The cylindrical tank with a diameter of 0.9 meters and a height of 1.3 meters is half filled with water. Water was started to be sent to this tank at a constant speed of 4.9 m/s through a pipe with a diameter of 0.05 meters. A valve placed on the outlet pipe with a diameter of 0.03 meters limits the outlet speed. The linear velocity in the outlet pipe is directly proportional to the liquid level in the tank and its coefficient is given as k= 8 s.

a) Do you think the tank will fill up or empty?

b) If the tank is emptying, find the time it takes for 98% of the tank to empty. If the system goes into a steady state without emptying 98% of the tank, then what is the required time? If the tank is full, choose option b for the full state.