For compressible working fluids, multiple turbine stages are usually used to harness the expanding gas efficiently.
Kochin's research was on meteorology, gas dynamics and shock waves in compressible fluids.
One can use the crossings of the characteristics to find shock waves for potential flow in a compressible fluid.
For gases and other compressible fluids, it depends on temperature and varies very slowly with pressure.
Book 2 also discusses (in ) hydrostatics and the properties of compressible fluids.
It is possible to use the fundamental principles of physics to develop similar equations applicable to compressible fluids.
Air is a compressible fluid - you can decrease its volume by squeezing it - but water is not.
Remarkably, this works well even for a highly compressible fluid like air as long as sound and shock waves can be ignored.
In a compressible fluid, such as air, the temperature and density are essential when determining the state of the fluid.
A similar approach is also taken with the thermodynamic properties of compressible fluids.