Displacement thickness

The displacement thickness , a term used in fluid mechanics ( boundary layer theory ), is a measure of the outward displacement of the streamlines due to the formation of a boundary layer . The displacement thickness corresponds to the distance by which the plate on which the boundary layer is formed would have to be displaced in order to obtain the same mass flow as in the case of a plate without a boundary layer. ${\displaystyle \delta ^{*}}$

The displacement thickness is defined as:

${\displaystyle \delta ^{*}=(\delta _{1})=\int _{0}^{\delta (\infty )}\left(1-{\frac {\overline {u}}{u_{0}}}\right)\cdot dy}$

With

• ${\displaystyle \delta }$: Thickness of the boundary layer
• ${\displaystyle {\overline {u}}}$: averaged speed curve
• ${\displaystyle u_{0}}$: Inflow velocity of the infinite outer flow.

The shape parameter of a boundary layer can be determined as the ratio of the displacement thickness and the momentum loss thickness : ${\displaystyle H}$ ${\displaystyle \theta }$

${\displaystyle H={\frac {\delta ^{*}}{\theta }}}$

literature

• Dominik Surek , Silke Stempin, Applied Fluid Mechanics , Vieweg + Teubner Verlag 2007, ISBN 3-8351-0118-8 , p. 245

See also

• Boundary layer equations