Problem 3 The two-reservoir system shown in Figure 3 consists of three concrete pipes with roughness k, = 0.35 mm for all pipes and an elevation difference of H= 50 m between two reservoir level. For minor losses consider: Kent = 0.5 (entry loss factor), Kext = 0.15 (exit loss factor). Ignore minor losses at diameter changes and consider the kinematic viscosity as: v= 1 x 10-6 m²/s and g = 9.81 m/s². a) Calculate the flow rate between the two reservoirs. [8 marks] b) A new alternative solution is being considered to link the two reservoirs consisting of one pipe having a constant diameter. The flow rate calculated in part (a) must be achieved and you can use the friction factor of Pipe 1 in part (a) for the new pipe. A control valve will also be added to the system with a minor loss coefficient of KL 3.2. What is the diameter required for the pipe? [6 marks] Water L-1000 m D-320 mm 1600 m, D₂400 mm L850 m, D-350mm Figure 3: Reservoir and pipe arrangement Water

Fig: 1