Putting vacuums in series (pneumatics)

[EPAIII]

You are going to 3D print a vacuum chamber, cylinder, and piston? No, wait, two cylinders and two pistons. And get a good vacuum seal? GOOD LUCK!

As others have said above, the pressure against the pulling force on the pistons is strictly due to the difference in the pressure on the two sides of those pistons AND to the effective area of the pistons. In your drawing BOTH of the pistons have one side at atmospheric pressure and the other side at the same, lower vacuum pressure. Your drawing has no dimensions, but both pistons seem to have the same dimensions and therefore the same effective area. So, at all times, both of those pistons will feel the same force. The math for this is:

Force = Pressure X Area

Total simplicity. Pressure is measured in units like pounds per square inch (PSI) or Newtons per square cm or some other combination of force and area and of course, area is measured as area.

Now, for how that force changes with the length of the pull, that will be complicated by the amount of air (or other gas) that was in the volume of your apparatus before you start pulling the pistons. As you pull on either of the pistons you will increase the volume that the initial amount of gas occupies. But, since that initial amount of gas is not removed by your simple apparatus, there will always be some remaining pressure inside that apparatus. Professional and scientific systems for creating "high" vacuums DO remove some percentage of the remaining gas at each stage of creating such "high" vacuums. So they can approach a "perfect" vacuum. I say "approach" because no one has ever created a perfect vacuum. Even the vast areas between the galaxies of the universe still has some small amount of gas.

If your 3D printed apparatus does reach a small remaining amount of pressure inside it, you will quickly reach a point where you will not be able to measure the remaining differences in force needed to further separate the pistons unless you spend a lot of money on the force scales needed. And even then, after selling your house, boat, and car, you still will quickly run out of the needed equipment to measure further differences.

One more thing about creating "high" vacuums: the very materials that you construct your apparatus with will have amounts of gas absorbed into their very structure. That gas will bleed out of the walls and pistons and everything else. This is a real problem which continued for a long time - not hours or days, but months and years. Things like vacuum tubes had devices built into them that were designed to continue to remove gas every time they were used.

3D print a vacuum chamber? Yea, sure. Good luck!