In the case of a fluid flowing parallel to a flat surface, the displacement thickness, δ ∗ , of any streamline that is located outside a laminar boundary layer adjacent to the surface is given by...

In the case of a fluid flowing parallel to a flat surface, the displacement thickness, δ ∗ , of any streamline that is located outside a laminar boundary layer adjacent to the surface is given by

Determine the value of the proportionality constant for streamlines that are located within the boundary layer, expressing this proportionality constant as a function of the normalized distance, η, from the flat surface. Recall that the normalized distance, η, is defined by Equation 11.11. (Hint: Use the values of the Blasius solution given in Table 11.1 along with the definition of the displacement thickness given by Equation 11.63.)