【正文】 ion forces exerted on the airflow prior to falling across the water curtain at the stack base. The application of the method of characteristics to the modelling of unsteady flows was first recognized in the 1960s [13]. The relationships defined by Jack [14] allows the simulation to model the traction force exerted on the entrained air. Extensive experimental data allowed the definition of a ‘pseudofriction factor’ applicable in the wet stack and operable across the water annular flow/entrained air core interface to allow bined discharge flows and their effect on air entrainment to be modelled. The propagation of air pressure transients in building drainage and vent systems is defined by the St Venant equations of continuity and momentum [9],(1)(2)These quasilinear hyperbolic partial differential equations are amenable to finite difference solution once transformed via the Method of Characteristics into finite difference relationships, Eqs. (3)–(6), that link conditions at a node one time step in the future to current conditions at adjacent upstream and downstream nodes, Fig. 2.. St Venant equations of continuity and momentum allow airflow velocity and wave speed to be predicted on an xt grid as shown. Note , . For the C+ characteristic:(3)when(4)and the C characteristic:(5)when(6)where the wave speed c is given byc=(γp/ρ).(7)These equations involve the air mean flow velocity, u, and the local wave speed, c, due to the interdependence of air pressure and density. Local pressure is calculated as(8)Suitable equations link local pressure to airflow or to the interface oscillation of trap seals.The case of the appliance trap seal is of particular importance. The trap seal water column oscillates under the action of the applied pressure differential between the transients in the network and the room air pressure. The equation of motion for the Ubend trap seal water column may be written at any time as(9)It should be recognized that while the water column may rise on the appliance side, conversely on the system side it can never exceed a datum level drawn at the branch connection.In practical terms trap seals are set at 75 or 50s obsession with odour exclusion [2], [3] and [4], depend predominantly on passive solutions where reliance is placed on cross connections and vertical stacks vented to atmosphere [5] and [6]. This approach, while both proven and traditional, has inherent weaknesses, including the remoteness of the vent terminations [7], leading to delays in the arrival of relieving reflections, and the multiplicity of open roof level stack terminations inherent within plex buildings. The plexity of the vent system required also has significant cost and space implications [8]. The development of air admittance valves (AAVs) over the past two decades provides the designer with a means of alleviating negative transients generated as random appliance discharges contribute to the time dependent waterflow conditions within the system. AAVs represent an active control solution as they respond directly to the local pressure conditions, opening as pressure falls to allow a relief air inflow and hence limit the pressure excursions experienced by the appliance trap seal [9]. However, AAVs do not address the problems of positive air pressure transient propagation within building drainage and vent systems as a result of intermittent closure of the free airpath through the network or the arrival of positive transients generated remotely within the sewer system, possibly by some surcharge event downstream—including heavy rainfall in bined sewer applications. The development of variable volume containment attenuators [10] that are designed to absorb airflow driven by positive air pressure transients pletes the necessary device provision to allow active air pressure transient control and suppression to be introduced into the design of building drainage and vent systems, for both ‘standard’ buildings and those requiring particular attention to be paid to the security implications of multiple roof level open stack terminations. The positive air pressure attenuator (PAPA) consists of a variable volume bag that expands under the influence of a positive transient and therefore allows system airflows to attenuate gradually, therefore reducing the level of positive transients generated. Together with the use of AAVs the introduction of the PAPA device allows consideration of a fully sealed building drainage and vent system. Fig. 1 illustrates both AAV and PAPA devices, note that the waterless sheath trap acts as an AAV under negative line pressure.Fig. 1. Active air pressure transient suppression devices to control both positive and negative surges.Active air pressure transient suppression and control therefore allows for localized intervention to protect trap seals from both positive and negative pressure excursions. This has distinct advantages over the traditional passive approach. The time delay inherent in awaiting the return of a relieving reflection from a vent open to atmosphere is removed and the effect of the transient on all the other system traps passed during its propagation is avoided. basis for the simulation of transient propagation in multistack building drainage networks.The propagation of air pressure transients within building drainage and vent systems belongs to a well understood family of unsteady flow conditions defined by the St Venant equations of continuity and momentum, and solvable via a finite difference scheme utilizing the method of characteristics technique. Air pressure transient generation and propagation within the system as a result of air entrainment by the falling annular water in the system vertical stacks and the reflection and transmission of these transients at the system boundaries, including open terminations, connections to the sewer, appliance trap seals and both AAV an