Er, um ok... I'll add more detail to the instructions.
This was not really so much a case of max psi. I have calculated that 300 psi will take a force of 154.5 pounds to achieve. If someone needs more pressure, they can either work harder

or use a smaller diameter tube/piston.
The premise for this pump was to make something which a lot of people would have the tools to replicate. If I were to fire up the lathe, then sure I could make a pump with virtually 0 dead space, and a check valve good to whatever pressure I wanted. But there would be only a few here that could reproduce it.
I believe that the check valve will easily go past 250psi, but no, I have not calculated a max rating. Even if I were to crunch the numbers, different manufacturing techniques (silver soldering ,sweating, epoxying) would alter the properties of the material sufficiently to render the result useless.
The primary reason for building a check valve, was to reduce the amount of dead space in the pump. With your wog check valve from lowes, you have a lot of dead space (comparatively). This would require a larger swept volume to achieve a similar pressure increase.
And Finally, in an ideal world, your chamber would take 14 strokes to fill to 200psi. So in a real world, lets say less than 20.
It may not be the solution for everyone, but it should suffice for many.
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