Fluid Dynamics...

[lpetrich]

True, but that's the way that the adiabatic index or heat capacity ratio is defined.

From the hydrodynamic equations, one can find a solution corresponding to expansion into empty space. One starts with the hydrodynamic equations

d(D)/dt + sumi d(Fi)/dxi = S

D = density, F = flux, S = source

(den) = mass density, v = velocity, P = pressure, u = energy per unit mass. That energy and pressure are related by
du = P*d(den)/(den)2 + T*d(s)
where s is the entropy for unit mass and T is the temperature.

Mass: D = (den), Fi = (den)*vi, S = 0

Momentum (component j): D = (den)*vj, Fi = (den)*vi*vj + P*dij, S = fj

Energy: D = (den)*((1/2)*v2 + u), Fi = ((den)*((1/2)*v2 + u) + P)*vi, S = f.v

For constant gamma, the equation of state is u = 1/(gamma - 1)*(P/(den)).

Here's a solution for expansion into empty space. It starts at a point and and expands at a constant rate. The expansion start moves at velocity -a, where a is the speed of sound in the un-expanded material. The solution:
w = x/t (w >= -a)
v = (2/(gamma+1))*(w + a)
den = (den)0*(v - w)2/(gamma-1)
P = (1/gamma)*(den)*(v - w)2

The density becomes 0 when w = (2/(gamma-1))*a

I found this solution very quickly with Mathematica.

[Gawdzilla Sama]

It just so happens I know the answer to this one. Steam under pressure builds up a shock wave at the mouth of a nozzle if it's squared off. The steam can pass through no faster than the speed of sound for steam at that pressure. However, if the nozzles are venturied, flaring outward instead of squared off, the shock wave doesn't build up and the steam can move through the nozzle much quicker.

[Blondie]

It just so happens I know the answer to this one. Steam under pressure builds up a shock wave at the mouth of a nozzle if it's squared off. The steam can pass through no faster than the speed of sound for steam at that pressure. However, if the nozzles are venturied, flaring outward instead of squared off, the shock wave doesn't build up and the steam can move through the nozzle much quicker.

The same principle holds for compressed bullshit I imagine..

I thought this thread was going to be about friction coefficients in a liquid medium and variable penetrative form factors.. Turns out it was much less interesting.

[Gawdzilla Sama]

It just so happens I know the answer to this one. Steam under pressure builds up a shock wave at the mouth of a nozzle if it's squared off. The steam can pass through no faster than the speed of sound for steam at that pressure. However, if the nozzles are venturied, flaring outward instead of squared off, the shock wave doesn't build up and the steam can move through the nozzle much quicker.

The same principle holds for compressed bullshit I imagine..

I thought this thread was going to be about friction coefficients in a liquid medium and variable penetrative form factors.. Turns out it was much less interesting.

The steam I worked with last was 900 psi at 850 F. I think that counts as compressed.

[GreyICE]

I'm still not convinced of the original principle.
Sound is a wave, where the medium doesn't translate, it just vibrates and passes on the energy.
In a rifle barrel, the air that's pushing the bullet isn't vibrating about a fixed point, it's being bodily moved and accelerated. So long as you can keep accelerating it, it will move faster and faster.
Imagine a dozen springs lying horizontally, not compressed, touching each other end to end. Push at one end, and the disturbance will travel to the other end at a slowish speed, like a sound wave.
But compress all of them fully, and let one end go. The freed end can reach speeds much higher than the "sound" wave, because it's being accelerated over a longer time.

You'll find that your compression waves don't exceed the speed of sound in metal. That is, after all, what sound is - compression and expansion waves.

The speed of sound in metal, however, is quite enormously higher than the speed of sound in air, so you can easily exceed the speed of sound in air.

[GrahamH]

I'm still not convinced of the original principle.
Sound is a wave, where the medium doesn't translate, it just vibrates and passes on the energy.
In a rifle barrel, the air that's pushing the bullet isn't vibrating about a fixed point, it's being bodily moved and accelerated. So long as you can keep accelerating it, it will move faster and faster.
Imagine a dozen springs lying horizontally, not compressed, touching each other end to end. Push at one end, and the disturbance will travel to the other end at a slowish speed, like a sound wave.
But compress all of them fully, and let one end go. The freed end can reach speeds much higher than the "sound" wave, because it's being accelerated over a longer time.

You'll find that your compression waves don't exceed the speed of sound in metal. That is, after all, what sound is - compression and expansion waves.

The speed of sound in metal, however, is quite enormously higher than the speed of sound in air, so you can easily exceed the speed of sound in air.

That's what sound is, but a bullet isn't a sound wave. I doubt that the speed of sound in metal has anything to do with limiting the speed of a projectile in a barrel, and we know that a bullet can be accelerated to more than the speed of sound in air at STP.

If a super-pressure balloon bursts in vacuum the air travels rather than propagates a pressure wave. Entropy is not constant.

[GreyICE]

I'm still not convinced of the original principle.
Sound is a wave, where the medium doesn't translate, it just vibrates and passes on the energy.
In a rifle barrel, the air that's pushing the bullet isn't vibrating about a fixed point, it's being bodily moved and accelerated. So long as you can keep accelerating it, it will move faster and faster.
Imagine a dozen springs lying horizontally, not compressed, touching each other end to end. Push at one end, and the disturbance will travel to the other end at a slowish speed, like a sound wave.
But compress all of them fully, and let one end go. The freed end can reach speeds much higher than the "sound" wave, because it's being accelerated over a longer time.

You'll find that your compression waves don't exceed the speed of sound in metal. That is, after all, what sound is - compression and expansion waves.

The speed of sound in metal, however, is quite enormously higher than the speed of sound in air, so you can easily exceed the speed of sound in air.

That's what sound is, but a bullet isn't a sound wave. I doubt that the speed of sound in metal has anything to do with limiting the speed of a projectile in a barrel, and we know that a bullet can be accelerated to more than the speed of sound in air at STP.

If a super-pressure balloon bursts in vacuum the air travels rather than propagates a pressure wave. Entropy is not constant.

Well check your assumptions. There is gas in the barrel before it reacts? No? Well what happens?

The same thing that happens in afterburners. An afterburner works because it takes a known quantity of gas, and creates more. You're rewriting the rules of the game on the fly. Gas is being created. Since a molecule of gas occupies a constant volume regardless of size, it more or less erupts into existence. This creates IMMENSE pressures on the rear of the bullet, that create enormous velocities. No wave is propagating, such as with jet engines or your hypothetical balloon in deep space (we'll get to that). Rather material is just literally existing in a space that is utterly insufficient to contain it. As for how it works, you're assuming it all burns at once. But it can't. Using a high explosive, such as TNT, with equal power to gunpowder, would detonate the barrel, destroy the gun, and wound or kill the user. Rather, gunpowder combusts. The initial combustion carries the particles of gunpowder down the barrel, where they continue to combust at high velocity. Think about that for a second. Is sound moving 'at the speed of sound?' Well, relative to a stationary observer, yes. Relative to the sun, the earth is orbiting at what velocity now? The sound wave only changes the rotational velocity very slightly. The combusting gas, similarly, is moving at high speed. It can then 'piggyback' those speeds with its own combustion reaction in the same manner that afterburners do.

Watch an assault rifle fire sometime. You'll notice flashes as each bullet exits the chamber (the classic 'star shaped' muzzle flash of a movie gun (they're not star shaped in real life). This is unburnt gunpowder exiting the muzzle of the gun, and briefly igniting. Powder burns? Anyone seen CSI? That's fire that the skin is reacting to.

Don't believe me? Calculate the energy in a gunpowder charge, take equal energy worth of TNT, and toss it in the gun barrel. Put the slug in, then back away. Like, different room. Or different city. Nice and safe distance, like, 2 miles or 3" Plexiglas at 50 ft. Set off the TNT. The smoking remains of the gun and shrapnel decorating the Plexi will explain the difference between 'explosion' and 'combustion.'

Compressing a spring, in contrast, creates no metal at all. It works perfectly in the textbook speed of sound models, and the compression/expansion wave will propagate at a rate no greater than the speed of sound.

As for your high pressure balloon in deep space? Sorry, speeds of sound are based on molecular velocity, a function of temperature. But want to break that? Accelerate the high pressure balloon up to 0.5c. Then burst it. The front contents are now traveling at 0.5c + speed of sound. That's what you're doing in a gun. Each molecule of gunpowder is its own balloon. If you think about 10s of thousands of those balloons, popping the rear ones would start the front ones moving, and then you could pop more to make them move faster, and more to make them move even faster, and so on and so forth.

[Blondie]

I'm still not convinced of the original principle.
Sound is a wave, where the medium doesn't translate, it just vibrates and passes on the energy.
In a rifle barrel, the air that's pushing the bullet isn't vibrating about a fixed point, it's being bodily moved and accelerated. So long as you can keep accelerating it, it will move faster and faster.
Imagine a dozen springs lying horizontally, not compressed, touching each other end to end. Push at one end, and the disturbance will travel to the other end at a slowish speed, like a sound wave.
But compress all of them fully, and let one end go. The freed end can reach speeds much higher than the "sound" wave, because it's being accelerated over a longer time.

You'll find that your compression waves don't exceed the speed of sound in metal. That is, after all, what sound is - compression and expansion waves.

The speed of sound in metal, however, is quite enormously higher than the speed of sound in air, so you can easily exceed the speed of sound in air.

That's what sound is, but a bullet isn't a sound wave. I doubt that the speed of sound in metal has anything to do with limiting the speed of a projectile in a barrel, and we know that a bullet can be accelerated to more than the speed of sound in air at STP.

If a super-pressure balloon bursts in vacuum the air travels rather than propagates a pressure wave. Entropy is not constant.

Well check your assumptions. There is gas in the barrel before it reacts? No? Well what happens?

The same thing that happens in afterburners. An afterburner works because it takes a known quantity of gas, and creates more. You're rewriting the rules of the game on the fly. Gas is being created. Since a molecule of gas occupies a constant volume regardless of size, it more or less erupts into existence. This creates IMMENSE pressures on the rear of the bullet, that create enormous velocities. No wave is propagating, such as with jet engines or your hypothetical balloon in deep space (we'll get to that). Rather material is just literally existing in a space that is utterly insufficient to contain it. As for how it works, you're assuming it all burns at once. But it can't. Using a high explosive, such as TNT, with equal power to gunpowder, would detonate the barrel, destroy the gun, and wound or kill the user. Rather, gunpowder combusts. The initial combustion carries the particles of gunpowder down the barrel, where they continue to combust at high velocity. Think about that for a second. Is sound moving 'at the speed of sound?' Well, relative to a stationary observer, yes. Relative to the sun, the earth is orbiting at what velocity now? The sound wave only changes the rotational velocity very slightly. The combusting gas, similarly, is moving at high speed. It can then 'piggyback' those speeds with its own combustion reaction in the same manner that afterburners do.

Watch an assault rifle fire sometime. You'll notice flashes as each bullet exits the chamber (the classic 'star shaped' muzzle flash of a movie gun (they're not star shaped in real life). This is unburnt gunpowder exiting the muzzle of the gun, and briefly igniting. Powder burns? Anyone seen CSI? That's fire that the skin is reacting to.

Don't believe me? Calculate the energy in a gunpowder charge, take equal energy worth of TNT, and toss it in the gun barrel. Put the slug in, then back away. Like, different room. Or different city. Nice and safe distance, like, 2 miles or 3" Plexiglas at 50 ft. Set off the TNT. The smoking remains of the gun and shrapnel decorating the Plexi will explain the difference between 'explosion' and 'combustion.'

Compressing a spring, in contrast, creates no metal at all. It works perfectly in the textbook speed of sound models, and the compression/expansion wave will propagate at a rate no greater than the speed of sound.

As for your high pressure balloon in deep space? Sorry, speeds of sound are based on molecular velocity, a function of temperature. But want to break that? Accelerate the high pressure balloon up to 0.5c. Then burst it. The front contents are now traveling at 0.5c + speed of sound. That's what you're doing in a gun. Each molecule of gunpowder is its own balloon. If you think about 10s of thousands of those balloons, popping the rear ones would start the front ones moving, and then you could pop more to make them move faster, and more to make them move even faster, and so on and so forth.

That was actually very interesting to read. So what it boils down to is relative motion of combustive particles in a more or less linear chain reaction?

[GrahamH]

That's what sound is, but a bullet isn't a sound wave. I doubt that the speed of sound in metal has anything to do with limiting the speed of a projectile in a barrel, and we know that a bullet can be accelerated to more than the speed of sound in air at STP.

Well check your assumptions. There is gas in the barrel before it reacts? No? Well what happens?

...
No wave is propagating

Where is the disagreement?

Is sound moving 'at the speed of sound?' Well, relative to a stationary observer, yes.

Relative to the nominally stationary medium the pressure wave is travelling through, not relative to a stationary observer. If the air is moving it adds to the SOS.

[GreyICE]

That's what sound is, but a bullet isn't a sound wave. I doubt that the speed of sound in metal has anything to do with limiting the speed of a projectile in a barrel, and we know that a bullet can be accelerated to more than the speed of sound in air at STP.

Well check your assumptions. There is gas in the barrel before it reacts? No? Well what happens?

...
No wave is propagating

Where is the disagreement?

Is sound moving 'at the speed of sound?' Well, relative to a stationary observer, yes.

Relative to the nominally stationary medium the pressure wave is travelling through, not relative to a stationary observer. If the air is moving it adds to the SOS.

Your mechanical analysis of the spring compression system as relevant to a bullet, and your statement about the balloon in space.

Or if those weren't wrong, you're a little bad at explaining what you mean. Okay, no, a lot bad.

[GrahamH]

That's what sound is, but a bullet isn't a sound wave. I doubt that the speed of sound in metal has anything to do with limiting the speed of a projectile in a barrel, and we know that a bullet can be accelerated to more than the speed of sound in air at STP.

Well check your assumptions. There is gas in the barrel before it reacts? No? Well what happens?

...
No wave is propagating

Where is the disagreement?

Is sound moving 'at the speed of sound?' Well, relative to a stationary observer, yes.

Relative to the nominally stationary medium the pressure wave is travelling through, not relative to a stationary observer. If the air is moving it adds to the SOS.

Your mechanical analysis of the spring compression system as relevant to a bullet, and your statement about the balloon in space.

Or if those weren't wrong, you're a little bad at explaining what you mean. Okay, no, a lot bad.

Ah, the springs were not my example.
My point was that molecules of hot compressed gas suddenly released (from explosive or otherwise) are a bit more like bullets (initially) than pressure waves, and that the SOS in the metal barrel has nothing to do with the expansion of gas within it.

[mistermack]

The spring example was mine, just a fanciful mind-picture.
But to clarify, I wasn't talking about a sound wave travelling through the metal, I meant a compression/expansion wave in the springs.
I don't think the speed of that would be anything like the speed of sound in metal. Not in the springs that I've handled, anyway.
.

[Tigger]

This thread is pretty lol. All Bri wants to know, I suspect, is how fast his projectile is going to be moving when it leaves the barrel.

[GreyICE]

The spring example was mine, just a fanciful mind-picture.
But to clarify, I wasn't talking about a sound wave travelling through the metal, I meant a compression/expansion wave in the springs.
I don't think the speed of that would be anything like the speed of sound in metal. Not in the springs that I've handled, anyway.
.

A sound wave is a compression expansion wave. That's exactly what they're defined as. The speed of your compression/expansion wave is going to stall out at 'sound.'

Note that that would be the upper limit that the compression/expansion wave propagates. Since it has to do work on the object to move it, it has a different energy balance than a sound wave. For the fluid version, that's wind.

[GreyICE]

This thread is pretty lol. All Bri wants to know, I suspect, is how fast his projectile is going to be moving when it leaves the barrel.

Impossible to calculate directly. I suggest using a strobe light and a shutter-free camera.