QUESTION 3 (23 Marks) Part (a) [17 Marks Total] A pump delivers a flow of Q = 0.3 m/s to an upper tank as shown in Figure 3. The pipeline is made of cast iron, with roughness height ==0.26 mm, total length L=L1+L2+L3=500 m and diameter D=500 mm. If the elevation of the water surface in the lowest tank is Z1=Om, the elevation of the bottom of the highest tank is 22=20 m and the water level in this highest tank is H=5m, find: (i) The minimum pump pressure head necessary to deliver the required flow. Assume that the temperature of the water is 10 C. Take into account minor and friction losses. [10 Marks) (ii) Sketch the energy and the hydraulic grade lines in the system (considering minor losses). The sketch is not expected to be to scale. An approximate schematic is acceptable. [5 Marks] (iii) Compute the power required by the pump to deliver the flow. [2 marks] 13 12 Z2 y. Z pump 45 elbows Figure 3: Layout of the system. Part (b) [6 Marks Total] (i) Provide a sketch of the hydraulic grade line for the case that Pipe 2 has half the diameter as Pipes 1 and 3. Show and explain trends, no calculations necessary. [1 Mark] (ii) Explain what would happen to the water surface elevation at Reservoir 2 if the elbows were 90 bends instead of 45, [1 mark] (iii) A scaled model of the system in Figure 3 is required to be built. Due to space limitations, the maximum total length possible for the model's pipe section is 10 m. Determine the diameter and roughness of the pipe, the velocity of the water, and the pump head within the scale model to achieve similitude. [4 Marks] QUESTION 3 (23 Marks) Part (a) [17 Marks Total] A pump delivers a flow of Q = 0.3 m/s to an upper tank as shown in Figure 3. The pipeline is made of cast iron, with roughness height ==0.26 mm, total length L=L1+L2+L3=500 m and diameter D=500 mm. If the elevation of the water surface in the lowest tank is Z1=Om, the elevation of the bottom of the highest tank is 22=20 m and the water level in this highest tank is H=5m, find: (i) The minimum pump pressure head necessary to deliver the required flow. Assume that the temperature of the water is 10 C. Take into account minor and friction losses. [10 Marks) (ii) Sketch the energy and the hydraulic grade lines in the system (considering minor losses). The sketch is not expected to be to scale. An approximate schematic is acceptable. [5 Marks] (iii) Compute the power required by the pump to deliver the flow. [2 marks] 13 12 Z2 y. Z pump 45 elbows Figure 3: Layout of the system. Part (b) [6 Marks Total] (i) Provide a sketch of the hydraulic grade line for the case that Pipe 2 has half the diameter as Pipes 1 and 3. Show and explain trends, no calculations necessary. [1 Mark] (ii) Explain what would happen to the water surface elevation at Reservoir 2 if the elbows were 90 bends instead of 45, [1 mark] (iii) A scaled model of the system in Figure 3 is required to be built. Due to space limitations, the maximum total length possible for the model's pipe section is 10 m. Determine the diameter and roughness of the pipe, the velocity of the water, and the pump head within the scale model to achieve similitude. [4 Marks]
