Speed of projectile launched propelled by air pressure

[Pharrahnox]

Homework Statement

I am wondering what the speed of a projectile would be if it were launched with compressed air at 115 psi (approx. 800 kpa). The weight of the projectile is 4 grams. I have converted the weight to mass (please correct me if I am wrong) which makes it 0.408 grams. The diametre of the outlet is 8mm.
Is there a way to figure this out without knowing the time taken?

Homework Equations

f = ma

where:
f = 40.2N
m = 0.408(unknown measurement)

pressure = force/area

The Attempt at a Solution

I have looked all over the internet for anwers to this question, yet couldn't find something helpful.
The force of the air is 40.2N.
The mass of the projectile is 0.408(i don't know what measurement to use...).
I have found the accelleration to be 98.529(i don't know what measurement it is...).

But I want to find the speed and not the accelleration. How do I get it to that, because I have looked on the internet through several threads and sites, but nothing has come up.

 

[LawrenceC]

One aspect of the problem that you have not mentioned is the volume of the compressed air. Generally, with airguns, there is a volume. As the projectile is pushed by the gas, the pressure of the gas drops due to increased volume thereby affecting the force on the projectile.

 

[technician]

Your calculation of the acceleration is fine. To get to the next step ASSUME the pressure (acceleration) is constant along the length of the barrell. Do you know this length...it would enable you to calculate (estimate) the velocity.
Alternatively ASSUME the pressure has dropped to zero when the projectile leaves the barrell... then use an average acceleration 0.5 x 98.5 to get a second estimate.
This does not give you an exact answer for which you need (as LawrenceC has mentioned) some more detailed knowledge of how the pressure varies along the barrell.

 

[Pharrahnox]

The length of the barrel is 82cm, and the total volume of compressed air is 24 litres, but it only uses 72.5805 cm3 of air at a time.
If this amount of volume is not sufficient to launch the projectile at its full potential with this pressure, assume it has all 24 litres behind it.

I am just wondering how you figured out the accelleration down te barrel with the equation: 0.5 x 98.5. What is the 0.5 for?

 

[technician]

Sorry!...the 0.5 is to give an average value to use for the acceleration.making a very big assumption that the acceleration is 98.5 at the start but drops to zero at the end of the barrel, because the air pressure had dropped.
Looking at your figures I would say that the pressure does not drop to zero and it may be OK to assume the pressure and therefore the acceleration is more or less constant.
I will go over your figures to see if I can get more to pass on

 

[Pharrahnox]

ok thanks.

 

[Pharrahnox]

I have found a formula posted on a site that says: speed = 2 * accelleration * distance of accelleration.

There were other factors at the start of the equations, but they didn't apply to my situation. It turns out that the projectile travels at around 160m/s (580km/h).

I have also realized now that the best way to increase the speed of the projectile, well more like the cheapest and easiest way, is to get a longer barrel. Using this formula, if the barrel was 10m long and it could maintain the full 115 psi, then it could launch the projectile at nearly 2km/s. But this sounds impossible.

Is there a limit of speed that air can travel? And what is the way of calculating the "speed limit" with the amount of pressure?