# Blow-gun physics question

1. Aug 22, 2007

### 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

2. Aug 22, 2007

### 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.

3. Aug 22, 2007

### funkyreuben

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

Chris

4. Aug 22, 2007

### 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

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