Thermodynamics - isentropic, polytropic and compressibility

[Friis]

Several questions:

1. What does compression actually means? In the case of isentropic calculations a changed in density (or specific volume) is included in the calculations (isentropic.jpg) so isentropic means that compressibility is included in those calculations or what?
   
2. In a previous thread, a compressibility factor k (untitled.jpg) is mentioned ( https://www.physicsforums.com/threa...or-pressure-for-calculating-fan-power.690663/ ). Any idea how this factor is derived?
   
3. Using k, the fan power is then calculated using W = (P2 – P1)*V*k - any idea of how this is calculated - because this is NOT the relation descibing work for an isentropic process?
   
4. Can you give me some references to literature where these compressibility factor are derived and the relations between isentropic and polytropic relations is derived for fans and pumps? I have been looking in standard thermodynamic literature (Smith, van Ness, Abbott ”introduction to chemical engineering thermodynamics”, 5th edition and Moran, Shapiro “Fundamentals of engineering thermodynamics 3rd edition”) but the literature is not detailed enough for fans and pumps. I need some advanced thermodynamics for isentropic, polytriopic proceses describing fans and pumps and including compressibility..
   

 

[Friis]

2) A small addition to my question 2): What confuses me is that the compressibility factor is used to correct for "non-ideality" - that is, for the gas law PV = ZNRT, Z is the compressibility which expresses the "degree of ideality". Z=1 means that it is the ideal gas law.

In other words if k = 1 = Z; then we have a process that can described with the ideal gas law. Apparently, the equation in 2) looks like something that is derived from an isentropic process - can the compressibility factor Z be drived from an isentropic process? I think not but I need to understand the details...