Is it rude to ask a professor you do not know and in a different department to borrow equipment?
I don't think it is rude, exactly, but I also don't expect that many would be willing to accommodate you unless you can first establish some relationship with them that is mutually beneficial - exchange of ideas, for example. 

But one researcher expressing a need to another isn't really rude, though perhaps a bit unusual and unexpected as you describe it. 

But since you suggest you are in the same institution, it has a higher likelihood of success I would guess.