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Unformatted text preview: The Laminar Flat Plate Boundary Layer Solution of Blasius (Example 10-10, engel and Cimbala) We go through the steps of the boundary layer procedure: Step 1: The outer flow is U(x) = U = V = constant. In other words, the outer flow is simply a uniform stream of constant velocity. Step 2: A very thin boundary layer is assumed (so thin that it does not affect the outer flow). In other words, the outer flow does not even know that the boundary layer is there. Step 3: The boundary layer equations must be solved; they reduce to This equation set was first solved by P. R. H. Blasius in 1908 numerically, but by hand! Similarity variable The similarity solution is f as a function of .
The key here is that one single similarity velocity profile holds for any x-location along the flat plate. In other words, the velocity profile shape is the same ("similar") at any location, but it is merely stretched vertically as the boundary layer grows down the plate. This is illustrated in Fig. 10-98 in the text. The similarity solution itself is tabulated in Table 10-3, and is plotted in Fig. 10-99. This one velocity profile, plotted in nondimensional form as above, applies at any x- location in the boundary layer. ...
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This note was uploaded on 07/23/2008 for the course ME 33 taught by Professor Cimbala during the Fall '05 term at Pennsylvania State University, University Park.
- Fall '05