Lumped Inertia Pipe with Orifice Waterhammer Theory
Some junctions in AFT Impulse use a pipe as a connector for some elements, although it is not a complete element by itself. Such an element may also include an orifice as shown in Figure 1. These connector pipes are modeled as pipes with lumped inertia (Wylie, 1993Wylie, E.B., V.L. Streeter & L. Suo, Fluid Transients in Systems, Prentice Hall, Englewood Hills, New Jersey, 1993.), such that their losses are included with the junction calculations.
Figure 1: Lumped inertia with friction schematic
Summing forces acting on the lumped section, 2,
or,
Now,
Substituting terms and dividing by area A2
Taking average values over time, and denoting current time by a prime,
Collecting terms and simplifying
where

(1) 

(2) 
If a connector pipe exists but no orifice then
If an orifice exists but no connector pipe
If neither exist then