Prandtl boundary-layer equation
= Prandtl boundary-layer equation
{c}
{wiki=Boundary_layer#Boundary_layer_equations}
For a steady two-dimensional incompressible boundary layer with tangential velocity $u(x,y)$, normal velocity $v(x,y)$, outer tangential velocity $U(x)$, and <kinematic viscosity> $\nu$,
$$
u u_x+v u_y=U\frac{dU}{dx}+\nu u_{yy},
\qquad
u_x+v_y=0.
$$
The pressure is uniform across the layer, and the outer Euler equation supplies $-p_x/\rho=U\,dU/dx$.