I know this may be impossible because they are two different units, but my Smart Parts Ion paintball gun has a psi gauge and that gauge (in PSI) tells me how fast i am shooting at. However paintball shots are measured in FPS. Is there any way?
PSI = Pounds per Square Inch
FPS = Feet Per Second
It is possible to convert between the two, but it won't be easy because there are quite a few variables to contend with.
First and foremost, the you'll need to know the pressure differential between the supply (the tank) and the outside ambient pressure. The higher the outside pressure, the lower your FPS will be. Also consider that the PSI of the tank continually decreases as it empties.
Next, you need to know the surface area and the weight of the paint ball. The higher the surface area, the more the paint ball is affected by the pressure. The higher the weight, the more energy required to move it.
To recap the variables you need:
Effective pressure = (Tank's absolute pressure) - (Absolute outside air pressure)
Ball Surface area = (4π(d/2)^2) [4 times pi times (diameter divided by 2) to the power of 2)
While it's possible to convert PSI to FPS mathematically, it's not really practical. I'd recommend getting an electronic speed gauge which actually measures the speed of the paint ball and allows you to calibrate your gun properly.
It is dimensionally impissible to convert psi to ft/s
Dimensions of psi are ML^(-2) (mass / length²)
Dimensions of ft/s are LT^(-1) (length/time)
So they are completely unrelated
There may be physical characteristics of your weapon that will apply some sort of fomula to do so but it is not by some constant
Clearly ML^(-2) * L³T^(-1) / M →LT(-1)
So dimensional analysis immediately states that some sort of process that multiplies pressure (psi (ie lb /in²)) by volume flow rate (in³/s) divided by mass (lb) will give speed (in/s) So divide that by 12 (to get ft/s).
But this does not tell HOW that formula is put together and what other dimensionless constants are involved.
These can only be determined experimentally and are dependent on the characteristics of the paintball gun and the paintball itself.
psi is pound per square inch, a measure of pressure. Foot pounds is a measure of work or energy (a scalar) and also a unit of torque (a vector). 1 foot pound = the energy expended when one pound-force acts through a distance of one foot along the direction of the force. Pressure, on the other hand, doesn't need any energy. A pressure of 100 psi can exist forever, without any use of energy.
You need 5 equations:
A = (1/4)πd^2
F = PA
m = W/g
F = ma
v^2 - v0^2 = 2as
d = bore diameter of the gun in inches
A = cross-sectional area of your paint ball, in^2
W = weight of the paint ball, lbf
m = mass of the paint ball, lbm
g = acceleration due to gravity, 32.2 ft/s^2
v = muzzle velocity, fps
v0 = 0 in this case.
s = L = length of your gun barrel
All this assumes negligible friction and no appreciable pressure drop during firing. The pressure you are reading is gage pressure, which is already the difference between the pressure and atmospheric.
v^2 = 2as
v^2 = 2aL
v^2 = 2FL/m
v^2 = 2FLg/W
v^2 = 2PALg/W
v^2 = 2P(1/4)πd^2Lg/W
v^2 = 32.2πPLd^2/(2W)
v = d√(16.1πPL/(12W))
(The 12 appears in order to to convert L from inches to ft.)
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