A cylindrical tank 5 m high and 1.15 m in diameter is initially filled with 1.5 m high water. Water is started to be fed to the tank at a flow rate of 0.025 m3/min. After 30 minutes, water starts to be taken from the outlet pipe at the bottom of the tank with the help of a valve. The flow rate in the valve changes in direct proportion to the water level in the tank.

a) What is the height of the water in the tank when the lower valve is opened?

b) What will be the water level in the tank 30 minutes after the bottom valve is opened. Note: The temperature and density of the water are constant, the Valve constant is 0.007 (hint F=kh).