Boundary Layer on a Flat Plate
We shall consider the viscous laminar high Reynolds number flow over a semi-infinite flat plate at zero angle of attack. This is the simplest case of a boundary layer that may serve as a model for the calculation of boundary layer effects on a thin airfoil. For incompressible flow the Navier – Stokes equations and the equation of continuity read
The boundary conditions are that the velocity vanishes on the plate and becomes equal to XJx far away from the plate surface. Thus for twodimensional flow
Q(x, 0) = 0 for x > 0, (4-2)
Q иЛ £ог г ^ . (4-3)
We have assumed that the leading edge of the plate is located at the origin (see Fig. 4-2). By assuming that the plate is semi-infinite one avoids the problem of considering upstream effects from the trailing edge. These are actually quite small and do not show up in the boundary layer approximations to be derived.
In the process of introducing nondimensional coordinates a minor difficulty is encountered because there is no natural length in the problem to which spatial coordinates could be referred. We will circumvent this by selecting an arbitrary reference length and thereby implicitly assume that the behavior of the solution for x — 0(1) and z = 0(1) will be studied.