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helpforassignment5 - 20 marks QUESTION 3 The streamfunction...

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Unformatted text preview: 20 marks QUESTION 3 The streamfunction ψ (r, θ ) = U0 r 1 − R2 sinθ r2 where U0 is constant, R is the radius of the cylinder and 0 < R ≤ r, describes steady, two-dimensional flow over a cylinder in cylindrical polar coordinates assuming that the fluid is inviscid (see sketch). r U0 R θ p0 a) Show that the cylinder surface is a streamline for this flow. b) i) Determine the velocity components, vr and vθ . ii) Identify the location of the stagnation points. iii) Show whether or not this flowfield is incompressible (use the conservation of mass equation). iv) Show whether or not this flowfield is irrotational. c) Is this a potential flow? If it exists, find the velocity potential function φ (r, θ ). d) i) Express the pressure of the fluid on the surface of the cylinder as a function of U0 , p0 and θ . Neglect the elevation change. ii) In the present conditions, it can be found that the total drag force on the cylinder is equal to zero. Is it what you would expect in a real flow over a cylinder? Explain briefly. 4 ...
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This note was uploaded on 09/14/2011 for the course ME 362 taught by Professor Ceciledevaud during the Winter '11 term at Waterloo.

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helpforassignment5 - 20 marks QUESTION 3 The streamfunction...

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