Boundary Layer Equations - Fluid Flow - Handout, Exercises of Fluid Dynamics

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

2012/2013

Uploaded on 10/02/2013

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M E 320 Professor John M. Cimbala Lecture 37
Today, we will:
Do a BL example, boundary layer on a flat plate
aligned with the flow
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:
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!
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M E 320 Professor John M. Cimbala Lecture 37

Today, we will :

  • Do a BL example, boundary layer on a flat plate aligned with the flow

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:

  • 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!

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.