What is the optimal barrel length for maximum distance in a blow-gun?

[funkyreuben]

I recently made a few mini-marshmallow blow-guns out of PVC and I noticed that different barrel lengths provided different firing ranges. Does anyone know how I can calculate the optimal barrel length for maximum distance? I haven't done anything physics related since college (2002) and I'm drawing a blank as to calculating this. Any help would be greatly appreciated.

Chris

 

[Danger]

Welcome to PF, Funkyreuben.
I'm not exactly sure how you would go about this. It depends upon the air source volume and pressure. Ideally, the barrel volume (area x length) should be such that the internal propulsive pressure reaches atmospheric just as the projectile is leaving the muzzle. If the barrel is too short, a lot of your air will be wasted; if it's too long, the marshmallow will begin to decelerate due to friction and air resistance before it can get out.
Trial and error might be the easiest approach.

 

[funkyreuben]

Thanks! I plan on doing some real world testing but I was hoping for a way to calculate it as well.

Chris

 

[Dbjergaard]

if you were to write velocity as a function of either area or length you could use calculus to maximize the escape velocity... I don't know how hard that would be though