Navier-Stokes_equations all you need for fluid dynamics, yes air is a fluid.
or more simple
Reynolds_transport_theorem
yeah i know very complicated, I had that class last year and its still confusing.
From my HomeWork last year
Smaller Pipe has higher velocity lower pressure, larger pipe has lower velocity and higher pressure.. This is because the same amount of fluid is being forced through.
The lowest flow rate of any 1 part in the system will dictate the flow for the system. Air is considered an in-compressable fluid meaning that it has constant density. So the rate will be constant for the entier system since the air cant get more dense from applying pressure (within a reasonable amount, you need to enter the supersonic region to change its density).