I am a methmetician and steering systems architectural engineer, not an exhaust expert and I never said I was so there's always the need for me to brush up on the subject, however you have no knowledge yourself other than to paste links from google....
Yes as I said calculations can give you a rough estimate of required cfm but its not completely definitive, you have to assume that everything is perfect. Although I will happily admit defeat at this stage after calculating the na rating of the
cupra r at 196, including the turbine pressure an estimated bhp of 350 we have a CFM of 525 intake requiring (I am using a subjective figure of 2.2 to ascertain exhaust flow) 770 assuming the pipe is straight with no turbulence it will flow 115 cfm per square inch, a 3 inch pipe is 7.065 therefore providing just about enough for a 340bhp application with 0 back pressure.
That's based on doing simple calculations though, now consider this: (ill use letters as my iPad does not have the correct formulae ability)
A - Exhaust gas velocity at the turbine
B - Absolute temperature of inlet gas
C - Gas law constant
D - Pressure of inlet gas
E - Pressure of outlet gas
F - The heat of the gas at constant volume
G - The change of the gas at cat exit
H - Is entropic expansion factor of the gas
I - Molecular mass of the gas at each state
You have the following
C 8314.5
B 90 (will depend on individuals setup, I'm using imperial)
I 29,9 27.4 29.7 (again it depends on what mixture is being ran and the general health of the engine)
H 1.239
D I don't know? Bill what's the boost pressure at 1 ATM for a hybrid running 350bhp?
E
Assuming we are at full throttle then we have 100% of an atmosphere, giving us 6000 litres
2112 degrees rankine exhaust temps
549 degrees rankine inlet temps
2112/549 = 3.84699
6000 x 3.84699 = 23081 litres/min
I can't do the rest of the calculations without more info however I can calculate the volume change of the gas at high temperatures assuming 1lb per 14.5lbs, molecular weight of octane at 114, erm.... Given the breakdown of air we the have an exhaust volume rating of 1.33? Assuming oxygen is 20% we have 26.6 so 80 + 26.6 is 106.6% of combustion volume
I need sleep as my daughter will be up early as usual. However I hope this demonstrates how difficult it is to calculate exactly what diameter is required.