The same theories about flow and thermal dynamics apply whether an engine is normally aspirated or boosted. However, when boost is part of the discussion, the priority is to keep up gas velocity before the turbine and that involves a big turboback system after it. Bigger diameter is better... but only to a point. A turbo exhaust manifold may incorporate relatively small area primary tubes (compared to an all-out NA set up). Exhaust manifolds are best composed of a material that locks in heat and they must obviously fit the available space (which may be reduced by the presence of a charger).
A primary goal of forced induction is to spool the turbo as quickly as possible. Of course, an unspooled turbo is a useless power-sapping flow restrictor. Once at operating speeds, however, it delivers more torque (through brute force) than can be attained by only relieving intake restriction. (That and creating negative pressure in the gas flow tracts via tuning "scavenging". Of course, maximum engine output is had by a mix of eliminating restrictions AND forcing yet more air through the system.
After a turbo, we want the least back pressure possible. There are NO exceptions. The more free-flowing the exhaust piping is, the lower the back pressure will be. The law of diminishing returns does apply as usual, however. A 4” (100mm) exhaust will not be doubly as effective as a 2” (50mm) but, yet, will definitely flow much more. What’s important is that an ideal pressure ratio be achieved before/after the turbine. When back pressure is lessened after the turbo, less positive gas pressure before it is required to spin the compressor wheel. In the end, reduced back pressure results in faster-spooling turbochargers which produce broader torque curves and significantly faster cars!
Compromises must always be made during the engineering process. Only one of them regards exhaust pipe diameter. The “best” diameter choice for a given project depends on system cost, packaging constraints, and only finally on desired output. The typical 250hp engine will get along very well with a 2.5” exhaust. A larger diameter won’t deliver much other than more weight and also extra noise and bass tone. (Big exhausts rumble. Small ones buzz and “zing”.) Achieve or exceed 300hp, though, and that 2.5” becomes a restriction. A 3” delivers well until approaching the 400hp level. (Remember that area increases at a rate greater than diameter. So, a 4” pipe, for example, has significantly more than double the flow area compared to a 2”.)
Let’s do some simple math and demonstrate how this pressure stuff works: Let’s suppose that the test vehicle is a K03-powered 1.8T. Suppose, for instance, that the expansion ratio pre/post-turbo is 1.7:1 and that at 2.5” exhaust produces 5psig (g = “gauge”) back pressure at the turbine discharge at redline. The total back pressure seen by the engine (upstream of the turbine) in this case is:
(14.5 +5)*1.7 = 44.1 psia (a = “actual”). Thus, the turbine produces 18.7 psig total back pressure at peak engine speed.
Changing nothing else, let’s add a larger system from the turbo back such as the Eurojet 3” exhaust. That is, we’ll keep the K03 turbo and peak boost pressure, same turbo, same boost, etc. Now we measure 3 psig back pressure after the turbine. Doing the math again, we see that the numbers demonstrate the following: (14.5 + 3) * 1.7 = 15.25psig. That’s an instant 22.5% reduction in back pressure. Is that “overkill” or is it just “KILLER”? Now imagine the difference in a hard-running big turbo setup. No matter what, a driver will experience more boost sooner with lower intake air temperatures (IAT) and that’s a very wonderful thing, indeed!
When choosing a quality performance turbo exhaust, make sure that the diameter is as large as you can afford so long as packaging is not compromised and weight is not excessive. Also, look for mandrel bends (NOT power-eating crush-bends from the local hack job exhaust "specialist" shop). Tight-radius turns are to be avoided; straight sections flow best. Sudden step changes in diameter don’t help. Nor do dirty welds or cuts at non-perpendicular angles. High-flow cats keep the environment clean and can actually increase power over a test-pipe (which itself is much better than a restrictive cat). Finally, make sure that muffler adds no more restriction than is required to reduce sound volumes to the required level.