The velocity profile shape u/U 1 exp (4.605y/) is a smooth curve with u = 0 at

Question:

The velocity profile shape u/U ≈ 1 − exp (−4.605y/δ) is a smooth curve with u = 0 at y = 0 and u = 0.99U at y = δ and thus would seem to be a reasonable substitute for the parabolic flat-plate profile of Eq. (7.3). Yet when this new profile is used in the integral analysis of Sec. 7.3, we get the lousy result sult 1/2 / 9.2/Rex δ x ≈, which is 80 percent high. What is the reason for the inaccuracy? [Hint: The answer lies in evaluating the laminar boundary-layer momentum equation (7.19b) at the wall, y = 0.]