As an engineer, I periodically need to size a run of natural gas piping. There are equations provided by codes like National Fire Protection Association (NFPA) but this usually involves a manual iteration in a spreadsheet till pressure drop is "appropriate". I feel the need for a numerical method but I just can't get it going. I am ignorant in too many ways to capture it. Please help.
My first guess is use Newton-Raphson to solve continuity equations on these "pipes" but I don't want to distract if there are better solutions!
There are boundary conditions I can set on certain pipes. Pipe XX has to have a certain outlet pressure. One pipe's inlet will be another pipe's outlet.
I can also initialize every pipe with very close values; i.e. I know the flows for sure, I can guess the nearly appropriate size, I could even approximate the pressure drop across but I DO THINK THE PRESSURE IS ONE TO SOLVE.
I had better stop here and see what you all come up with. I appreciate any and all help!