Pascals's Principle and Airsoft?

[Chemical Bros]

Alright I was just thinking about the internals of an airsoft gun and I began to wonder how to calculate the force exerted on the BB as it leaves the barrel. Here is an image of the internals:

Link to image:

http://www.google.ca/imgres?imgurl=...age=1&ndsp=21&ved=1t:429,r:14,s:0&tx=60&ty=36

I then decided to use hooke's law for the force of the spring as that would be the force exerted on the piston. My next step, as I was never really taught fluid dynamics, was if I was to use Pascal's principle to calculate the force at the nozzle (black piece right before the BB).

F(1)=-kx

therefore (using pascal principle)

F(1)=F(2) * (A1/A2)

-kx=F(2)*(A1/A2)

F(2)=(-kx)/(A2/A1)

I looked up the principle and most of the time it says it works if its static and confined. My question is if the equation can be used in this circumstance or if there is another way to find the force exerted on the BB? I also came across this website:

http://www.engineeringtoolbox.com/pneumatic-cylinder-force-d_1273.html

Are these equations viable or would they not suit this type of piston/cylinder? Thanks in advance!

 

[omoplata]

I don't know how accurate it will be. Maybe your results will be comparable to experiment. But if you are looking for an alternative approach, I guess the http://en.wikipedia.org/wiki/Bernoulli's_equation#Compressible_flow_equation" can also be used? You'll have to use the Compressible flow equation because air is compressible.