Normally a calculation algorithm calculates a pneumatic conveying system in the time domain in positive time increments, starting at the beginning of a pipeline.

That approach leads to a numerical integration calculation algorithm, embedded in an iterative calculation algorithm.

Also imbedded in the numerical integration algorithm, there are several root finding algorithms, f.i. to find heat losses through convection and radiation.

The necessity for an iterative approach is because the input variables (pressure, capacity) are dependent of each other.

To overcome the problem of this iterative calculation approach, one could consider calculating from the end of the pipeline backwards to the beginning of the pipeline, based on a given capacity and airflow.

The end conditions are then the air end velocity and the material end velocity.

As the calculation is calculation back in time, the time increments have a negative value.

The problem is then that the air end velocity and the material end velocity are dependent of the history.

In this approach the history is unknown and must be calculated.

And, if the history is unknown, the air end velocity and the material end velocity are unknown.

If this approach works, then an iterative algorithm is still required.

Also, this approach (if it is possibly at all) is highly counter intuitive and leads to much confusion to understand the results. ■