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4. Allow approximately 32 minutes for this question. (a) A concrete open channel with a trapezoidal cross-section is used to transport water between two storage reservoirs at the Mt. Grand Water Treatment Plant. The cross-section has a bottom width of 0.5 m, a depth of 1.4 m (including freeboard) and side slopes of 50°. It has a Manning coefficient (n) of 0.015, a grade of 0.2 % and is 55 m long. A minimum freeboard of 0.25 m in the channel must be maintained at all times. i) Assuming normal flow conditions in the channel, determine the maximum possible volumetric flow rate in the channel while maintaining the required freeboard. ii) A V-notch weir (Cd = 0.62) is to be installed at the bottom end of the channel to control the volumetric flow rate of the water as it enters the lower reservoir. The invert of the weir is located above the water level in the reservoir. The weir needs to be designed such that the depth of the water flowing through it is equal to 1.10 m. Determine the required angle of the V-notch weir so that the above design conditions are met. (b) The natural watercourse at the exit of a catchment has been directed into a pipe in order to convey it into the Local Authority's stormwater system. The pipe has an internal diameter of 600 mm and is laid at a grade of 1 in 580. Its surface roughness is characterised by a Manning coefficient (n) of 0.016. What is the volumetric flow rate in the pipe when it is: i) flowing half-full, and ii) flowing full? State, with reasons, which of the following flow conditions would produce the highest flow velocity in the pipe: i) when the pipe is flowing one-quarter full; ii) when the pipe is flowing half-full; or iii) when the pipe is flowing three-quarters full. (6 marks) (6 marks) (6 marks)