I am designing an machine that is going to use a pneumatic cylinder to accelerate a projectile. I have a tentative cylinder specified, and am working on the control and supply side. I have verified that I can generate enough force, have enough air pressure and volume, etc. The next thing I need to figure out is roughly how fast I can expect the cylinder to be moving by the end of its stroke. Is there a way to estimate this that takes into account fluid dynamics?
Here's what I know: the cylinder has a 4" bore and a 6" stroke. The air pressure available is approximately 100psi (I expect I'll probably need to regulate it down to moderate the speed.) The inlet port on the cylinder is 3/8 NPT, fed from a large tank via a short piece of 3/8" schedule 40 piping for a true ID of approx .493". The outlet port is also 3/8" NPT venting directly to the atmosphere. (I will probably add a muffler, but we can ignore it for the purposes of this estimate.)
Simplistically, I know that once the full inlet air pressure is acting on the piston, the force on the cylinder is the effective area (12.6 square inches) times the air pressure (100 psi) for a force of 1,260 pounds-force. The mass of my projectile + the piston is around .3 slugs, so my acceleration should be roughly 4,200 feet per second squared. From that, I get a final velocity of roughly .875 feet per second.
Is this an appropriate way to make the estimate, or am I right in assuming that the cylinder will take an appreciable amount of time to reach full force and my actual final velocity will be lower than this? Is there a conventional way to estimate this behavior of the cylinder? If not, is there a way I can calculate what the pressure acting on the cylinder will be as a function of time to plug in to my model above?