Pump formula (Water Overlay): Difference between revisions

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Pumps are hydraulic structures can pump water from areas with a lower water level to areas with a higher water level.  
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__


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.


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


If a lower threshold Tl is defined:
If a lower threshold T<sub>l</sub> is defined:
 
: ''Q<sub>lth</sub> = max( 0 , T<sub>l,t</sub> - w<sub>t</sub> )''
    Qlth = max( 0 , Tl,t - wt )


If a positive Inlet q is defined:
If a positive Inlet q is defined:
: ''Q<sub>t</sub> = Δt * q<sub>t</sub>''


    Qt = Δt * qt
If a capacity Q<sub>total</sub> is defined:
 
: ''Q<sub>c</sub> = Q<sub>total</sub>''- ΣQ<sub>0..t-1</sub>
If a capacity Qtotal is defined:
 
    Qc = Qtotal- ΣQ0..t-1


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''


    Δw = max( 0 , min( Qlth , Qt , Qc ) ) / A
''Case 2 '''Outlets''':''<br>
 
Case 2 Outlets:
When calculating outlets, first the capacities are calculated.
When calculating outlets, first the capacities are calculated.


If an upper threshold Tu is defined:
If an upper threshold T<sub>u</sub> is defined:
 
: ''Q<sub>uth</sub> = min( 0 , T<sub>u</sub> - w<sub>t</sub> )''
    Quth = min( 0 , Tu - wt )


If a negative Inlet q is defined:
If a negative Inlet q is defined:
: ''Q<sub>t</sub> = Δt * q<sub>t</sub>''


    Qt = Δt * qt
If a capacity Q<sub>total</sub> is defined:
 
: ''Q<sub>c</sub> = -Q<sub>total</sub> - ΣQ<sub>0..t-1</sub>''
If a capacity Qtotal is defined:
 
    Qc = -Qtotal - ΣQ0..t-1


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''
    Δw = min( 0 , max( Quth , Qt , Qc) ) / A


Where:
Where:
* w<sub>t</sub> = The water level on at time t, relative to [[Datum|datum]].
* T<sub>l,t</sub> = The LOWER_THRESHOLD attribute of the inlet at time t.
* T<sub>u,t</sub> = The UPPER_THRESHOLD attribute of the inlet at time t.
* q<sub>t</sub> = [[Inlet q (Water Overlay)|INLET_Q]] attribute at time t.
* Δt = Computational timestep.
* Q<sub>total</sub> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] attribute of the inlet.
* Q<sub>0..n</sub> = The calculated previous amounts of flow.
* Q<sub>lth</sub> = The amount of water inflow desired based on the inlet's [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] attribute.
* Q<sub>uth</sub> = The amount of water outflow desired based on the outlet's [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] attribute.
* Q<sub>t</sub> = The amount of water inflow (or outflow when negative) possible based on the INLET_Q attribute and timestep Δt.
* Q<sub>c</sub> = The amount of water outflow possible based on the total capacity of the outlet.
* A = 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.
* Δw = The amount of water flow which takes place.


    wt = The water level on at time t, relative to datum.
    Tl,t = The LOWER_THRESHOLD attribute of the inlet at time t.
    Tu,t = The UPPER_THRESHOLD attribute of the inlet at time t.
    qt = INLET_Q attribute at time t.
    Δt = Computational timestep.
    Qtotal = The INLET_CAPACITY attribute of the inlet.
    Q0..n = The calculated previous amounts of flow.
    Qlth = The amount of water inflow desired based on the inlet's LOWER_THRESHOLD attribute.
    Quth = The amount of water outflow desired based on the outlet's UPPER_THRESHOLD attribute.
    Qt = The amount of water inflow (or outflow when negative) possible based on the INLET_Q attribute and timestep Δt.
    Qc = The amount of water outflow possible based on the total capacity of the outlet.
    A = Size of the Inlet/Outlet area in m2, based on the amount of cells and cell size. Current implementation only has one cell.
    Δw = The amount of water flow which takes place.
==See also==
==See also==
* [[Pump_(Water_Overlay)|Pump]].
* [[Inlet (Water Overlay)|Inlet]]
* [[Inlet_formula_(Water_Overlay)|Inlet formula]].
 
* Moving water from higher water levels to lower water levels can be done with [[Weir_(Water_Overlay)|weirs]].
{{Template:WaterOverlay_nav}}
{{Template:WaterOverlay_nav}}

Revision as of 14:10, 15 April 2019

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 Tl is defined:

Qlth = max( 0 , Tl,t - wt )

If a positive Inlet q is defined:

Qt = Δt * qt

If a capacity Qtotal is defined:

Qc = Qtotal- ΣQ0..t-1

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( Qlth , Qt , Qc ) ) / A

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

If an upper threshold Tu is defined:

Quth = min( 0 , Tu - wt )

If a negative Inlet q is defined:

Qt = Δt * qt

If a capacity Qtotal is defined:

Qc = -Qtotal - ΣQ0..t-1

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( Quth , Qt , Qc) ) / A

Where:

  • wt = The water level on at time t, relative to datum.
  • Tl,t = The LOWER_THRESHOLD attribute of the inlet at time t.
  • Tu,t = The UPPER_THRESHOLD attribute of the inlet at time t.
  • qt = INLET_Q attribute at time t.
  • Δt = Computational timestep.
  • Qtotal = The INLET_CAPACITY attribute of the inlet.
  • Q0..n = The calculated previous amounts of flow.
  • Qlth = The amount of water inflow desired based on the inlet's LOWER_THRESHOLD attribute.
  • Quth = The amount of water outflow desired based on the outlet's UPPER_THRESHOLD attribute.
  • Qt = The amount of water inflow (or outflow when negative) possible based on the INLET_Q attribute and timestep Δt.
  • Qc = The amount of water outflow possible based on the total capacity of the outlet.
  • A = Size of the Inlet/Outlet area in m2, based on the amount of cells and cell size. Current implementation only has one cell.
  • Δw = The amount of water flow which takes place.

See also

Template:WaterOverlay nav