Flow around a circular cylinder can be described by potential flow. Task 1: From what you have learnt in the module, explain how flow around a circular cylinder can be obtained using uniform flow, source and sink potentials. From the potentials of uniform flow, source, and sink, derive the radial and tangential velocity (v,,ve) as well as the stream function and potential function of flow around a circular cylinder. (20 marks) Task 2: Using MATLAB, visualize the stream and potential function given that the freestream velocity is 5 m/s and the radius of the cylinder is 0.5 m. The plot must be clearly and neatly presented, with plot titles, and axis labels stated clearly. Derive and indicate clearly on the plot above where the stagnation point(s) is/are located using MATLAB. MATLAB must be used to plot the location of the sink, manually adding a marker on the plot in powerpoint or word is not accepted. (20 marks) 27 Task 3: The potential function of a cylinder rotating in uniform stream of air can be described by modifying the potential function of a flow around a circular cylinder, by adding the term to the potential function. Using this new potential function, derive the corresponding stream function for flow around rotating cylinder. Visualize the stream and potential function for flow around rotating cylinder for = 5 and for r = 20 separately. You can assume that the freestream velocity is 5 m/s and the radius of the cylinder is 0.5 m, as in Task 2. Comment on the difference in plots between Task 3 and Task 4. m m (30 marks) Taks 4: Bernoulli's theorem states that for two points 1 and 2 in a steady, incompressible and inviscid flow, p +pv + pgh = P + pv + pgh. Discuss if Bernoulli's theorem applies for the flows considered in this assignment. Derive the pressure distribution along the surface of the cylinder for flow around a circular cylinder, and for flow around a cylinder rotating in uniform stream of air with I = 20 Visualize the pressure distribution at the surface of the cylinder for either case. Comment on the pressure distributions and identify if there will be lift force produced in either case. = (30 marks)