Calculating Force Generated by Gas Powered Launcher

[Quaboble]

A student designs a gas powered launcher that consists of a pressure tank, a valve and a barrel. When the valve is turned the gas, in this case air, expands propelling whatever is in the barrel. The pressure tank and barrel have the same dimensions while the valve connecting the two has a diameter of 25 mm. Assume the valve instantly opens. How much force in Newtons is generated when the valve is opened at the exit end of the valve (point X)?

Please help me, I'm totally lost :( I actually made this question as I have built this launcher and am wondering what its power theoretically is. I was never taught how to do this.

 

[Shooting Star]

If you need to know the muzzle velocity of the projectile, why are you asking for force, because that won't be constant? Have you done adiabatic expansion.? Show some attempt, and help will come. Read up your books or notes.

 

[Quaboble]

Cant really attempt it... I've only had 1 complete term of basic physics, and this isn't even a question assigned to me by school. How will muzzle velocity of the projectile help me?. I am just curious to know if it is possible to calculate the force expelled by the expanding air.

 

[Shooting Star]

At the moment the valve is opened suddenly, it is possible to calculate how much force the compressed air exerts on an object that is pressed against the outlet of the valve. It is the product of the pressure in the tank minus atmospheric pressure multiplied by the cross-sectional area of the end of the valve , in any self consistent system of units.

 

[Quaboble]

Thanks! So it should work like this:

pressure: 140 Psi - 14.7 Psi = 125.3 Psi (converting to pascal = 863,913 Pa)
cross sectional area of valve: .0125 ^2 x Pi = .00049 meters squared

then: 0.00049 meters x 863,913 Pa = 423.317 Newtons

Does that sound about right?

 

[Shooting Star]

I haven't checked the numbers, but the concept is correct.

 

[Quaboble]

Alright thanks a bunch for the help man!

 

[TVP45]

Usually it's not the valve area, but the cross-sectional area of the barrel that mostly determines the force. You'd have to check the flow through the valve to see if that's limiting, but it's possibly not. Keep in mind that the supply tank will lose pressure as the potato (pumpkin, whatever) goes up the barrel. And, as noted earlier, this is adiabatic; I've seen ice fly out of these things.

And, I got to ask you, man. What material are you putting 140 psi in? Should I introduce you to ole 3 fingers McGurk who exploded a tire at 100 psi? Because air is compressible, pressure is somewhat dangerous.

By the way, most people do the muzzle velocity by "borrowing" the baseball radar gun from the coach's office. Once, we even got the local police to come out and do it.

 

[Quaboble]

Hmmm... well the ammunition is coca cola bottles and cans (both have a near perfect fit for 70 mm piping). The rounds are put directly against the valve which protrudes a bit into the actual barrel so the gas hits the projectile before it expands into the barrel. The pressure tank is made out of PVC piping and i have taken it to 140 Psi already. Hmm well I live in Europe (though i used to like in the USA) so baseball is rare and i doubt my school even has a radar gun. European schools really miss out on the sports when compared to American schools :P