The storage tank of a water tower is a vertical cylinder of diameter D = 7 m, the initial depth of water within it is ho =6 m and the free surface is exposed to the atmosphere. The base of this tank is supported at a height H = 15 m above the ground and a single vertical drainage pipe leading from its base has a diameter d = 140 mm and a length L = 14 m. The inlet to the pipe is sharp-edged and has k in = 0.5, the outlet valve when fully open has k out = 1 and the pipe may be considered to have a constant friction factorf= 0.007. The water is allowed to discharge to the atmosphere at the exit from the drainage pipe.
a). Find the time taken for the liquid level in the tank to fall to hI = 1 m after the valve has been fully opened.