Who discovered the urinary system?
We don't know
Unlike other body systems, human beings have known about the urinary system for thousands of years. The earliest data we have on the urinary system goes back to Aristotle's view on the function of the kidneys in his work De Partibus Animalium (the kidney had two functions, to separate the surplus liquid from the blood and to modify this liquid which will be eliminated via the ureters, bladder and urethra).
However, it is suggested that by the time Aristotle wrote this, there was already knowledge of the workings of the urinary system. It is, after all, one of the simplest systems, consisting of only the bladder, kidney, ureter and urethra. The person or people who first classified its workings probably did so in a time before writing, and unfortunately might never be named.
I hope I helped!