Can i make an equation for this(practically) or is there already one

[bunkerking]

i want to make an equation for science class that relates the presssure (psi) and the density of an object. I am firing paintballs from my gun at different pressures. I want to be able to predict based on the density of each paintball the velocity it will shoot at a particular psi. ex: if i am shooting at 110 psi. i get a velocity of 295. (not actual numbers, just an example.) I think that it will be some for of inverse variation, like velocity=psi/density, or something along those lines.

thanx for the assistance,
ferris

 

[brewnog]

They will be related, but dependent on a number of factors. The volume of air in the charge, the shape of paintballs, friction between the paintball and the barrel, barrel geometry, ambient air conditions, release mechanism, and paintball parameters will all affect your result. Finding a formula which simply relates the pressure behind the paintball to the velocity at which it fires would not be very useful, in a general sense.

 

[El Hombre Invisible]

Won't it depend on how long the paintball is subject to that pressure? You can determine the force acting on the ball if you know its area by F = PA, then determine the acceleration from it's mass by F=ma, but unless you know the duration of the force then I'm not sure you can determine the final velocity this way. However, you could do this experimentally and (hopefully) get a value for the duration which you could then use as a constant by using different guns of different pressures?

There's probably an easier way...

 

[bunkerking]

i know that it won't be very useful...i am trying to use this a denonstration for my velocity=psi/density formula that i want to make. i am actually trying to predict the velocity of an object moved in space by a certain burst of air related to the objects density. such as a man on a space walk who would use bursts of air to propel themselves around. i want to know based on the density and or mass of the man how much pressure psi is required to move him at a desired velocity...the paintball idea was only to be an example. I am looking to do this on a fairly basic level so if it isn't perfect that is ok, i am really wondering if i am just really off base or not..


thanx again
ferris

 

[brewnog]

Be careful typing things like "velocity=psi/density". You'll notice that units of pressure divided by units of density do not give units of velocity.


If you want to do this at a basic level, your idea of a space-walk thing might be much better for you. Read up on the principle of conservation of momentum, it's simple, and you can apply it to lots of things. You won't be inventing a new formula though, sorry.