# Calculating the energy in projectiles from burst pressure vessels

1. Apr 19, 2010

### Airou

Hi everyone,

I'm writing a safety case for pressure testing equipment using gaseous nitrogen (hydraulic pressure testing in this case is impractical) and I am trying to estimate the energy transferred to a projectile in the case of something bursting so I can sensibley mitigate against this eventuality.

I tried to estimate this by calculating the velocity acheived by the pressure acting on a projectile of given area and mass as it rides the expanding pressure wave and is accelerated by it. The figure I came up with seemed rather low in doing this.

Should I just assume that any projectile will travel at the speed of the burst/explosion (which I guess will be the speed of sound)? Or is there a more sensible way of working this out?

Many thanks.

2. Apr 19, 2010

### xxChrisxx

Nah, you don't get supersonic chunks of steel from exploding pressure vessels. This is a very very tough one to figure out, as you never really know how the thing is going to fail. I use a similar method to you, don't know if it's right or not.

Can you give some more information on the test? Pressure, whats the vessel rated to, rough dimensions etc etc? What sort of figures have you been getting from your calculations?

This is the sort of thing of 'if in doubt, make it stout'. Ie you never ever get to the point where it does fail. Good suck it and see engineering.

3. Apr 19, 2010

### Airou

Thanks for the reply.

The rigs I'm looking to test are made out of a whole load of components, not just one pressure vessel - refrigeration parts, flat plate heat exchangers, a compressor, pump, copper pipe etc. They are experimental rigs and are assembled by hand, so all the brazing is done by technicians. I know when most metal containers burst they just split, but I can't rule out that one technician might put in a sloppy braze after a night on the fizzy pop and something flies out if there is a failure.

I'm trying to change the relaxed attitude to health and safety in the workshop and would like to have all pressure testing that can't be done hydraulically to be done behind a lexan screen or something that can either absorb or deflect any likely projectiles. I want to include the calc for a safety case, and then use it to size the thickness of screen needed.

Currently the pressure test is done at 20 bar with an internal system volume in the assembly of approx 4 litres. For a 5mm diameter, 5 gram projectile I was calculating an ejection velocity of 0.14 m/s when assuming it was ejected from the surface of a spherical body of diameter 5cm. Intuitively this seemed very low, the air rifles I shot as a kid can't have held much pressure but were perfectly capable of putting a hole through 1/4" wooden boards. Looking at my calcs I wasn't sure how to tail off the pressure as the projectile is ejected, that is probably why it is on the low side, but I have no idea what is a likely figure - the pressure will be present for sometime as the gas filters through to the burst from the convoluted paths in the system, but it's not like there is a barrel to constrain the pressure and make the maths easy!