Boundary-layer Thickness - Momentum Thickness

The momentum thickness, θ or δ₂, is the distance by which a surface would have to be moved parallel to itself towards the reference plane in an inviscid fluid stream of velocity to give the same total momentum as exists between the surface and the reference plane in a real fluid.

The definition of the momentum thickness for compressible flow is based on mass flow rate:

The definition for incompressible flow can be based on volumetric flow rate, as the density is constant:

Where and are the density and velocity in the 'free stream' outside the boundary layer, and is the coordinate normal to the wall.

For boundary layer calculations, the density and velocity at the edge of the boundary layer must be used, as there is no free stream. In the equations above, and are therefore replaced with and .

For a flat plate at no angle of attack with a laminar boundary layer, the Blasius solution gives

The influence of fluid viscosity creates a wall shear stress, which extracts energy from the mean flow. The boundary layer can be considered to possess a total momentum flux deficit, due to the frictional dissipation.

Other length scales describing viscous boundary layers include the energy thickness, .