muzzle velocity calculations

That is a heavy potato. I'm sure somebody else has some sort of math. I'd not expect more than 200 or maybe 225 feet per second.

One approach I suppose you could use that would give you an approximation due to neglecting friction is to make the stored energy in your compressed gas (air?) equal to the kinetic energy of your projectile.

The equation I use (particularly for calculating the stored energy in pneumatically testing equipment) is:

∆U = (k/k-1) P₁V₁[ 1- P₂^(k/k-1)/P₁ ] * 144

Where: W = work, ft-lbs (N-m or joules)

∆U = stored energy, ft- lbs (N-m)

P₁ = Upper pressure, psia (N/m²)

P₂ = Lower pressure, psia ( N/m²)

V₁ = volume of gas, ft³ ( m³)

K = specific heat ratio, c_p/c_v at test pressure. (for air and nitrogen k = 1.4, for helium k = 1.66)

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NOTE that you need to provide the volume of air (which you didn't mention)

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So then, equating stored energy to kinetic energy:

∆U= (1/2)mv²

OR: Velocity = √[(2·∆U)/m]

And please "play" safe - compressed gases are dangerous.

Or perhaps this is the equation, taken from ASME PCC-2 (I don't feel like checking if the two equations are equal, but for sure this one is correct):

E =[1/(k − 1)]·P₁·V·[1 − (P₂/P₁)^{[(k − 1)/k]}]
where
E = stored energy
k = ratio of specific heat for the test fluid
P₂ = absolute lower pressure, psia
P₁ = absolute higher pressure, psi

V = total volume under test pressure, ft³

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And I just had another thought ................. these equations are assuming a constant volume, but your volume will be changing - so these are definitely approximations, hopefully someone could shed some light on how to account for the change in volume (it's Friday night and my brain was shut off a couple hours ago ).

Force on the projectile is pressure(Lbs/square inch) times area that pressure is applied to (pI time radius squared, given 3 inch diameter).

From the force and mass you can back out acceleration. From there use the equations here...

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html

P.S. Regardless of the math, I want to know the results. Actually what exactly are you intending to shoot that weighs 4.5 lbs?

I've heard of Potato cannons, but never actually seen one launch a potato.

Apparently you can get one to throw a potato a hundred yards.

Del the Cat was kind enough to put up a clip of his repeating crowbow.

Potato gun calculation:

http://s87572736.onlinehome.us/Writeup.html

Excellent link!

As for previous poster, my children and I had great fun with straw bale forts and potato cannons! Always buy Aquanet hairspray. Wear appropriate safety equipment. We did construct one that used replaceable gas fuel canisters, but had difficulty getting the mix just right for ignition.

And no, there is nothing reasonable or eco friendly about using a food stuff for entertainment, but potatos didn't cost .99 cents a pound then.

As for 4.5 pounds, I would have to guess the poster is going to launch a smallish pumpkin.

I have used oxy-acetylene before ............ trust me, PVC does not stand up under the right mixture. We upgraded to a cast iron unit