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. 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:

Q_p,t = Δt * q_t

If a lower threshold T_l is defined as well:

Q_lth = max ( 0, w_t,l - T_l,t )

If an upper threshold T_l is defined as well:

Q_uth = max ( 0, T_l,t- w_t,u )

If a capacity Q_total is defined:

Q_c = Q_total- ΣQ_0..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( Q_lth,Q_uth , Q_t , Q_c ) ) / A

Where:

• w_t,l = The water level at the lower water level entry on at time t, relative to datum.
• w_t,u = The water level at the upper water level entry on at time t, relative to datum.
• T_l,t = The LOWER_THRESHOLD attribute of the inlet at time t.
• T_u,t = The UPPER_THRESHOLD attribute of the inlet at time t.
• q_t = INLET_Q attribute at time t.
• Δt = Computational timestep.
• Q_total = The INLET_CAPACITY attribute of the inlet.
• Q_0..n = The calculated previous amounts of flow.
• Q_lth = The amount of water inflow desired based on the inlet's LOWER_THRESHOLD attribute.
• Q_uth = The amount of water outflow desired based on the outlet's UPPER_THRESHOLD attribute.
• Q_t = The amount of water inflow (or outflow when negative) possible based on the INLET_Q attribute and timestep Δt.
• Q_c = 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

• Inlet