Pump formula (Water Overlay)

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

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

• Pump.
• Inlet formula.
• Moving water from higher water levels to lower water levels can be done with weirs.