Chapter 9, Problem 22P

Using numerical results for the Blasius exact solution for laminar boundary-layer flow on a flat plate, (Section 9.2 on the web) plot the dimensionless velocity profile, u/U (on the abscissa), versus dimensionless distance from the surface, y/δ (on the ordinate). Compare with the approximate parabolic velocity profile of Problem 9.8.

9.8 Velocity profiles in laminar boundary layers often are approximated by the equations

$\begin{array}{l}\text{Linear}:\frac{u}{U}=\frac{y}{\delta }\\ \text{Sinusoidal}:\frac{u}{U}=\sin \left(\frac{\pi }{2}\frac{y}{\delta }\right)\\ \text{Parabolic}:\frac{u}{U}=2\left(\frac{y}{\delta }\right)-{\left(\frac{y}{\delta }\right)}^2\end{array}$

Compare the shapes of these velocity profiles by plotting y/δ (on the ordinate) versus u/U (on the abscissa).