Prandtl's Boundary Layer Equations

Prandtl simplified the Navier-Stokes Equations for the Laminar Boundary Layer. The main simplification is that the pressure is constant along the height of the boundary layer.

Continuity Equation

$$\nabla \cdot \vec{U}=0$$

Momentum Equation

$$\begin{array}{rl}\rho \left(u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}\right)& =-\frac{dp}{dx}+\mu \frac{{\partial }^{2}u}{\partial y^2}\end{array}$$

Note: $y-$ momentum equations are not considered ‘cause they are trivial (we assume there’s no change)

Addendum

$$\frac{\partial p}{\partial y}=0$$