Effect variable cylinder radius has on airflow

[serveboy]

Can someone shed some light on the following problem? I'm unable to get any traction on it as I know nothing about fluid dynamics (I'm a computer engineer).

It's a problem I made up over a lunch discussion with a friend. I've illustrated it as folows:

 

[mpreds]

I don't believe your r2/r1 ratio will have much of an effect.

Try researching venturi tubes, as yours appears to be the inverse of one.

On the most basic of terms.
mass flow rate in = mass flow rate out
and
mass flow rate = density*velocity*cross sectional area
and
volume flow rate = velocity*cross sectional area

 

[justsomeguy]

I don't believe there will be any difference with or without the w1 section either. For there to be any change in the net flow rate, work needs to be done somewhere in the pipe, which itself would just be counted as a restriction of flow no matter if the pipe is changing diameter or not.

 

[SteamKing]

Since the working fluid is air under pressure, this problem is not as simple as it seems. The velocity of the air from the high pressure side depends, in part, on the friction in the connecting duct. If the velocity is high enough, then the flow into the low pressure reservoir could choke, which means that there is a maximum flow rate which is attained.

Since this is a 'made-up' problem, I don't know what I can tell you do other than consult someone who is knowledgeable in fluid dynamics and gas dynamics.