Aero-thermodynamic Fundamentals
The following equations outline a fully three-dimensional mathematical problem that is very difficult to solve even with simplifying assumptions. Until recently, limitations in computational power, forced these equations to be simplified to an Inviscid two-dimensional problem with pseudo losses. Before the advent of computers, these equations were almost always simplified to a one-dimensional problem.
Solving this one-dimensional problem is still valuable today and is often termed mean-line analysis. Even with all of this simplification it still requires large textbooks to outline and large computer programs to solve practically.
Read more about this topic: Centrifugal Compressor