The True Solution of Blasius’s Flat Plate Boundary Layer Equation

Blasius’s flat plate boundary layer equation has always been a model for a better understanding of the boundary layer concept and a didactic example of the exact solution for a particular case of Navier Stokes equations. However, considering problems in the equation deduction, the meaning of some related parameters, such as displacement thickness,
I, and the momentum thickness,
I, and the existence of a unique value of the similarity parameter at infinity, i.e.,
, set valid for the entire plate, may change such a reputation, turning it unreliable. These issues have been calling the attention of researchers for more than a century, who incorporated comments, critics, techniques, arguments, and suggestions to improve the classical theory and its results. Unfortunately, most of these contributions have not succeeded in explaining the common doubts related to an incompressible fluid advancing over an ideal flat plate. In fact, they hampered the determination of a model capable of describing this physical phenomenon. This work explains how it occurs and presents new equations compatible with Prandtl’s concept of boundary layer used to describe the flat plate boundary layer. The proposition of a new equation and solution requires that the ordinary third-order differential equation be solved with just three boundary conditions, as mathematically recommended; preserves the original flow design, and velocity gradients for a chosen station, x, determined in terms of positions situated all along the boundary layer thickness.