Pipe Flow Expert generates initial estimates for the flow rate in each pipe. The pressure losses within the system are then calculated using friction factors obtained from the Colebrook-White equation, and the friction pressure loss for each pipe is obtained from the Darcy-Weisbach equation. 


The initial flow estimates are unlikely to give a balanced pressure result over the whole system and these values must be iteratively adjusted using a variation on the Newton method for complex systems, in order to converge to a final result where all of the flow rates and pressures within the system are balanced. 


The Pipe Flow Expert software defines the elements of the pipeline system in a series of highly non-linear matrix equations. Once an approximate solution has been obtained, the initial results are refined using developed mathematically techniques and proprietary algorithms, to ensure the final results converge to a balanced flow and pressure result. 


Note: Finding the solution to a highly non-linear system of equations (which a complex pipe system inevitably generates) is a difficult mathematical problem. The Pipe Flow Expert software uses advanced mathematical methods together with novel algorithms to converge the equations to a solution.


For compressible gas systems, the algorithms are extended further, to switch to iterative adjustment of nodes pressures, once the solution using equations as described above has been found. This allows the Pipe Flow Expert software to use compressible gas flow equations to calculate flow rate between two pressure conditions while taking account of density changes that occur with any compression or expansion of the gas as it travels down the pipe.