[potentialverand]

I'm curious about your measured pressure drop between the pressure at the pump, and the pressure at the group head. Since coffee machines are low flow and travel through a short distance of presumably stainless steel pipe, my quick calculations indicate a minimal pressure drop compared to the expected 9 bar of pressure used to pull a shot.

Temperature is another kettle of fish as you have demonstrated.

[johnbuckman]

The problem is that your mental model of how a boiler based espresso machine works is not how they are actually wired.

Here is how they actually work: 9 bar of pressure are generated between the pump and a flow constrictor which is placed before the boiler, pumping cold water into the boiler. This cold water then displaces the water in the boiler, which then gets pushed to the espresso.

Thus, the final pressure depends on the compressibility of the steam (or airspace) in the boiler. In practice, you get about half a bar less at the espresso than the pump got behind the boiler. But, the real numbers depends on lots of factors, many of which are invisible.