Displacement Thickness

It is not exactly true that the boundary layer does not affect the potential flow at all. The potential flow streamlines just above the boundary layer will be slightly displaced away from the wall by the boundary layer:

Suppose a potential flow streamline in the matching region would be at a distance h from the wall if there was no boundary layer, then it has streamfunction value . The displaced distance follows from:

The displacement of the streamline follows:

Since the integrand disappears above the boundary layer, this displacement is the same for all streamlines in the matching region. Assuming we use the boundary layer solution for the velocity profile, we may as well write

The result of this displacement is that as far as the potential flow is concerned, the body is thicker by an amount :

From the solution of the Blasius profile, it follows that for a flat plate in a uniform flow,

Exercise:

Find the displacement thickness at the end of the plate from two exercises back.

Exercise:

For the inlet of question 7.1, determine how the pressure changes near the start of the inlet.