Pump formula (Water Overlay)

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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. 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 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 INLET_CAPACITY attribute of the pump.
  • 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 INLET_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.

See also

Template:WaterOverlay nav