Very often a network involves pumps and pressure force main sub-networks and to model such gravity-pressure combined system requires hydraulic models to not only simulate the system dynamic behaviour of both gravity subsystem and pressure subsystem and the hydraulic interactions between gravity and pressure sub-systems.

From hydraulic dynamic modelling point of view, the governing hydraulics for the gravity and pressure sub networks is different, the gravity sub-network is governed by open channel hydraulics while the pressure sub-network is governed by pressure closed conduit hydraulics and the pump hydraulics and pumps play important role in the sub-network hydraulic behaviour. In order to provide reliable numerical modelling solution for sewer or storm network involving pumps and force mains, a sewer dynamic hydraulic model has to be comprehensive and sophisticated to be able to simulate these two different hydraulics features.

As an integrated part of the numerical sewer modelling engine, a pressure hydraulic solver is also included for the pump(s) and the pressure (force main) sub network(s). The gravity and pressure hydraulic solvers are solved simultaneously within every time step so that the dynamic hydraulic interactions (inflow to the wet well and backwater effect from downstream gravity system) between the gravity sub network and pressure sub network are fully considered in the integrated numerical engine. Normally a pressure force main branch can be identified pre-calculation and the pressure hydraulics will be applied to a force main branch all time, there can be instances, however, a gravity branch receives pump flows and partially or fully pressurized during some times, the Pressmann slot method in the gravity solver then is used for the branch. A force main branch is pre-identified if the downstream end has the highest invert so that the flow within the branch is always in the pressure condition.

The challenges to accurately simulate the pump-force-main subsystem are:

• Each pump can have its own pump curve
• Each pump can have its own control schemes
• The dynamic head of each pump is affected by the system response so that it is also affected by other pump's behaviour
• Each pump therefore has its own operating point
• The whole system outflow is therefore very dynamic and dependent of every pump
• There are interactions with upstream and downstream gravity element hydraulic conditions as well

Drainage and Utilities allows you to add a short suction pipe between a pump and a wet well. This is done by connecting a pressure pipe between the wet well and the pump and making the “Is Virtual” attribute set to False.

The model will consider the friction loss in the suction pipe and use this loss to modify the pump curve, so that the pump head is still based on the wet well HGL. The suction loss will not be reflected in its profile although the loss effect is considered in the calculation as described above.

In order to model complex pumping scenarios with robustness and accuracy, an iterative relaxation technique is used. At each time step t during the dynamic computation, all pump outflows are simultaneously iterated in a relaxation way until they converge to a stable value for every pump and its associated pressure sub-network:

in which i represents the outflow from the pump i, k+1 represents an updated value for the next iteration, and * represents a value determined from the pump curve and current system hydraulic conditions under current k iteration, i.e., the flow value for Q(t)i* is determined using the head difference across the pump from the previous iteration and the pump head characteristic curve. The pump flow equations are solved along with simultaneously solving all the pressure pipe and junction equations in the pressure sub-network. When there are multiple mumps, all the pumps and their pressure sub-networks are solver simultaneously as well, with some subsystems no longer iterating when a convergence is achieved during the iteration. The hydraulic conditions are obtained by solving the force main pipes using current pump outflows, ? is a relaxation factor (0<?<1.0) and ?=0.8 is found to provide robust and fast converging results and it is used in the pressure solver (not a calculation option).