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I am designing a simple air gun to launch a 1 kg projectile 50 m at 100 m/s. I estimated the drag & calculated the necessary angle for this, but I ran into a bit of difficulty with the pressure/valves.

I need to use an air compressor at around 125-150psi to power it. I'm still a freshman undergrad and for some reason, we skipped this topic in general physics. I thought through it, and I think I did the math correctly for a 3 inch valve into a 3 inch pipe. However, for a 2 inch valve into a 3 inch pipe I'm not sure - do I just calculate the force on a 2 inch diameter opening & use that as my force, even though it is a 3 inch diameter pipe?

I attached my math on both the projectile & the pressure/barrel. (I realize for the projectile I just calculated drag for the initial velocity (even though it changes with velocity) but for only 50m at 100 m/s it isn't a very significant decrease.)

EDIT: I hope this is in the right forum. It isn't really a homework/schoolwork/coursework problem, but I'm not sure if it would fit better in that forum. Sorry if I picked the wrong one!

I need to use an air compressor at around 125-150psi to power it. I'm still a freshman undergrad and for some reason, we skipped this topic in general physics. I thought through it, and I think I did the math correctly for a 3 inch valve into a 3 inch pipe. However, for a 2 inch valve into a 3 inch pipe I'm not sure - do I just calculate the force on a 2 inch diameter opening & use that as my force, even though it is a 3 inch diameter pipe?

I attached my math on both the projectile & the pressure/barrel. (I realize for the projectile I just calculated drag for the initial velocity (even though it changes with velocity) but for only 50m at 100 m/s it isn't a very significant decrease.)

EDIT: I hope this is in the right forum. It isn't really a homework/schoolwork/coursework problem, but I'm not sure if it would fit better in that forum. Sorry if I picked the wrong one!

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