Pipe Flow Expert uses a two-step approach to calculate a balanced steady flow state for a system.


An initial approximate solution is obtained using Linear Theory methods and an iterative approach to adjust the flow rates until an approximate pressure balance is achieved. This approach provides estimates for the initial flow rate in each pipe, and these are then used as a starting point to move towards a more accurate and final solution. The initial flow estimates are unlikely to give an accurate pressure result over the whole system and they must be further refined to adjust the flow rates until a final pressure balance is achieved. 


Pipe Flow Expert defines the elements of the pipeline system in a series of matrix equations and uses variations on the Newton method to adjust the estimates for the flow rate in each pipe. 


Once an approximate solution has been obtained, the results are refined using a variation of the  method to ensure convergence until a balanced pressure result is obtained.


A flow balance tolerance and an approximate pressure balance tolerance are used to allow Pipe Flow Expert to find an approximate solution quickly. This approximate solution is then refined until the system is solved within the final pressure balance tolerance.


The flow and pressure balance tolerances and the maximum number of iterations allowed, have been carefully chosen to provide the best overall performance in finding a solution. It is recommended that these values are not changed, as most systems will solve without adjustment to these parameters.