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. 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:

Q_p,t = Δt * q_t

If a lower threshold T_l,t is defined as well:

Q_l,t = min ( 0, w_l,t - T_l,t )

If an upper threshold T_u,t is defined as well:

Q_u,t = max ( 0, T_u,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_l,t , Q_u,t , Q_t , Q_c ) ) / A

Case 2: Draining:
First the flow capacities are calculated.

If a negative Pump q is defined:

Q_p,t = Δt * q_t

If a lower threshold T_l,t is defined as well:

Q_l,t = max ( 0, w_l,t - T_l,t )

If an upper threshold T_u,t is defined as well:

Q_u,t = min ( 0, T_u,t- w_t,u )

If a capacity Q_total is defined:

Q_c = Q_total - abs ( 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 , max( Q_l,t , Q_u,t , 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 pump at time t.
• T_u,t = The UPPER_THRESHOLD attribute of the pump at time t.
• q_t = PUMP_Q attribute at time t.
• Δt = Computational timestep.
• Q_total = The pump capacity of the pump, based on the pump's INLET_CAPACITY attribute.
• Q_0..n = The calculated previous amounts of flow.
• Q_l,t = The desired amount of water at the entry based on the pump's LOWER_THRESHOLD attribute.
• Q_u,t = The desired amount of water at the exit based on the pump's UPPER_THRESHOLD attribute.
• Q_t = The amount of water pumped (or drained when negative) possible based on the INLET_Q attribute and timestep Δt.
• Q_c = 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

• Pump