Since your apartment is on the second floor, it's unlikely that the drain pipe will terminate at the outside unit on the roof. However, it could be connected to a pipe that runs down the side of the building and empties into a designated drain.
If you're having trouble locating the drain pipe, I'd recommend checking with the building management or contacting a professional air conditioning technician. They'll have the expertise to help you find the pipe and ensure that everything is working properly.
In the meantime, you might want to look into the best pipe relining system available to reinforce your drain pipes and prevent any potential leaks or damages.
This message was last edited by Maxiflyer on 2/20/2023.