Anyone feel free to correct me --
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... and how does the length of the barrel affect inital velocity (ie what is the ideal volume ratio and barrel length)
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You have to think of the pressure in the cannon as a force. As long as the pressure differential in the cannon (while the balloon is in there) is greater than the atmospheric pressure, then the balloon will have some velocity when leaving the cannon. As long as the pressure in the tank is greater than the pressure in the cannon, the balloon will continue to accelerate. This also means that if the cannon is too long, the pressure will reach a peak value and then decrease, robbing your beloved balloon of its balistical distance.
Let's figure this out. You want 100m minimum right? Using the 3 kinematic equations and vector analysis of gravity vs distance (ignore air resistance for a second), figure out the Vi (initial velocity) at angle 45 degrees that the balloon must have to reach 100m. This must be the exit velocity of your cannon. Look these equations up.
From here, look at the available equations that deal with pressure, force, velocity, and mass. Velocity = acceleration * time (v = a * t) and Force = mass * acceleration (F = m * a). Also, looking up equations that show the relationships between two pressure states and their volumes in a closed system, you'll find Boyle's Law: p1 * V1 = p2 * V2 (p = pressure, V = volume). Note that it assumes 100% valve efficiency. What this really means is that if the volume of your barrel is greater than the volume of air coming from your tank, the pressure (therefore force) inside the barrel will be *less* than the pressure inside the tank. Practically, in order to facilitate proper pressure of both connected systems when the balloon is at the exit point, the volume of air of the tank must be at least 1.5 * the volume of the barrel. Finally, the unit of pressure (psi) gives away how to find the force from the pressure: F = p / A (A = cross-sectional area of the barrel).
There may be a better way, but I like holding a few things constant so I can get some starting #'s, then work from there. V1 and p1 are constant, and V1 > 1.5 * V2, so what volume of the barrel do I want? Well, the balloon (aka the ammo) has special constraints (too much surface tension will make it bust), so I want to keep its volume relatively low. This means a small balloon -- so pick a diameter -- the 3" you've picked seems to be ok. From here, figure out the length of the barrel -- V2 = L * A (L = length of the barrel & A = Cross-sectional area of the barrel) that is
less than V1 / 1.5. When you plug this back into Boyle's law, you should have a theoretical working pressure, p2, inside the barrel.
From here you can calculate the acceleration of the balloon in the barrel: You know the force of the air from p2, and you know the mass of the balloon. You're almost there -- V = a * t -- so now you have to figure out how long it take for a constant acceleration to move certain distance. Since you're knowledgable about the kinematic equations by now, you can figure out the time, and therefore calculate the exit velocity of your balloon. If that velocity isn't at least as high as what you calculated back in the first step, you'll have to play with the constraints in the system to figure out what it takes for it to work.
Good Luck.
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Would a heavier or lighter water balloon go further? Is there an ideal weight somewhere?
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In physics you will learn that in an ideal situation the mass does not affect the velocity given a constant acceleration (aka gravity). However, since your cannon applies constant force instead of constant acceleration, acceleration is a result of the force:
F = m * a -> a = F / m
Therefore the smaller the mass, the larger the acceleration, giving a higher exit velocity.
As for air resistance and your water balloon, in order to increase the mass to add momentum that would easily overcome air resistance, you would have to increase the size of the balloon by adding more water. This would increase the surface area of the balloon, therefore making more air resistance. Hence, for air resistance purposes, size doesn't matter.