Viscous boundary layer

A viscous boundary layer is a boundary layer next to a surface in which viscosity remains important even when the outer flow has a large Reynolds number. It reconciles the outer inviscid velocity with the no-slip boundary condition.

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 $\nu$,The pressure is uniform across the layer, and the outer Euler equation supplies $-p_x/\rho =UdU/dx$.

For streamwise length $L$, outer speed $U$, and layer thickness $\delta$, balancing $u{u}_x\sim U^2/L$ with $\nu u_{yy}\sim \nu U/{\delta }^2$ gives