Off road snorkel size?

[crazy_canadian]

I am building a snorkel for my OBS.
Since no one offer a kit for these trucks, I will built my own.
I already have the airbox, it's from a 2000 excusion V10. The box as a cone air filter, and the air inlet would point directly at the fender.

But adding about 4' of piping increase air resistance. So I need to go bigger in diameter.
The turbo inlet is 2.5" right?
The stock piping from the turbo to the airbox will be used.
Then I plan to go 4" I.D. from the airbox, to the roof of the truck.
Will it be enough ?
I really don't want any restriction in the air intake.
Truck will remain stock exept for the exhaust and a tune.