Air cleaner hose?

[magnethead]

My truck doesn't have an air cleaner hose going from the air cleaner housing snorkel to the grille, but i can see where it goes. The previous owner had it taken off to run cooler lines through the hole.

right now the air cleaner lid is flipped and i think the vacuum activated thing in the snorkel doesn't work (it's closed and wont open). What kind of fuel mileage increase would i get if i flipped the lid around so it's on there correctly then somehow got that valve to open and ran the tube back to the grill and cut a section of it to let the cooler lines go through it? I was thinking of using something like 3" or 4" universal home ducting (for A/C or dryer venting) and using it, or should i just get a factory one from the junkyard?

right now, the hole is letting ambient air into the bay, and i'm sure it's cooling it down some, so should i drill another 2" or so diameter hole in the same general area to let the ambient air in? (i assume it also helps push the hot air out?)