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Topics covered in this course include fluid properties, fluid statics, fluid kinematics, control volume analysis, dimensional analysis, internal flows, differential analysis, external flows CFD, compressible flow and turbomachinery. Key words for this lecture are: Boundary Layer Equations, Boundary Layer Procedure, Laminar Flat Plate Boundary Layer, Uniform Stream of Constant Velocity, Velocity Profile Shape, Nondimensional Form, Actual Flow, Imaginary Flow, Displacement Thickness
Typology: Exercises
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Today, we will :
Review: The Boundary Layer Equations
Review: The Boundary Layer Procedure
Example: The Laminar Flat Plate Boundary Layer
We go through the steps of the boundary layer procedure:
This equation set was first solved by P. R. H. Blasius in 1908 – numerically, but by hand!
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.
Similarity variable
The similarity solution is f ′ as a function of η.