Chapter 7, Problem 5P

By using order of magnitude analysis, the continuity and Navier–Stokes equations can be simplified to the Prandtl boundarylayer equations. For steady, incompressible, and two-dimensional flow, neglecting gravity, the result is

$\begin{array}{l}\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0\hfill \\ u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=-\frac{1}{\rho }\frac{\partial p}{\partial x}+v\frac{{\partial }^{2}u}{\partial y^2}\hfill \end{array}$

Use L and V₀ as characteristic length and velocity, respectively. Nondimensionalize these equations and identify the similarity parameters that result.