brand new firman generator, ran for 30 min or so and noticed a small oil leak coming from the air filter housing. took it apart and saw that the "leak" was coming from this hose that isnt connected to anything inside the air filter housing, as if it its just a vent. Thought i knew engines, but cant recall seeing anything like this.

Can somebody please tell me what this hose is for?

Looks like your crankcase vent /breather tube.

ETA - more info: Crankcase vent system

thank you. I figured it was some type of intentional overflow and i just put too much oil in it.