worksheet5 - Fluid Dynamics 3 2011/12 Sheet 5 Homework to...

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Unformatted text preview: Fluid Dynamics 3 2011/12 Sheet 5 Homework to be handed in 18th November: questions 2,4,5 1. Consider the axisymmetric flow produced by the superposition of a uniform stream of speed U and a three-dimensional source of strength m . Choose cylindrical polar coordinates with the z-axis in the direction of the mean flow and the source in the origin. A r z (i) Show that the Stokes stream function of the uniform stream is str ( r, z ) = U 2 r 2 . (ii) Superimpose the two flows to find the stream function of the whole flow problem. Show that there is a stagnation point at a distance a upstream from the source (denoted A in the Figure) and find a in terms of U and m . What is the value of at A? Thus show that r 2 = 2 a 2 bracketleftBigg 1 + z z 2 + r 2 bracketrightBigg describes the surface of a solid body that would produce the same flow pattern if it were placed in a uniform stream (called the Rankine body). Hint: The surface of the body is a streamline....
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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.

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worksheet5 - Fluid Dynamics 3 2011/12 Sheet 5 Homework to...

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