rcgldr said:
I'm thinking that the small hole also reduces the pressure within the hose. The pressure in the CO2 tank is probably many times greater than what the hose could tolerate.
That doesn't make any sense, though. The throat is at the end of the hole, so that hose is going to be essentially at tank pressure throughout its length.
rcgldr said:
In this situation, the pressure in the tank is much greater than the atmospheric pressure that the flow exits into.
Yes, and this key fact is the first clue everyone should have that this flow is going to be compressible and that Bernoulli's equation is entirely irrelevant. The "Venturi effect" is not only unlikely to be present in the traditional sense, but if the flow is at any point supersonic (and it very well might be given the shape and pressure), then the so-called Venturi effect is the exact opposite of what happens. This is why you never her "the Venturi effect" referenced in a fluid dynamics course. It gives the wrong idea that pressure and duct diameter are the important parameters, whereas in reality, pressure and velocity are the important parameters.
rcgldr said:
I assume that most of the acceleration of the CO2 through the small hole is due to the pressure differential between the tank side and the hose side of that small hole, rather than Venturi effect.
I think you described the two sides of that hole you are referencing incorrectly by accident, but either way, for a subsonic flow, the Venturi effect and flow acceleration due to pressure gradient are indistinguishable phenomena. There is no one or the other. They are the same. For a compressible flow, the Venturi effect is not even a thing, as the behavior of a flowing gas changes substantially beyond Mach 1.
woolyhead said:
Is it as boneh3ad said to reduce the mass flow rate? Is that the only reason? If so why can't the hole be positioned further up the tube leading to the horn?
I think the fundamental issue here is that we need to think for a moment about how these actually work. CO
2 is stored in the bottle as a liquid and travels through the hose (at least largely) in that same state. The flow restriction here effectively functions the same way as a thermal expansion valve in a refrigeration system. The general idea is that it accelerates the flow, causing a pressure drop and at least a partial phase change. It also restricts the total mass flow rate based on its diameter.
The second function is that, as the high pressure gas exits, it is generally going to be at a much higher pressure than the surroundings. In fact, it will be so much higher that the (mostly) gas coming out of that restriction is going to be moving at the speed of sound. As I mentioned before, when you reach Mach 1, the area-velocity relationship flips, so that expanding cone is actually still functioning as a nozzle for at least some of its length, speeding up the flow and further lowering the pressure. In effect, the whole system is one giant thermal expansion valve.
Now, it's unlikely there is enough pressure to carry this out all the way to the end of the cone, so the flow coming out the end isn't likely to be supersonic. There is therefore likely a termination shock somewhere inside that cone to make sure the final exit pressure matches the atmosphere. It's that acceleration and pressure drop that causes the phase change, and that is a result of the restriction and cone.
This explanation has been somewhat simplified because I've mostly ignored the multiphase nature of this flow.