QUESTION 1 (15 Marks) (a) Find the absolute pressure in point A of the manometer configuration shown in Figure 1, where the specific gravity of the oil is 0.8 and the temperature of the water is 10°C. The following distances have been measured: ₁ = 0.4 m, l2 = 0.6 m, l3 = 0.8 m, 4 = 0.2 m and ls = 0.5 m. Note that manometer has one end open to the atmosphere. Oil (S=0.8) (5 Marks) +A Water 30° b3 Note that the moment of inertia of a triangular section is I = base* (height)³/36. Figure 1: Configuration of the manometer system. (b) As shown in Figure 2, a triangular panel (with base B = 5 m and height H = 10 m) is partially submerged. When the depth of the water h reaches 6 m, the base of the submerged part of the triangular panel is B₁ = 4 m. For this case, assume that the water temperature is 10°C and find: (i) The resultant force on the panel due to pressure. (ii) The location where this force acts. (iii) The force R needed to keep the panel in the position. [4 Marks] [3 Marks] [3 Marks] Lateral view of B the panel B h 30% Hinge Ground level H Submerged part Figure 2: A hinged triangular panel. (TOTAL: 10 Marks) QUESTION 2 (16 Marks) (a) Oxygen (p = 1.429 kg/m³) and methane (p = 1.82 kg/m³) are mixed in a container, as shown in Figure 3. Given that the flow of oxygen is Q₁ = 0.5 m³/s and the flow of methane is Q2 = 1.2 m³/s, find the mass flow rate exiting the container. (3 Marks) (b) Q1(Oxygen) Q2(Methane) Container Q3(Mix) Figure 3: A filling tank. Figure 4 shows a frontal section of a junction that connects three pipes. The junction shape is a cube of side L= 0.3 m and mass 0.5 kg. The junction connects three pipes that carry water at 60°C. Given the properties in Table 1, where some partial results are computed, find: (i) The flow Q3 [1 Marks] [4 Marks] (ii) Neglecting losses and elevation difference, find the pressure in pipe 3 (iii) Find the x and z components of the reaction force required to keep the junction in place. Flange Junction Q₂ Q1 Z Q3 30° Figure 4: Frontal section of the connection. Table 1: information available [8 Marks] Data Pipe 1 Pipe 2 Pipe 3 Flow (m³/s) 1.00 0.6 ? Diameter (m) 0.80 0.70 0.40 Area (m²) 0.50 0.38 0.13 Velocity (m/s) 1.99 1.56 ? Pressure (kPa) 200 200.8 ? TOTAL (13 marks) QUESTION 3 (12 Marks) (a) NASA is asking you to help preparing a plan to colonise the planet Mars. Given that Mars' atmosphere does not have enough oxygen to sustain human life, pumps will need to pump air from a filtration centre to the colony through pipelines. NASA is asking you to test a small model (scale 1:500) on Earth, assuming that the air used in the pipelines on Mars will have the same composition of the air as on Earth, but the pressure and temperature of the air on Mars will be 600 Pa abs and - 20°C, respectively, while, on Earth, you will be testing air at 20°C and at atmospheric pressure. If the air velocity in the pipelines on Mars is supposed 5 m/s, at which velocity should you test the model on Earth? Assume the change in pressure will not affect the air viscosity. (6 Marks) (b) During the packaging process, warm honey (assume v=0.00115 m²/s) flows by gravity through a vertical smooth pipe (D = 10 cm, L = 2 m). The end of the pipeline is open to the atmosphere while the initial part is connected to the bottom of a storage tank, where the honey level is maintained 1 m above the bottom. (i) Sketch the system [1 Mark] (ii) Compute the velocity of the honey in the pipe. Neglect minor losses. If you need to do iterations to solve this question, start from an initial value of f=0.2 and compute two iterations. QUESTION 4 (20 Marks) [5 Marks] (TOTAL 6 Marks) (a) A hydro-electric plant whose layout is shown in Figure 5 needs to discharge a flow Q = 2 m³/s. Assume the water temperature is 10°C and neglect minor losses: (i) Compute the turbine head if the length of the pipeline is L=1000 m, the diameter D = 1 m and the pipe material is ductile iron cement lined (DICL) pipe (roughness height & = 0.35 mm). Assume that the diameter at the discharge side of the turbine is the same as the diameter of the pipeline. State all other assumptions that you make. [5 Marks] (ii) If the turbine efficiency is 90%, what is the power produced? [2 Marks] H = 35m Penstock Turbine and generator Figure 5: Layout of the system (TOTAL 7 marks) QUESTION 4 (CONTINUED) (b) The system shown in Figure 6 delivers water from a lower storage (the bottom of the storage is at an elevation z₁ = 20 m) to an upper storage (the bottom of the storage is at an elevation z2 = 75 m). Note that a pump, a half-open gate valve and two 45° elbows are present in the system. The pipeline is made of cast iron (e = 0.26 mm) and has a total length of 5000 m. (i) List all the minor losses and the related minor loss coefficients. [1 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 (i.e. do not compute numerical values). [5 Marks] (iii) Assume fully rough turbulent flow in the pipe and neglect all of the minor losses: compute the minimum pipe diameter required to deliver a flow of 0.5 m³/s if the pump head hp = 85 m. If you need to do iterations, start from a value of f-0.02 and compute 2 iterations. [5 Marks] (iv) For the diameter found in (iii), compute the total value of the minor losses. If you did not solve point (iii), consider a diameter equal to 0.5 m. [2 Marks] H₁ = 1 m QUESTION 5 (21 Marks) Half open gate valve Pump 45° Elbow H₁₂ = 5 Figure 6: Layout of the system. (TOTAL: 13 Marks) (a) The concrete channel shown in Figure 7 (Manning's value n=0.015) has a slope of 0.005. (i) If the water depth y is 0.5 m, what is the discharge? 1 (ii) What is the Froude number? [4 Marks] [3 Marks] (TOTAL 7 Marks) 1 Figure 7: Section of the triangular channel y QUESTION 5 (CONTINUED) (b) A flow Q-20 m³/s flows at a water depth y=2 m in a rectangular channel with width B=10 m. (i) Find the critical depth of the flow (ii) Find if the flow is subcritical or supercritical. Give a brief explanation. [2 Marks] [2 Marks] (iii) If the bottom of the channel rises by 3 m (see Figure 8), find the water depths before and on the upstep. [7 Marks] Y₂? Q У1? AZ=3m Figure 8: Longitudinal section of the channel. (TOTAL: 11 Marks) (c) In a rectangular channel, the water depth after a hydraulic jump is y = 4 m. What is the conjugate depth if the flow per unit of width in the channel is 6 m²/s? QUESTION 6 (16 Marks) (3 Marks) A triangular channel has a section similar to the one in Figure 7. The channel can be divided in three sections of different slopes as shown in Figure 9. (i) (ii) Classify the flow profiles knowing that the critical depth is ye=1.83 m, the normal depths are ynl=0.75 m and yn3 = 1.24 m for sections 1 and 3, respectively, and that a hydraulic jump occurs in section 1. [6 Marks] Use 2 steps of the direct step method to compute at which distance from the rise in terrain the flow will reach the uniform flow in section 3. Section 3 has a slope of 0.05 and a Manning's coefficient equal to 0.015. The flow in the channel is 10 m³/s. [10 Marks] (1) (2) (TOTAL: 16 Marks) Rise in terrain Figure 9: Layout of the system. (3)