Explosive Force: Comparing CO2, Aerosol, & Firework

[SPLife]

I'm not really sure if this is the appropriate place to ask this and am not familiar with this forum so I apologize if I posted in the wrong place, but I would like some help.

I need to compare the explosive force of a 12 gram CO2 canister(Like in BB Guns), a regular 275 gram aerosol can(such as air freshener or bug spray) both of which are pressurized and will rupture with heat(The force of that rupture, explosion basically, is what I need to figure out). Also for comparison I need to find out the explosive force of a legal(In any state), consumer available(no license required) firework - Preferably one small, like a bottle rocket(From Black Cat Fireworks website - "We load our rockets...with the maximum 130 milligrams of report powder", though I'm not sure it that's what's needed), and one large like multiple shot artillery shells/mortars.

For the aerosol can and Co2 canister I need it as is, not emptied and filled with something else. The explosion would have to be the result of heat causing pressure to build until rupture. The fireworks would obviously be when it goes off.

If given the formulas to calculate this for each and told what to plug in where I can do the exact math myself, but all help is appreciated.

This information will be going toward a court case, and as such is not going to be tested physically, the numbers are all that are needed.

I appreciate any help, thank you.

 

[russ_watters]

Force is really meaningless here. It depends on the mechanics of the explosion, how far you are from it, and what media is transmitting the energy. What you probably really want is energy.

To get the energy of an exploding gas, you take the internal energy at the beginning and subtract the internal energy at the end. All you need is the starting pressure and temp. You have to use the ideal gas law to find the final temperature (it drops as the gas expands). Here's the ideal gas properties for air: http://energy.sdsu.edu/testcenter/testhome/Test/solve/basics/tables/tablesIG/igAir-Eng.html

 

[photonsquared]

I agree with Russ. For your mechanical explosions (no chemical reaction) the rupture pressure of the cans is the pressure you need to calculate, which can be approximated using hooks law and the material properties of the container. The firework is a different matter. In general you can approximate pressures due to propellants using the ideal gas law Russ mentioned setup as a ratio of initial and final conditions and solve for the final pressure. However there are assumptions that must be made in order to keep this calculation reasonably simple these are that the process is fast enough to be adiabatic. You also need to determine if you are going to assume constant pressure (i.e. the initial and final volumes are different) or constant volume (i.e. the initial and final pressures are different). Depending on which best approximates your scenario you would need the isochoric or isobaric flame temperature of the propellants of interest. Because these are not easily obtainable numbers for propellants this may be difficult. If you had these numbers you could calculate the final pressure in a constant volume system. One additional catch is to determine the volume of gas produced at STP for the propellant, which is a function of Bulk Burn Rate, Geometry of the Grain, and the density and gas output of the propellant. Data that is hard to come by for propellants. I know that Paul W. Cooper has written several books on explosives that may help.

 

[SPLife]

Thanks for the responses.

My main thing is I need to approximate the potential danger of each in comparable terms. Is that what this will help me do?

I obviously have not taken a physics course as of yet, and no other specific abilities really apply here so I am clueless as to what exactly I need to do to get the proper assessment, so I'm sorry if I sound completely ignorant.