Hello fellow experts,

I have been mulling a particular question lately, it has to do with the ever popular tank discharge/filling issue. In my industry I often work with vacuum processes, and that means lots of rigid chambers and manifolds being alternatively pressurized, exposed to atmosphere, or depressurized (the working fluid is usually air.)

Oftentimes it is important for me to determine how quickly a manifold or a chamber, once exposed to ambient conditions via a small hole or hose, equalizes pressure. There's two ways to think about this:

1. Take the start and end conditions and use the ideal gas law to determine the difference in air mass between the pressurized/depressurized chamber and the ambient chamber. Then it's a matter of computing the mass flow rate. Of course this is a crass estimate at best because this problem is highly transient with a very small time scale (usually).

2.  Conceptually, the pressure should equalize in the time it takes the pressure wave to propagate through the fluid, i.e. the speed of sound (minus the speed of the escaping fluid) * the length of the manifold. This approach seems more correct but less intuitive. Since there is no tension in the walls of the chamber (it is a rigid wall and not something like a balloon or a flexible hose), the pressure should equalize almost instantly no matter what size the hole is that exposes the chamber to ambient pressure.

What is the right approach here? What do you think?