Pump formula (Water Overlay): Difference between revisions
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If a lower threshold T<sub>l,t</sub> is defined as well: | If a lower threshold T<sub>l,t</sub> is defined as well: | ||
: ''Q<sub>l,t</sub> = | : ''Q<sub>l,t</sub> = min ( 0, w<sub>l,t</sub> - T<sub>l,t</sub> )'' | ||
If an upper threshold T<sub>u,t</sub> is defined as well: | If an upper threshold T<sub>u,t</sub> is defined as well: | ||
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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> | : ''Q<sub>c</sub> = Q<sub>total</sub> - ΣQ<sub>0..t-1</sub>'' | ||
After calculating the capacities, the actual water pumped upwards 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 = max( 0 , min( Q<sub> | : ''Δw = max( 0 , min( Q<sub>l,t</sub>,Q<sub>u,t</sub> , Q<sub>t</sub> , Q<sub>c</sub> ) ) / A'' | ||
''Case 2: '''Draining''':''<br> | ''Case 2: '''Draining''':''<br> | ||
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If a lower threshold T<sub>l,t</sub> is defined as well: | If a lower threshold T<sub>l,t</sub> is defined as well: | ||
: ''Q<sub>l,t</sub> = | : ''Q<sub>l,t</sub> = max ( 0, w<sub>l,t</sub> - T<sub>l,t</sub> )'' | ||
If an upper threshold T<sub>u,t</sub> is defined as well: | If an upper threshold T<sub>u,t</sub> is defined as well: | ||
: ''Q<sub>u,t</sub> = | : ''Q<sub>u,t</sub> = min ( 0, T<sub>u,t</sub>- w<sub>t,u</sub> )'' | ||
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> | : ''Q<sub>c</sub> = Q<sub>total</sub>- abs ( ΣQ<sub>0..t-1</sub> )'' | ||
After calculating the capacities, the actual water pumped upwards 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 = max( 0 , | : ''Δw = max( 0 , max( Q<sub>l,t</sub>,Q<sub>u,t</sub> , Q<sub>t</sub> , -Q<sub>c</sub> ) ) / A'' | ||
Where: | Where: | ||
Revision as of 14:44, 15 April 2019
Pumps are hydraulic structures can pump water from areas with a lower water level to areas with a higher water level. A negative pump speed is also allowed. In this article we will refer to this as a drain.
The amount being pumped or drained is dependent on the water levels on both sides of the pump.
Case 1: Pumping:
First the 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 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 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.
- Ql,t = The amount of water inflow desired based on the inlet's LOWER_THRESHOLD attribute.
- Qu,t = 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.