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# Boundary-layer thickness

In a fluid with velocity flowing over a surface or a body moving through a fluid, viscous effects are limited to regions with fluid shear. Consider a stationary body with flow over it such that the flow is steady. In situations with a solid boundary, the fluid satisfies the no-slip boundary condition in the boundary-layer and asymptotically approaches the free stream mean velocity, uo. Therefore it is impossible to define a clear thickness of the boundary layer. It is commonly accepted that the boundary-layer thickness be defined as the location away from the wall where

u = 0.99uo

(1)

This definition holds for both turbulent and laminar boundary layers. More physically significant measures of boundary-layer thicknesses are given by the displacement thickness and the momentum thickness.

For laminar boundary-layers over a flat plate, the Blasius solution gives

$\delta \approx 4.5 \sqrt{ {\nu x}\over u_o}$

(2)