Fundamental Equations

The continuity equation applied to a constant area pipe yields:

(1)

The one-dimensional momentum equation applied to a constant area pipe yields:

(2)

Assuming the pipe is straight over the computing section, Figure 1 shows the relationship between dx and dz:

(3)

Figure 1: Relationship between distance along pipe (dx) and vertical elevation change (dz).

The fourth term on the left of Equation 2 accounts for pressure changes due to body forces. AFT xStream models body forces due to gravity. The default value of g in Equation 2 is the standard earth acceleration (i.e., 32.174 ft/sec2 or 9.81 m/sec2).

From the equation of state for a real gas:

(4)