Displacement thickness

Displacement thickness is the distance by which a surface would have to be moved parallel to itself towards the reference plane in an ideal fluid stream of velocity $u\_0$ to give the same mass flow as occurs between the surface and the reference plane in a real fluid.

In practical aerodynamics, the displacement thickness essentially modifies the shape of a body immersed in a fluid. It is commonly used in aerodynamics to overcome the difficulty inherent in the fact that the fluid velocity in the boundary layer approaches asymptotically to the free stream value as distance from the wall increases at any given location. The mathematical definition of the displacement thickness for incompressible flow is given by

:$\{delta^*\}=\; int\_0^\{infty\}\; \{(1-\{uover\; u\_0\})dy\}$

and for compressible flow, by

:$\{delta^*\}=\; int\_0^\{infty\}\; \{(1-\{\; ho\; uover\; ho\_0\; u\_0\})dy\}$

where $ho\_0$ and $u\_0$ refer to the density and velocity outside the boundary layer.