I have a challenge on my second floor where a curved steel roof insulated with spray foam makes the best option for a half (toilet/sink) bathroom fan's vent to route down and laterally out the side of the home. I know appliance vent pipes need to keep a slope up and out. But a "fart fan" - is there any code prohibiting the vent duct to go down and over?
I don't think there is any restriction against an exhaust going downward.
A slightly downward direction is standard in some installations, like when a soffit exhaust vent (common in extremely cold and snowy environments) is used with a fan box which sits above the ceiling joists.