Im looking to build a formula for the velocity of a spud gun projectile. the ordianry velocity forumlas wont?

Question

work because i cant include pressure in them . the variables are D=diamter of pressure vessel, d= diamter of barrell, L= length of pressure vessel, l = length of barrell, t = time for valve to open, g = weight of projectile, p = pressure in psi/bar and i can use the frictional force of the barrel material and projectile material if needed

Answer 1

first, can you assume the volume of the barrel is small compared to the pressure vessel, or is it significant?
if it negligible then the process is essenitially
pressure in vessle
minus the pressure drop across the valve (usually given in the valve spec sheet)
times area of barrel
equals the applied force.
force times the length of the barrel is the energy input into the projectile. (this is where the size in important. if the pressure drops as the projectile moves down the barrel then it becomes a calculus problem)
the energy input is divided between the frictional force overcome sending the projectile down the barrel and the kinetic energy of the projectile.
hope this gets you started

Answer 2

To determine the velocity, you first have to determine the acceleration, Sum of the forces = m a. To do that you need to do the chemistry of the propellent.

This is no easy feat.