When this Solution Method is used, all heat transfer data entered for individual pipes is neglected. The other pipe data is left as entered by the user in case the user switches back to one of the marching methods.

Elevation data is also ignored by the Solver. The output will still show the elevation as entered by the user. Since elevation effects are usually not very important in gas systems, neglecting elevation changes is frequently an acceptable approximation. One application where this is definitely not the case is in Rotating Systems.

An analytical solution to Equations 1, 2 and 5 for adiabatic flow neglecting elevation changes is given by the following (e.g., see Saad, 1993, page 209):

(42)

This equation is valid for real gases as long as the following approximation is accepted:

using a suitably averaged value of _cp. Integrating from 0 to L obtains:

(43)

Equation 43 is then solved for each pipe, using an average value of friction factor and g for each pipe. The solution of Equation 43 typically is iterative where the unknown is M₂.