Question 1 (a) Waves with height 5 m and period 10 s propagate in a water depth of 50 m. A position "X" is 25 m below the still water level. What are the maximum horizontal and vertical water particle velocities at X, and at what wave phases do these maxima occur? What is the magnitude and direction of the velocity at X six seconds after a wave crest has passed over X? [6 marks] (b) The waves in part (a) interact with an offshore structure in the 50 m water depth. A vertical cylindrical member of the structure is 20 m long and has outer diameter 0.8 m. The top of the member is 15 m below the still water level (Figure Q1). Determine the maximum wave force on the structural member and the wave phase at which this occurs. Use a seawater density of 1025 kg/m. Drag and inertia coefficients can be obtained from the graphs of the coefficients against Keulegan-Carpenter number, KC, shown in the Aide Memoire. Use the maximum horizontal water particle velocity at 25 m depth to evaluate KC. [14 marks] (c) A pressure transducer is attached to the top of the vertical structural member in part (b). Plot a graph of the theoretical dynamic pressure per metre wave amplitude against wave period for 3T 15 s. If the lowest dynamic pressure that can be detected by the transducer is 2 kN/m, what is the lowest wave amplitude that can be detected for waves with period 6 s? [5 marks] 50m 15m .. 35m ..... Figure Q1