An outboard engine has a cowling defining an engine compartment and an outlet fluidly communicating therewith. An engine housed in the engine compartment includes an engine block and an output shaft defining an output shaft axis, an axial direction, a radial direction and a circumferential direction. An outer end thereof extends outside the engine block. A flywheel mounted thereto rotates therewith. A cover fixed with respect to the engine block defines a chamber housing the flywheel disposed axially between the engine block and the cover, and radially between the output shaft and the cover. The cover includes a channel member defining a channel between a first end and a second end fluidly communicating with the outlet. The channel member defines a cross-sectional area of the channel. A circumferentially-extending portion of the channel is continuous with the chamber and has a cross-sectional area increasing towards the second end.