Gas pressure in variable diameter pipe

[anasasis]

This may be an elementary question, but I am still in the elementary stages of physics. My question is this: if you have a 4" fan at the end of a 4" pipe which is sucking air through the pipe, and the pipe narrows to 3" about 24" from the fan, does the 24" section of 4" pipe experience a vacuum relative to the 3" section of pipe? Assume the volume of air being pulled by the fan is either constant or increasing.

 

[russ_watters]

Yes. That's bernoulli's principle and the venturi effect. Have a look at the wiki for those subjects and then we can take it deeper if you like.

 

[anasasis]

Okay, well a little background on what I'm trying to do. I have a project vehicle that I would like to run compound boost on. It is a 5.3L engine currently with a roots-style, positive displacement blower on it. I put the blower on, and it is plenty powerful on the low end. Torque is immediately available, and that's what this type of blower is made for...but it lacks severly on the high end powerband. My solution is to put a turbocharger in front of it to help with the high end.
The problem people run into with compound setups is uncontrolled boost because the pressures multiply once they reach the blower. I would like to fix this by making the compound boost sequential instead of simultaneous, whereas vacuum in front of the turbo compressor activates a bypass valve on the blower to allow it to flow pressure freely while the turbo is making boost.
Now, all I need to do is figure out what dimensions to use when I fabricate the inlet on the turbo so that it will create the vacuum necessary to trigger the blower bypass valve. It takes 15 inHg to open the valve all the way. My idea is that by narrowing the inlet pipe some distance from the opening of the compressor in the turbo, that certain distance will experience a vacuum relative to the rest of the inlet pipe. I've got the concept, but where is a good place to start?