Are My Mathematica Calculations for Pneumatic Gun Velocity Accurate?

[axemaster]

Ok, so I'm building a pneumatic gun with a barrel 0.3m long, operated using air pressure. The barrel is square, 1cm on each side, and the projectile is a 5g elongated cube. I wrote some code in mathematica to plot the speed in m/s versus the air pressure in psi.

I was wondering if anyone could verify that my calculations are accurate, and if not, where I may have gone wrong. I'm pretty confident, but as I'm spending money on this I want to be sure.

The mathematica code is below:

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(*Variables;
x is the distance over which it accelerates;
m is projectile mass in kg;
area is area that the force acts on in cm (square barrel 1cm on each \
side);
*)

x = .3;
m = .005;
area = 1;

(* Constants and conversions *)
psiToPascalsConstant = 6894.7573;

pressforce[pressure_] := (pressure*psiToPascalsConstant)*
area; (* gives N *)

velocity[force_] := ((force/m)*Sqrt[(2 x)/(force/m)])/100;

Plot[velocity[pressforce[psi]], {psi, 0, 150},
AxesLabel -> {Psi, Velocity}]

-------------------------------

Thanks for your help!

-Axemaster

 

[Achy47]

Dear Axemaster,

Thank you for sharing your project with us. It is great to see individuals like you exploring the world of science and engineering.

I have looked over your code and calculations, and everything seems to be in order. Your approach to calculating the velocity of the projectile using the force applied and the distance over which it accelerates is correct. Additionally, your use of constants and conversions is also accurate.

The only suggestion I would make is to double check the units in your final calculation for velocity. It appears that you are converting from meters to centimeters, but then dividing by 100 again. This may result in a small error in your final velocity calculation. I would recommend keeping all units in meters for consistency.

Overall, your calculations seem to be accurate and your approach is sound. However, as with any project, there may be unforeseen variables or factors that could affect the outcome. I would suggest testing your pneumatic gun in a controlled environment to validate your results and make any necessary adjustments.

Keep up the great work and happy experimenting!