How does gas behave/flow in different sized tubing/piping?

I understand that gas flow through a circular tube or pipe will have some understandable effects... for example the pressure drops, and the maximum flow diminishes. I also know that turbulence and the tubing surface has an effect...

Without getting too specific, I just want to understand generally what happens with gas flowing from a larger diameter tube to a lower diameter tube... and not having to factor in turbulence and such... just assuming a smooth flow.

Actually, I'd like to understand flow the other way too... from a small diameter to a larger one. I suppose flow will still go down... but does pressure recover?

What is the numeric relation of things like pressure and flow to changes in diameter?

My intuition suggests that any change to a smaller diameter might be thought of as an orifice of sorts, and that nothing downstream can tell whats happening in the upstream pipe provided that the pressure is the same.

I'd love to see an interactive simulator... it would help me visualize.

Thanks

bigfooted
Gold Member
What goes in must come out...
If you put 1 kg of air into the pipe every second, then 1 kg of air has to come out of the pipe. This is true at every location in the pipe, so at every location in the pipe 1 kg of air will flow through every second. So if the pipe area gets larger, the velocity drops. This is because air density times pipe area times velocity gives you the mass flow rate: $m=\rho \cdot A\cdot V=\textrm{constant}$. If the pipe area gets smaller, the velocity increases.

What goes in must come out also holds for energy. The kinetic (motion) energy is $\frac{1}{2}\cdot\rho\cdot V^2$. The kinetic energy plus the pressure that go into the pipe should also come out of the pipe: $p+\frac{1}{2}\rho V^2=\textrm{constant}$. This is the Bernoulli equation. It says (together with the conservation of mass equation) that if your pipe area increases, your velocity decreases and that means that your pressure increases to keep the energy constant.
There are two things I will mention that mess this perfect world up. The first is wall friction. Part of the energy is used to overcome the wall friction and the total energy contained in the air decreases.
The second is that if your pipe area increases too fast, the flow cannot keep up with the pipe walls anymore and you will get flow separation and recirculation zones. This will also use energy.

I hope this helps. Read a bit about the Bernoulli equation to understand its range of applicability.