I totally agree that an adiabatic solution makes far more sense than a constant pressure or even constant temperature solution, especially for a fast process such as a launcher. I haven’t followed through your math yet, but I’m concerned with a few of your assumptions.

- the open system … is the air contained within a pneumatic cylinder, plus the air in the hose leading up to it
- The cylinder itself is considered to have a mass M and sees the cylinder pressure, a resistive force Fload, and atmospheric pressure.
- No heat transfer; _Qin = 0
- Mass transfer into the system has negligible velocity (v) and head height (gz), leaving only enthalpy h(T).

Here are the issues I noticed with these assumptions:

- is a definition and OK by itself, but impacts assumptions 3 and 4 below.
- The constant Fload is a good first approximation, and probably OK if the cylinder is directly moving the load in a relatively constant orientation. However, if the load is moving on a rotating arm or other non-linear transfer, this will cause the net load force to change along the stroke.
- As heat-carrying mass [air not at zero kelvins] is entering, heat is entering as well.
- Does not make sense because the boundary of the system is a relatively small tube; the air will be moving at a decent speed. Perhaps later in the math you added something so that the head (pressure) is applied at a large diameter (the tank) and you applied Bernoulli’s equation across a small air mass. Even then, the implicit assumption of an infinitely large tank will break down at some point.