Projectile Velocity from Pneumatic Test 1

[The Iceman]

Hi All,
I am trying to design a pneumatic testing bay and want to make sure it will be robust enough.

Need some help determining worst case velocity of a projectile in case of a failure. My projected worst case is if one of the fittings fails and comes shooting out.(the tank is overdesigned and should handle the pressure)

My approach was to calculate the overall stored energy in the vessel using the Baker Equation. I figure that would be worst case and if I take that energy and convert it to Kinetic Energy of a potential projectile I can calculate the worst case velocity of that projectile. Basically PE=KE=(1/2 mass(of the projectile) times V²) and just solve for V

Does that all make sense? I am getting some awfully high numbers for possible velocities of a fairly light projectile.

Someone suggested I use the mass of the overall pressurized unit as the mass in the KE equation. In that case I could just weld some heavy weight to the outside of the unit and that would slow the projectile significantly. I can see that slowing the pressure tank's movement but not a fitting that were to fail and come shooting out.

Thoughts on this or do you have a completely different method of determining a worst case velocity?

 

[EdStainless]

How about sonic velocity?
My air rifles will fire pellets at 1150fps.
We used to use 1000fps when we had to address these issues.

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[LittleInch]

Total energy and very conservative.

Once the item leaves the vessel there is no energy transfer.

F= m x accl maybe?

What case is usually a plug or similar.

Unrestricted you could see maybe 50 m+



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[rb1957]

mass should be the mass of the thing who's KE you're calculating (ie the projectile, not the tank).

Some of the explosive PE is consumed in recoil, I think.

Yes, light masses will have higher velocities.

Be careful with units !

"Hoffen wir mal, dass alles gut geht !"
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[The Iceman]

EdStainless,
Yeah I had thought about an air rifle but that has the whole barrel to be building up speed with the pressure behind it. This would be nearly instantaneous.

 

[The Iceman]

LittleInch,
F=mA is actually what I was thinking if it were Hydrostatic testing. That would be much less violent than the pneumatic.

 

[The Iceman]

rb1957,
Yeah I have been trying to convince my higher ups that we should just be using the mass of the projectile. But I am also open to other methods and I realize my method would be worst case, just not sure how to get the actual case.

 

[LittleInch]

I thought there was an energy requirement for a projectile 5000J?

But what are you trying to design?

The test bay needs to be open to allow any air to escape but how do you stop projectiles?

Got a sketch or plan?

Or just build 200mm ir 250mm thick reinforced concrete?

There's not much to actually design as opposed to just make it big and strong.....

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[rb1957]

Are you using all the chemical PE ? that'd be conservative. Can you use another gun as an example ? one which you know the muzzle velocity (and the charge) to gauge how much PE is converted to KE ? But that would only be a minor change in velocity ... what are you calculating that gives you such doubt ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[EdStainless]

I agree with the issue about having time/distance to accelerate.
My favorite story is when we were testing U-bend tubes for ID clearance.
We would blow a carbide ball (depending on the tubing usually about 0.500") through them using 10psi air.
These tubes were usually 60-100' long.
One day the operator grabbed the wrong air supply and blew a ball with 150psi shop air.
Fortunately no one was in the way as the ball cleanly passed through the block wall of the building.

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[The Iceman]

Wow!!! That was a bad mistake that I could see myself making. Long time ago as teenage lifeguards our manager(a slightly older teenager) made a CO2 powered screw gun using copper pipe, the CO2 tank from our Coke machine and just a regular phillips screw. Fun times...

 

[LittleInch]

With a pneumatic test the force can continue for longer than a hydro test and you have the velocity of the air escaping until the item is say 200mm away from the hole?

So that gives you a "barrel" length.

See what you get from that?

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[GregLocock]

There's no way the entire tank's potential energy can be used to accelerate a fitting. One thing to do would be to calculate the airsteam velocity at the hole as a function of time, and then calculate/measure/guess/research the velocity field further away, and then use a=1/m*Cd*rho*A*v^2 where Cd is probably 1. You'll almost certainly get mach choking as the tank pressure only has to be 14 psig .

https://www.grc.nasa.gov/

http://www/k-12/airplane/mflchk.html

Cheers

Greg Locock


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[rb1957]

maybe I misread the situation, focused on "gun".

So now a picture a tank of pressurised air, leading to a "barrel" with a projectile in it.

So when the "trigger" is released the projectile has tank pressure acting on it driving it along the barrel. We can assume that the tank is much bigger than the barrel so that the tank pressure doesn't fall.
This pressure force will accelerate the projectile, F = PA = ma. lets assume the barrel is horizontal, so we don't need to worry about weight.
The projectile will experience this force whilst it is travelling along the barrel, so the velocity will be ... v = at, S = vt/2 = at^2/2, so t = sqrt(2S/a), and v = sqrt(2Sa) = sqrt(2S(PA/m))
where S is the barrel length, P is the tank pressure, A is the area of the projectile (or the barrel), m is the mass of the projectile.

Of course this is not accurate, but should be reasonable. Be careful with your units.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[JStephen]

If a tank peels apart, you could potentially have one piece flung off with more velocity than overall energy vs overall mass would indicate. Sort of the way a trebuchet sling increases the velocity.
My first thought is to put the "bay" below grade, so stuff either has to go up or else hits a wall with soil behind it.
Trying to figure what is required to stop a projectile is basically a matter of testing it, which is difficult without a well-defined projectile and well-defined velocity.

 

[rb1957]

ok, re-read the OP. So you're looking at a case when a vessel looses containment because a small piece "lets go" ? So the force driving the motion of the "projectile" the the pressure acting on the base of the part 9or projectile). So initially this is P*A ... tank pressure * area. This force acts on the part as it departs the tank only for a very short time, a second ? a fraction of a second ? ... because the tank is venting to ambient. So the initial velocity would be a*1, and PA = ma, so PA/m*1 (if the pressure is assumed to apply for 1 second. In this case, if you're interested in the "flight' path, you need to consider weight ... a typical ballistic problem.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[IRstuff]

The OP is overdesigning, since the energy of entire pressurized system cannot used to propel the chunk; the instant the chunk loosens from the vessel, the pressure wave is limited by sonic velocity at the hole, and the pressure wave immediately spreads into the ambient, so the pressure propelling the chunk immediately drops. The surface area of the chunk will dictate duration of the propulsion, although beyond a point, the internal pressure will drop quickly and the sonic velocity will no longer be applicable.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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[EdStainless]

As a science experiment (not just for fun) we deliberately blew air test fitting chucks off of tubes.
We smoothed the locking mechanism so that they would slide easily.
1" OD tube, very thin wall (0.020"), 250psi test pressure, the chucks were Al and light (about 0.5lb) and they would leave the tube at roughly 500fps. We could send them about 800', the length of the plant.
The supply end chucks had a hose and chain to restrain them.
The closed end chucks had a steel baffle plate to defect them downwards.
If the equipment worked correctly the tubes were under water when pressurized so they would only travel a foot or so (and blow 5gal of water into the air), being old analog controls occasionally they would pressurize before submerging.

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[GregLocock]

You have all the fun!

Cheers

Greg Locock


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[Geoff13]

Have you looked into ASME PCC-2 Article 5 "Pressure and Tightness Testing of Piping and Equipment"?

Appendix II of this article calculates the stored energy of the system under pneumatic test conditions.

Appendix III then calculates safe distances based on that energy. One distance is for ear damage, and the other is for fragment throw distance.

Not sure what your dimensions and pressures are, and perhaps this method is overkill for you, but it can be a rough check of your other answers.