Pump 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__
[[pump (Water Overlay)|Pump]]s are hydraulic structures can pump water from one location to another.


The amount flowing in or out of inlets is calculated for the cell the inlet resides on.
The direction the pump pumps in is based on the water level at either end of the pump. A pump pumps water from the area with a lower [[water level (Water Overlay)|water level]] to the area with a higher [[water level (Water Overlay)|water level]]. If no (differing) water levels are defined, the [[terrain height (Water Overlay)|surface height]] is used instead. The direction is determined during the initialization phase of the hydrological model, and does not change during the calculation even when water levels change.


''Case 1: '''Inlet''':''<br>
A negative pump speed is also allowed. This will cause the pump to be "draining", rather than "pumping". This will cause water to be moved in the opposite direction.
When calculating inlets, first the capacities are calculated.


If a lower threshold T<sub>l</sub> is defined:
The amount being pumped or drained is dependent on the water levels on both sides of the pump.
: ''Q<sub>lth</sub> = max( 0 , T<sub>l,t</sub> - w<sub>t</sub> )''


If a positive Inlet q is defined:
''Case 1: '''Pumping''':''
: ''Q<sub>t</sub> = Δt * q<sub>t</sub>''
 
First the flow capacities are calculated.
 
If a positive Pump q is defined:
: <math>Q_{p,t} = \Delta t \cdot q_t </math>
 
If a lower threshold T<sub>l,t</sub> is defined as well:
: <math>Q_{l,t} = min ( 0, w_{l,t} - T_{l,t} )</math>
 
If an upper threshold T_{u,t} is defined as well:
: <math>Q_{u,t} =  max ( 0, T_{u,t} - w_{t,u}  )</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 pumped upwards is calculated. If any of the terms are undefined, they are not included.
: <math>\Delta w = \frac {max( 0 , min( Q_{l,t} , Q_{u,t} , Q_{t} , Q_{c} ) ) }{A}</math>


After calculating the capacities, the actual water inflow is calculated. If any of the terms are undefined, they are not included.
''Case 2: '''Draining''':''<br>
: ''Δw = max( 0 , min( Q<sub>lth</sub> , Q<sub>t</sub> , Q<sub>c</sub> ) ) / A''
First the flow capacities are calculated.


''Case 2 '''Outlets''':''<br>
If a negative Pump q is defined:
When calculating outlets, first the capacities are calculated.
: <math>Q_{p,t} = \Delta t \cdot q_t </math>


If an upper threshold T<sub>u</sub> is defined:
If a lower threshold T<sub>l,t</sub> is defined as well:
: ''Q<sub>uth</sub> = min( 0 , T<sub>u</sub> - w<sub>t</sub> )''
: <math>Q_{l,t} = max ( 0, w_{l,t} - T_{l,t} )</math>


If a negative Inlet q is defined:
If an upper threshold T<sub>u,t</sub> is defined as well:
: ''Q<sub>t</sub> = Δt * q<sub>t</sub>''
: <math>Q_{u,t} =  min ( 0, T_{u,t} - w_{t,u} )</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} - abs ( \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 pumped upwards 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 { max( 0 , max( Q_{l,t} , Q_{u,t} , Q_t , -Q_c ) ) }{ A} </math>


Where:
Where:
* w<sub>t</sub> = The water level on at time t, relative to [[Datum|datum]].
* <math>w_{t,l}</math> = The [[Surface water level formula (Water Overlay)|water level]] at the lower water level entry at time t, relative to {{datum}}.
* T<sub>l,t</sub> = The LOWER_THRESHOLD attribute of the inlet at time t.
* <math>w_{t,u}</math> = The [[Surface water level formula (Water Overlay)|water level]] at the upper water level entry at time t, relative to {{datum}}.
* T<sub>u,t</sub> = The UPPER_THRESHOLD attribute of the inlet at time t.
* <math>T_{l,t}</math> = The [[Pump lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the pump at time t.
* q<sub>t</sub> = [[Inlet q (Water Overlay)|INLET_Q]] attribute at time t.
* <math>T_{u,t}</math> = The [[Pump upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the pump at time t.
* Δt = Computational timestep.
* <math>q_t</math> = The [[Pump q (Water Overlay)|PUMP_Q]] of the pump at time t.
* Q<sub>total</sub> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] attribute of the inlet.
* <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)|timestep]].
* Q<sub>0..n</sub> = The calculated previous amounts of flow.
* <math>Q_{total}</math> = The pump capacity, defined in [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] of the pump.
* Q<sub>lth</sub> = The amount of water inflow desired based on the inlet's [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] attribute.
* <math>Q_{0..n}</math> = The calculated previous amounts of flow.
* Q<sub>uth</sub> = The amount of water outflow desired based on the outlet's [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] attribute.
* <math>Q_{l,t}</math> = The desired amount of water at the entry based on the pump's [[Pump lower threshold (Water Overlay)|LOWER_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.
* <math>Q_{u,t}</math> = The desired amount of water at the exit based on the pump's [[Pump upper threshold (Water Overlay)|UPPER_THRESHOLD]] attribute.
* Q<sub>c</sub> = The amount of water outflow possible based on the total capacity of the outlet.
* <math>Q_t</math> = The [[Pump q (Water Overlay)|PUMP_Q]] at time <math>t</math> for timestep <math>\Delta t</math>, which is the amount of water the pump can possibly pump (or drain, when negative).
* 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.
* <math>Q_c</math> = The maximum amount of water flow based on the total capacity of the pump.
* Δw = The amount of water flow which takes place.
* <math>A</math> = Size of the entry/exit area in <math>m^2</math>, based on the amount of cells and cell size. Current implementation only has one cell.
* <math>\Delta w</math> = The amount of water flow which takes place.


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


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{{WaterOverlay formula nav}}

Latest revision as of 13:13, 5 March 2024

Pumps are hydraulic structures can pump water from one location to another.

The direction the pump pumps in is based on the water level at either end of the pump. A pump pumps water from the area with a lower water level to the area with a higher water level. If no (differing) water levels are defined, the surface height is used instead. The direction is determined during the initialization phase of the hydrological model, and does not change during the calculation even when water levels change.

A negative pump speed is also allowed. This will cause the pump to be "draining", rather than "pumping". This will cause water to be moved in the opposite direction.

The amount being pumped or drained is dependent on the water levels on both sides of the pump.

Case 1: Pumping:

First the flow capacities are calculated.

If a positive Pump q is defined:

If a lower threshold Tl,t is defined as well:

If an upper threshold T_{u,t} is defined as well:

If a capacity Qtotal is defined:

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

Case 2: Draining:
First the flow capacities are calculated.

If a negative Pump q is defined:

If a lower threshold Tl,t is defined as well:

If an upper threshold Tu,t is defined as well:

If a capacity Qtotal is defined:

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

Where:

  • = The water level at the lower water level entry at time t, relative to datum.
  • = The water level at the upper water level entry at time t, relative to datum.
  • = The LOWER_THRESHOLD of the pump at time t.
  • = The UPPER_THRESHOLD of the pump at time t.
  • = The PUMP_Q of the pump at time t.
  • = Computational timestep.
  • = The pump capacity, defined in INLET_CAPACITY of the pump.
  • = The calculated previous amounts of flow.
  • = The desired amount of water at the entry based on the pump's LOWER_THRESHOLD attribute.
  • = The desired amount of water at the exit based on the pump's UPPER_THRESHOLD attribute.
  • = The PUMP_Q at time for timestep , which is the amount of water the pump can possibly pump (or drain, when negative).
  • = The maximum amount of water flow based on the total capacity of the pump.
  • = Size of the entry/exit area in , 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
Pump
Models
Surface model