Pump formula (Water Overlay): Difference between revisions
Jump to navigation
Jump to search
No edit summary |
mNo edit summary |
||
| Line 1: | Line 1: | ||
Pumps are hydraulic structures can pump water from areas with a lower water level to areas with a higher water level. This direction is determined during the initialization phase of the hydrological model. | Pumps are hydraulic structures can pump water from areas with a lower water level to areas with a higher water level. This direction is determined during the initialization phase of the hydrological model. | ||
A negative pump speed is also allowed. In this article we will refer to this as ''draining''. | A negative pump speed is also allowed. In this article we will refer to this as ''draining''. | ||
| Line 43: | Line 43: | ||
* w<sub>t,l</sub> = The water level at the lower water level entry on at time t, relative to [[Datum|datum]]. | * w<sub>t,l</sub> = The water level at the lower water level entry on at time t, relative to [[Datum|datum]]. | ||
* w<sub>t,u</sub> = The water level at the upper water level entry on at time t, relative to [[Datum|datum]]. | * w<sub>t,u</sub> = The water level at the upper water level entry on at time t, relative to [[Datum|datum]]. | ||
* T<sub>l,t</sub> = The LOWER_THRESHOLD attribute of the pump at time t. | * T<sub>l,t</sub> = The [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] attribute of the pump at time t. | ||
* T<sub>u,t</sub> = The UPPER_THRESHOLD attribute of the pump at time t. | * T<sub>u,t</sub> = The [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] attribute of the pump at time t. | ||
* q<sub>t</sub> = [[Pump q (Water Overlay)|PUMP_Q]] attribute at time t. | * q<sub>t</sub> = [[Pump q (Water Overlay)|PUMP_Q]] attribute at time t. | ||
* Δt = Computational timestep. | * Δt = Computational timestep. | ||
| Line 51: | Line 51: | ||
* Q<sub>l,t</sub> = The desired amount of water at the entry based on the pump's [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] attribute. | * Q<sub>l,t</sub> = The desired amount of water at the entry based on the pump's [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] attribute. | ||
* Q<sub>u,t</sub> = The desired amount of water at the exit based on the pump's [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] attribute. | * Q<sub>u,t</sub> = The desired amount of water at the exit based on the pump's [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] attribute. | ||
* Q<sub>t</sub> = The amount of water pumped (or drained when negative) possible based on the | * Q<sub>t</sub> = The amount of water pumped (or drained when negative) possible based on the [[Pump q (Water Overlay)|PUMP_Q]] attribute and timestep Δt. | ||
* Q<sub>c</sub> = The maximum amount of water flow based on the total capacity of the pump. | * Q<sub>c</sub> = The maximum amount of water flow based on the total capacity of the pump. | ||
* A = Size of the Entry/Exit area in m<sup>2</sup>, based on the amount of cells and cell size. Current implementation only has one cell. | * A = Size of the Entry/Exit area in m<sup>2</sup>, based on the amount of cells and cell size. Current implementation only has one cell. | ||
Revision as of 13:59, 15 May 2019
Pumps are hydraulic structures can pump water from areas with a lower water level to areas with a higher water level. This direction is determined during the initialization phase of the hydrological model. A negative pump speed is also allowed. In this article we will refer to this as draining.
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:
- Qp,t = Δt * qt
If a lower threshold Tl,t is defined as well:
- Ql,t = min ( 0, wl,t - Tl,t )
If an upper threshold Tu,t is defined as well:
- Qu,t = max ( 0, Tu,t- wt,u )
If a capacity Qtotal is defined:
- Qc = Qtotal - ΣQ0..t-1
After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.
- Δw = max( 0 , min( Ql,t , Qu,t , Qt , Qc ) ) / A
Case 2: Draining:
First the flow capacities are calculated.
If a negative Pump q is defined:
- Qp,t = Δt * qt
If a lower threshold Tl,t is defined as well:
- Ql,t = max ( 0, wl,t - Tl,t )
If an upper threshold Tu,t is defined as well:
- Qu,t = min ( 0, Tu,t- wt,u )
If a capacity Qtotal is defined:
- Qc = Qtotal - abs ( ΣQ0..t-1 )
After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.
- Δw = max( 0 , max( Ql,t , Qu,t , Qt , -Qc ) ) / A
Where:
- wt,l = The water level at the lower water level entry on at time t, relative to datum.
- wt,u = The water level at the upper water level entry on at time t, relative to datum.
- Tl,t = The LOWER_THRESHOLD attribute of the pump at time t.
- Tu,t = The UPPER_THRESHOLD attribute of the pump at time t.
- qt = PUMP_Q attribute at time t.
- Δt = Computational timestep.
- Qtotal = The pump capacity of the pump, based on the pump's INLET_CAPACITY attribute.
- Q0..n = The calculated previous amounts of flow.
- Ql,t = The desired amount of water at the entry based on the pump's LOWER_THRESHOLD attribute.
- Qu,t = The desired amount of water at the exit based on the pump's UPPER_THRESHOLD attribute.
- Qt = The amount of water pumped (or drained when negative) possible based on the PUMP_Q attribute and timestep Δt.
- Qc = The maximum amount of water flow based on the total capacity of the pump.
- A = Size of the Entry/Exit 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.