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 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,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 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 INLET_CAPACITY attribute of the pump.
• 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