Simple and brutal... cut the pipe and see which end the water carries on coming out of. Just hope it's not the sulphuric acid pipe or the floor might get damaged.

Simple and brutal... cut a piece out of the pipe so there is a gap between the ends and see which end the liquid carries on flowing from. The question doesn't ask that the pipe network stays functional and this solution requires minimum tools (a saw or a pipe cutter would be enough) and will work on any pipe type and any liquid type. Though it might get messy and you'd better hope it's not a pipe carrying sulphuric acid or the floor might get damaged. And if it's a gas rather than a liquid you might need some streamers to show the gas flow.