These comments are compliments of "Diesel Freak"
"I agree that untill you are over 350 RWHP you probably do not need a complete 4" exhaust system (a straight piped 3" works VERY well), unless you just want the cool sound. Four inch ID pipe has a cross sectional area of 12. 56in^3, three inch ID pipe has an area of 7. 07in^3. As a gas expands, it cools, so if you do not have enough exhaust volume to fill a 4"pipe it could cool so much that just the action of moving the cooler more dense gas out of the pipe could raise backpressure to more than it would be if a 3" straight pipe were used. Keep the Gas hot and moving! Why do you think header wrap came into existance?
As for turbo spool up and back pressure... ... Turbines abhore backpressure!
All turbines whether they are in a Turbo, Gas Turbine, Steam Turbine, and even a Hydroelectric Power Plant require a differential pressure to work, and in some instances a temperature difference (condensing turbines).
Lets do an analysis on the gas flow through the exhaust side of the turbo.
As we add fuel to the engine, it speeds up and exhaust temperature gets hotter ... Higher mass flow rate and kinetic energy (flow work)
the effective nozzle area of the turbo housing is conatant 9, 12, 14, 16 (these numbers are completely arbitrary for this analysis) as we all know them.
As the mass flow rate out of the engine rises exhaust manifold pressure rises(potential energy) and consequently so does the mass flow rate into the turbine.
The velocity of the gas rises through the nozzle due to a differential pressure. The high velocity gas impinges on the turbine blades and the kinetic energy of the gas decreases and the rotational energy of the turbine increases (it accelerates)
If the differential pressure across the turbine nozzle is raised the gas velocity at the nozzle outlet will be faster therefore the turbine wheel will accelerate faster.
How can the differential pressure be raised?
Add more fuel to raise manifold pressure or change compressor wheels to raise boost and lower intake charge temperature and consequently raise mass flow rate through the engine which raises exhaust manifold pressure.
The easiest thing to do to raise the dP across the turbine is to put a low restriction exhaust on the engine... the closer you can get to atmospheric pressure at the turbine outlet the better!
Be careful with this (see my first paragraph)
The temperature drop across the turbine is mainly due to the drop in pressure across the turbine nozzle. As a gas expands it cools.
The reason that some people have had trouble with larger exhaust systems at high altitudes is due more to the efficiency of the compressor wheel and the air density at the intake manifold than due to exhaust modifications.
The key to optimum engine performance is air density at the intake manifold and the ability of the engine to breathe. Raise the volumeteric efficiency of the engine and turbo as a whole will make the engine run like it should.
Lower the back pressure on the turbine as much as possible, put a "properly" modified turbo on the engine to match the power output, and rpm range you want. "
There are a couple of very good 4" exhaust threads started by Ted Jannetty.
Here they are:
https://www.turbodieselregister.com/forums/showthread.php?s=&threadid=29611&highlight=exhaust
https://www.turbodieselregister.com/forums/showthread.php?s=&threadid=29612&highlight=exhaust
https://www.turbodieselregister.com/forums/showthread.php?s=&threadid=29610&highlight=exhaust