- #1

- 73

- 1

The question will probably be related to mechanical engineering / chemical engineering / aeronautics. I come from the field of optics and have no background at all on fluid dynamics.

I'm trying to calculate the dependence of pressure on distance, i.e. P(x) in a gas flow problem: I assume a tube (pipe) filled with some gas (say argon), with pressure P1. At some moment, a small hole (orifice) in the pipe is opened and a gas starts to flow outside, into a vacuum (P2=0). As a result, the pressure decreases towards the hole. I want to calculate this reduction

__as a function of distance__from the hole.

The setup is something like this:

And I want the solution P(x), like the green graph here.

From a "quick" search (that already lasts 3 days) I first found a barometric formula, but realized I have no external forces in my case to use it. Next, I found the formula that relates the pressures with the Mach number M and ratio of specific heats gamma:

but, the Mach number is the ratio of the gas speed to the local speed of sound, and gas speeds w(x) are unknown. So, I 'm sort of came back from what I started from.

I also found a formula that relates the gas speed (w2) at the orifice to the pressures and initial gas speed (w1), volume(v1):

but, this gives me only one point on x axis, and this point I actually already know (it's P2, or very close to it).

I'm already after reading a couple of dozens websites on the subject, some books (Caro, Bansal, Sutton).

I appreciate any help, advice and / or suggestions where to dig in next. Thanks!