Velocity of air in compressed air tube

[Aqueous]

This is more like personal homework and I have searched everywhere to find the answer to this with no luck.

I was watching mythbusters re-runs the other night and the hurricane episode was on. They were trying to prove that straw could go through a tree in hurricane force winds. What perplexed me was the air cannon they used. Here is a little info on the setup:

Setup
"Jamie and Adam built an air gun to simulate the strongest possible hurricane wind: 318 mph. They were limited to 150 psi in the shop, so they compensated with the long barrel.
The air gun: * Air compressor * 4' air tank (SCH 40 pipe) * pressure gauge * valve. Pilot-assisted diaphragm valve * 80' long barrel (1/2" diameter copper pipe)
A test shot with a cotton ball at 8 psi went 321 mph, which was within 1% of their target speed."

Why does an 80ft long barrel increase the velocity?? and is there some velocity to distance to pressure type equation to determine velocity? I always believed there would be a pressure drop due to friction, which would slow objects down over a distance? again I have searched everywhere for an answer to no avail. Thanks for your help in advance.

 

[LowlyPion]

Why does an 80ft long barrel increase the velocity?? and is there some velocity to distance to pressure type equation to determine velocity?

Welcome to Physics Forum. I wonder can you think of perhaps some formula that relates force to acceleration? And is there a formula that relates pressure to force? I'd think that would be an excellent starting point.

Who knows but that you might be able to come up with such a formula that you are looking for yourself?

 

[stewartcs]

This is more like personal homework and I have searched everywhere to find the answer to this with no luck.

I was watching mythbusters re-runs the other night and the hurricane episode was on. They were trying to prove that straw could go through a tree in hurricane force winds. What perplexed me was the air cannon they used. Here is a little info on the setup:

Setup
"Jamie and Adam built an air gun to simulate the strongest possible hurricane wind: 318 mph. They were limited to 150 psi in the shop, so they compensated with the long barrel.
The air gun: * Air compressor * 4' air tank (SCH 40 pipe) * pressure gauge * valve. Pilot-assisted diaphragm valve * 80' long barrel (1/2" diameter copper pipe)
A test shot with a cotton ball at 8 psi went 321 mph, which was within 1% of their target speed."

Why does an 80ft long barrel increase the velocity?? and is there some velocity to distance to pressure type equation to determine velocity? I always believed there would be a pressure drop due to friction, which would slow objects down over a distance? again I have searched everywhere for an answer to no avail. Thanks for your help in advance.

With compressible flow, friction and heat causes an increase in outlet velocity for subsonic flows in pipes.

If you look at a Rayleigh curve on a Mollier diagram you'll see that as heat is added to the flow the Mach number tends to 1 (choked flow) for subsonic flow and just the opposite for supersonic flow.

The long pipe obviously adds frictional losses and a small heat transfer through the pipe walls. Both result in an increase in flow velocity, but only until the flow becomes choked.

Hope this helps.

CS

 

[Aqueous]

Thanks for the replies!

LowlyPion I am assuming you are referring to Newtons law or Acc=F/m for acceleration and since force is pressure times area it would result in Acc= (PA)/m. Now my question is on finding the mass of the air. Would I need to find the mass of the air over the 80ft distance? I am sure its relatively simple but my mind is boggled this week as I'm cramming for my Diff. Eq. and Calc3 finals and I am spending way too much time on this non-school work

 

[Aqueous]

ttt