Chapter 9, Problem 10P

Evaluate θ/δ for each of the laminar boundary-layer velocity profiles given in Problem 9.8.

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

Linear: $\frac{u}{U}=\frac{y}{\delta }$

Sinusoidal: $\frac{u}{U}=\sin \left(\frac{\pi }{2}\frac{y}{\delta }\right)$

Parabolic: $\frac{u}{U}=2\left(\frac{y}{\delta }\right)-{\left(\frac{y}{\delta }\right)}^2$

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