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Unformatted text preview: Laminar Boundary Layer Order of Magnitude Analysis u Assumptions (in addition to incompressible, steady & 2-D) Changes in direction x occur over a distance c ) 1 ( write we or, 1 ~ C O x C x = Changes in direction y occur over a distance ) 1 ( or, 1 ~ O y y = C << (boundary layer is thin) 1 Re >> = c u (Reynolds number is large) Changes in velocity x are proportional to u ) ( = u O u Changes in pressure are proportional to 2 u ) ( 2 = u O p Now, lets do the order of magnitude analysis: Conservation of Mass = + y v x u Now, we introduce our assumed orders. For example: ) ( c u O x u = c y x ) ( x Laminar Boundary Layer Order of Magnitude Analysis 16.100 2002 2 Since we have not assumed an order for v variations, just leave this as simply v and say, ) ( v y v = Since =...
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