Question 2 A circular water tank, 3m in diameter, tapers into a cone as shown in the figure below. It is open to the atmosphere at the top. The tank is used to store water and distribute it to a local town. It is supplied with water through a horizontal pipe 200 m long and 220 mm diameter. A pump feeds the pipe and maintains a constant gauge pressure of 150 kPa at the entry to the pipe. The pipe may be assumed to have a constant friction factor A = 0.02 and losses other than those due to wall friction may be neglected. The tank discharges water to the town through an opening at the base of the cone, that has a diameter of 300 mm and a Cd = 0.68. Assuming the outflow is closed: (a) What is the piezometric head maintained by the pump at the inlet to the pipe? (b) Write an expression for the frictional head loss along the pipe due to a flow rate Q, and hence find an expression for Q when the water level of the tank is a height h above the pipe If the tank is filled to a height of 7 m prior to the outflow being opened: (c) Find the time taken for the water level to reduce to 2 m, assuming the inflow is maintained throughout.

Fig: 1