3. Water with a density of 1000 kg/m³ and dynamic viscosity of 1.0 x 10-³ Pa.s flows under gravity from a reservoir through a galvanized iron pipe with an equivalent roughness of 0.15mm at a flow rate of 600 litres per minute into the local atmosphere. The flow path comprises a sharp edged entrance from the reservoir into the pipe (loss factor (KL) of 0.5, based on average outlet velocity), a 4m horizontal length of the galvanized pipe of 80mm internal diameter, a fully open gate valve (KL = 0.15, based on average inlet velocity) and a 6m horizontal length of the galvanised pipe of 40mm internal diameter. There is no fitting or restriction at the outlet of the pipe into the local atmosphere and so no additional minor head loss. The liquid surface of the reservoir is exposed to the local atmosphere. a) Sketch the system and calculate the mean velocity and the Reynolds number of the flow in the two different pipe sections and state whether the flow is laminar or turbulent in each. [6 marks] b) Determine the height of water in the reservoir required above the sharp edged entrance into the pipe to achieve the required flow rate. Note, the major and minor head losses can be summed in this flow path, like resistors in series, and the general equation for energy conservation in pipes compares the pressures at the inlet and outlet of the system only. [10 marks] c) The gate valve is replaced by a fully open globe valve (K₁ = 10, based on average inlet velocity). Determine the change in the height of water in the reservoir required above the sharp edged entrance into the pipe to achieve the required flow rate. d) Provide an explanation for the result obtained in part c). [4 marks] [5 marks] Ref: ME20214G74-2

Fig: 1