The kinetic energy of the water inside the gap between the cylinder and the floor can be found by integrating in cylindrical coordinates; the speed of the water can be obtained from the continuity equation by using the cylindrical symmetry.
Please submit the solution to this problem via e-mail to physcs.cup@gmail.com. There will be no more hints for the Problem 1. The problem will remain open for submissions for two more weeks, until 23:59 GMT, 1st January 2023.