lysanderxiii
Member
Limiting fluid flow to Mach 1 in a barrel would not only limit single stage guns to whatever the local sped of sound is it would make multiple stage guns pointless as their maximum velocity would be limited to that velocity.I did a little more research (even touched my fluids and thermal text books {ewww...}) and I am fairly convinced we cannot treat these combustion gases as an ideal gas. Nearly all the products of combustion are supercritical fluids while in the gun bore and thus the ideal gas law no longer works. The ideal gas law assumes there is more space than particles and that the particle do not chemical react or are not attracted to each other, they simple act like perfectly elastic particles bumping into each other. CO2 at 20,000 psi and 800K is nearly the same density as water at room temperature. And there is no doubt that the particles in the gun barrel are interacting as more than simple elastic particles since a fair portion of them are combusting with each other.
I have found research paper measuring CO2 (a product of combustion in our discussion) above the critical point (7.39 Mpa/1071 psi and 31C/88F) and they have experimental measure the speed of sound in super critical CO2 at over 500 m/s at ~10MPA (1500 psi) only slightly elevated temperatures (~400K). Take that temperature up to 2500+ K and I think we would have a very high speed of sound.
In many ways supercritical fluids behave like liquids rather than gasses. The speed of sound in air at standard conditions is, as we all know, ~340 m/s in a liquid like water at room temperature is nearly 1500 m/s. As I stated in the first paragraph CO2 at only 20,000 psi has nearly the density of water. In that light I think a speed of sound in combustion gases approaching 2000 m/s seem plausible. That said I really wish I could find something more definitive.
-rambling
A simple two stage gun, operated by the Navy was capable of launching 250 grams at 15,000 fps and a 60 gram projectile at 27,000 fps. The first stage was basically an old 12 inch gun breech, and used regular smokeless propellant, and second stage of this gun was auto-ignition of a pre-balanced hydrogen-oxygen atmosphere driving a 2 inch sabot carrying the payload.
Also, even a speed of sound of 2,000 m/s would be to low if you limit guns to sonic gas velocities. Project HARP manage to get muzzle velocities of 7,100 fps (2164 m/s) out of a single stage 16 inch gun.
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