Junctions with Demands

Junctions with demands have two behaviors during a transient analaysis:

(a) If the pressure P is positive, then it acts like an orifice discharging to atmosphere wherein the outflow/demand is Q =

Qi. summed over all the connected branches, i. The pressure varies quadratically with the discharge from the initial conditions - so that the diameter of the orifice is not explicitly required by the transient solver;

(b) on the other hand when the pressure drops below zero, there is no net inflow or outflow (Q = 0), while if the pressure declines to the vapor pressure of the liquid, the rate of change of the vapor volume, Xi, in each branch is described by the relation dXi / dt = - Qi.

Junctions without Demands

The continuity equation for the junction of two or more pipes states that the net inflow Q =

Qi is zero when the pressure P exceeds the liquid's vapor pressure. On the other hand, at vapor pressure, the volume in each branch Xi grows in time according to the ordinary differential equation dXi / dt = - Qi.

Dead End Junctions

During a transient analysis, a junction with no demand and only one pipe connected to it is treated as a dead-end junction by the transient solver.

Dead ends are important during a transient analysis because large positive pressure waves tend to 'reflect' off a dead end as negative pressure waves of the same magnitude. If the initial static pressure is too low, this can cause cavitation.

When the pressure reaches the vapor pressure of the liquid, the equation dX1 / dt = - Q1 serves to provide the rate of change of the volume of the cavity.