is defined:

If a capacity Qtotal is defined:

After calculating the capacities, the actual water inflow is calculated. If any of the terms are undefined, they are not included.

Case 2 Outlets:
When calculating outlets, first the capacities are calculated.

If an upper threshold Tu,t is defined:

If a negative inlet q Qt is defined:

If a capacity Qtotal is defined:

After calculating the capacities, the actual water ouflow is calculated. If any of the terms are undefined, they are not included.

Where:

  • = The water level on the surface relative to datum, at time t.
  • = The LOWER_THRESHOLD of the Inlet at time t.
  • = The UPPER_THRESHOLD of the Inlet at time t.
  • = The INLET_Q of the Inlet at time t.
  • = Computational timestep.
  • = The INLET_CAPACITY of the Inlet.
  • = The calculated previous amounts of flow.
  • = The desired lower water level at the Inlet's location, based on the LOWER_THRESHOLD of the Inlet.
  • = The desired upper water level at the outlet's location, based on the outlet's UPPER_THRESHOLD of the Inlet.
  • = The amount of water inflow (or outflow when negative) possible based on the INLET_Q of the Inlet and timestep .
  • = The total amount of water inflow (or outflow when negative) allowed based on the total capacity of the Inlet.
  • = Size of the Inlet/outlet area in m2, based on the amount of cells and cell size. Current implementation only has one cell.
  • = The amount of water flow which takes place.

Related

The following topics are related to this formula.

Structures
Inlet
Models
Surface model