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Unformatted text preview: Fluid Dynamics 3 2011/12 Sheet 4 Questions 1,2,3 to be handed in on 11th November 1. Consider a vortex with centre along the z-axis, so the flow field is of the form u = f ( r ) in cylindrical polars. (i) Show that u = 0. (ii) Using Eulers equation in cylindrical coordinates, show that the pressure satisfies p ( r ) = f 2 ( r ) r . (iii) Compute the vorticity = u and show that it vanishes if f = A/r . Compute the pressure for this case. 2. Consider the impingement and subsequent spreading of a horizontal, two-dimensional jet of water of speed U and width d onto a plane surface, inclined at an angle to the horizontal. Sufficiently far from the point of impingement the jet flow becomes smooth, uniform and parallel to the inclined plane and the pressure returns to atmospheric pressure. U U 2 U 1 b 2 b 1 d (i) Use an expression of the conservation of mass to show that U 1 b 1 + U 2 b 2 = Ud, where U 1 and b 1 are the velocity and breath of the flow along the plane on one side of...
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This note was uploaded on 01/20/2012 for the course MATH 33200 taught by Professor Eggers during the Fall '11 term at University of Bristol.
- Fall '11