a) You are requested to design a raft constructed from identical cylindrical logs, each of which are 0.6 m in diameter and 3.5 m long. The mass of each log is 550 kg. Calculate the minimum number of logs are required in order to carry a vehicle of mass 2500 kg when placed in water with a density of 1000 kg/m3. b) A circular spill valve, pivoted along a horizontal diameter through the centre of the valve is located in the base of a tank which is inclined at 30° to the horizontal. The diameter of the valve is 0.5 m and the centre of the valve is 4 meter below the surface of the water (density1000 kg/m3) held in the tank.[Note that: second moment of area of a circular laminar of diameter d, about its centroid (i.e. a diameter), is Trd/64] (i)Calculate the total force acting on the valve and its line of action (i.e. Centre of Pressure). (ii) Calculate the torque needed to open the valve. A pipe bend is 200 mm in diameter at inlet and 150 mm in diameter at outlet. The inlet section is horizontal and the bend turns the flow downwards (in the direction of gravity),then through 120° such that the outlet is centred 1 metres below the centre of the pipe at inlet. The fluid flowing through the bend is water (density = 1000 kg/m³) and the flow rate is0.2 m/s. The volume of the water contained in the bend is 0.085 m3 and the hydrostatic pressure at inlet is 140 kPa. Assuming the flow is friction less Draw a schematic of the system and calculate the outlet pressure. (ii) Calculate the magnitude and direction of the force acting on the pipe bend

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