1. (a) A cylinder of radius 1m is placed in a flow of 25m/s. In potential flow the stream function is: 0 (-) Use potential flow theory to: (1) Calculate the velocity magnitude at the top and bottom of the cylinder. [2 marks] (ii) Calculate the pressure coefficient at the top and bottom of the cylinder. [1 mark] (iii) Sketch the streamlines around the cylinder. [2 marks] (iv) Sketch/plot the distribution of pressure coefficient (y-axis) with angular position (0- 360 on the x-axis). [2 marks] (v) Q1 Continued/... Use potential flow theory to: (1) (ii) Vc = Ursino For a real viscous flow with a Reynolds number of ~3x105 re-sketch the streamlines, the pressure coefficient and explain why they differ from (iii) and (iv). [5 marks] Continued/... b) Circulation (spin) is now added to the cylinder in part (a) such that it generates lift of 5000N/m. In potential flow the stream function now becomes: (iii) (iv) Page 1 of 9 Vc = Usine --- -In- 2 R Calculate the circulation, K. Calculate the pressure coefficient at the top and bottom of the cylinder. [2 marks] Calculate the location of the stagnation points and sketch the streamlines around the cylinder. [2 marks] [1 mark] Sketch/plot the distribution of pressure coefficient (y-axis) with angular position (0- 360 on the x-axis). [3 marks]