A medical syringe with at least three ports, in conjunction with a urinary catheter, can be used for closed manual irrigation of a bladder. The three syringe ports are located on a port body. Each of the three syringe ports can be manually selected by rotating a barrel that has a closed end located inside the cup-shaped port body. Rotation of the barrel inside the port body occurs about an axis that is aligned with the central axis of the hollow cylindrical barrel. The system is configured to selectively fill the syringe with an input fluid, irrigate the bladder by passing fluid into and out of the urinary catheter, and drain bladder contents into a drainage vessel without ever needing to remove the syringe from the catheter.