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Water (density 998 kg/mº, dynamic viscosity 0.001 Pa s) is pumped between two reservoirs at a volumetric flow rate of 0.006 m/s through a 120-m long pipe of 5 cm diameter. The roughness ratio of the pipe is a/d = 0.001. There are some fittings and valves in the pipe system, as shown in Figure Q1. The loss coefficients of the valves and fittings can be found in Table Q1. The Darcy friction factor can be found in the Moody chart at the end of the exam paper. (a) Calculate the total minor head loss of water in the system between the two reservoirs [3] (b) Calculate the head loss of water due to pipe friction in the system between the two reservoirs [3] Now the pump is replaced by a turbine and water flows from reservoir to reservoir as driven by the gravity. Assume all other parameters of the system are unchanged. There can now be energy conversion from the flowing water to the rotor of the turbine. (c) Present the Bernoulli equation that applies to the water flow in this system. [7] (d) Calculate the power can be extracted from the turbine (in units of Watts). [7] 2 = 40 m Screwed regular 90* elbow Sharp exit 21 6 m Sharp entrance Half-open gate valve 0.3 m bend radius Pump 120 m of pipe, d = 5 cm Open globe valve Figure Q1 Table Q1 Loss coefficient 0.5 6.9 Fittings and valves Sharp entrance Open globe valve 0.3 m radius bend Regular 90° elbow Half-open gate valve Sharp exit 0.25 0.95 3.8 1.0
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