i want to calculate the velocity in m/s of all these spud gun projects i see on the internet.?

Question

can someone suggest a formula? where the variables are
v= velocity in m/s (what we want to know)
D=internal diamter of pressure vessel (mms)
L = length of pressure vessel
d= internal diameter of barrell (also i.d of valve leading to pressure vessel)
l = length of barrell
M = mass of projectile in grammes
P = pressure of pressure vessel in psi (which i will covert to bar....anyway know how to convert bar to pascals?)
T = time valve is open in seconds
the spud gun will consist of a pressure vessel storing compressed air, with a valve in front of it leading to the barrel. when the valve is opened air will be released pushing a projectile out the barrell
couls soem one build me an equation to calculate the velocity of the projectile using these variables? i see all these spud gun sites on the net and id love to know how fast they go...
also whats the speed of sound?

Answer 1

I'd suggest you first try the site listed below where you can find a downloadable spreadsheet that predicts velocity. You can deduce the author's equations from it. It's actually a time-stepping simulation rather than analytical equations. However, a bit of theory wouldn't hurt either. First, to keep it simple, let's assume the pressure is constant for T, the lesser of the time the valve is open and the time the projectile remains in the barrel. This is actually not a good assumption since many spudguns have pressure vessels that are smaller than or not much bigger than the barrel volume. Anyway, during T the spud is subjected to a force F=P*barrel area = P*pi*d^2/4. The net force accelerating the spud is F - friction force, so its acceleration A=(F-Ffriction)/M and its velocity v=A*T. I don't know the practice on valving. It may be that open valve time is always less than barrel transit time, but if not, you can compute the distance S that the spud would travel during the open valve interval T; S=0.5*A*T^2. If S>l, then T is the time spent in the barrel, which is SQRT(2*l/A), and you should recompute v.
Another assumption would be that each shot entirely empties the pressure tank. In this case we simplify by disregarding pipe friction, thermodynamic losses (like failure to fully expand due to cooling) and any other losses you can think of, and assume the potential energy of the compressed air is converted to kinetic energy. The potential energy PE = 0.5*P*vol (where vol is tank volume = L*pi*D^2/4). The kinetic energy of the spud is 0.5*M*v^2. Thus v=SQRT(P*vol/M).
About other questions, 1 psi = 6894.75729 Pascals, and speed of sound =340.29 m/sec.
Note that with what you have given in your question, you have a lot of units conversion to do.
EDIT: See friction stuff added above. The spreadsheet includes friction effects.

Answer 2

Allot of issues we did when we were young children are not allowed on the instantaneous, till now too lengthy, the youngsters will want a license to fart. I discovered a thanks to shoot on my cousin;s farm even as i became 9 y/o, and had a bb gun at abode. i quite desire I nonetheless had it, and would get yet another one now that i imagine of it.

Answer 3

Spud gun?