# A Acceleration of air threw a funnel

1. Mar 26, 2016

### Ed Lenarduzzi

You have a cylindrical chamber with a 5cm ID and 55cc capacity filled to 4,000psi of air at 70*F and want to released the air threw a tube of .5cm ID. What's the initial velocity (in fps please) as the air leaves the chamber's end directly threw the .5cm tube? What's the initial velocity as the air leaves the same chamber end if it's shaped like a funnel for say half the length of the chamber out the .5cm tube? I don't know what it's called but the funnel is horn shaped. No real accuracy is required as it mostly a hypothetical question.
Thanks, Ed.

Last edited: Mar 26, 2016
2. Mar 26, 2016

### Staff: Mentor

Welcome to PF!

At that pressure, there is only one answer: the speed of sound (about 1100 fpm).

Also, you don't actually intend to do this, do you? It is very dangerous.

3. Mar 26, 2016

### Ed Lenarduzzi

Thank you for your concern but it's done all the time with precharged pneumatic air rifles. In fact this rifle shot a pellet near mach 2.
My real question is how much faster would it have gone if the air chamber had a funnel horn before the barrel or would it have made any difference at all.

4. Mar 28, 2016

### Ed Lenarduzzi

I don't have a post secondary education so I don't know if I asked an impossibly difficult question.
Perhaps this is the sort of question that's more easily answered by an experimentation that math.

5. Mar 28, 2016

And what he is saying is that with that sort of pressure, the answer is simply that the flow will be moving with the local speed of sound. It will be what we call choked flow. The local sound speed, in turn, will depend on the temperature. The only way you could give it a faster velocity would be to add a diverging section.

6. Mar 28, 2016

### Ed Lenarduzzi

The air must be going faster than the speed of sound if it is driving a pellet out the muzzle at 2,031fps.

7. Mar 28, 2016

That would imply that the design features a diverging section already.

8. Mar 28, 2016

### Ed Lenarduzzi

I don't know if you saw the video I included in my last message but it might show a 'diverging section' not that I don't know what that means.
Ed.

Last edited: Mar 28, 2016
9. Mar 28, 2016

### Staff: Mentor

This:
https://en.wikipedia.org/wiki/De_Laval_nozzle

I (we) suspect that this air rifle has already been carefully engineered for optimum exit velocity. Re-shaping the throat is unlikely to help increase the velocity.

10. Mar 28, 2016