Question

Question 1 (40 points) From potential flow theory, the combination of a doublet and a uniform flow gives the flowfield around a cylinder. The resulting velocity potential for the flow is given by: A cos Ur cos e The resulting velocity field in cylindrical coordinates is given by - = 4 r ae ar where e, and eo are the unit vectors in cylindrical polar coordinates, Uo is the free-stream velocity and A an arbitrary parameter. a) (10 points) Determine the location of the stagnation points and the relation between A and the cylinder's radius R. b) (10 points) Using Bernoulli's equation, show that the pressure distribution around the cylinder is given by p P O 1-4sin2 0 1 ZPUZ c) (20 points) The inviscid flow solution given in b) is notrealistic. Sketch relation b) and also the real pressure profile around a cylinder for high Reynolds number (~10) flow. Explain what causes the difference between the two curves /2 1

Answer 1

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