Three main parameters (described below) that are used to characterize the size and shape of a boundary layer are the boundary layer thickness, the displacement thickness, and the momentum thickness. Ratios of these thicknesses describe the shape of the boundary layer.
There are other such thicknesses, but they are not as common.
The boundary layer thickness, signified by , is simply the thickness of the viscous boundary layer region. Because the main effect of viscosity is to slow the fluid near a wall, the edge of the viscous region is found at the point where the fluid velocity is essentially equal to the free-stream velocity.
In a boundary layer, the fluid asymptotically approaches the
free-stream velocity as one moves away from the wall, so it never
actually equals the free-stream velocity. Conventionally (and
arbitrarily), we define the edge of the boundary layer to be the point
at which the fluid velocity equals 99% of the free-stream velocity:
There are no general equations for boundary layer thickness. Specific
equations exist for certain types of boundary layer. For a Blasius
(flat-plate, incompressible, laminar) boundary layer, the boundary
layer thickness is given by
The displacement thickness, symbolized by , is the distance a streamline just outside the boundary layer is displaced away from the wall compared to the inviscid solution. Another way to describe it is the distance the wall would have to be displaced to yield the same solution for flow outside the boundary layer as the boundary layer equations yield.
Still another way to describe displacement thickness is in
Figure 4. The displacement thickness is the distance that,
when multiplied by the free-stream velocity, equals the integral of
velocity defect, ,
across the boundary layer. That is,
The displacement thickness is important in iterative boundary layer solutions. After employing the boundary layer equations to calculate the displacement thickness along the wall, a virtual wall is created by displacing the wall outward by the displacement thickness. A new inviscid solution is computed using this virtual wall. This yields slightly different free-stream conditions than the initial calculation. The boundary layer solution is then recalculated, using the new free-stream conditions, for the real wall. The process is repeated until the displacement thickness stops moving with each iteration.
The momentum thickness, symbolized by ,
is the distance
that, when multiplied by the square of the free-stream velocity,
equals the integral of the momentum defect,
the boundary layer. That is,
The momentum thickness is somewhat harder to visualize than the displacement thickness. One can visualize it using Figure 4, except that specific momentum flux distribution replaces the velocity distribution .
The momentum thickness is useful in determining the skin friction drag on a surface. The total skin friction drag per unit depth on the surface is given simply by , evaluated at the trailing edge.