Consider a laminar boundary layer flow over a flat plate for which the velocity profile can be approximated by cubic equation, u/U = 3(y/δ)/2 − (y/δ)3/2 (see profile in text Fig. 9.12).
- Show that this profile satisfies the appropriate boundary conditions.
- Using the momentum integral relation, equ. (9.26), derive expressions for δ/x and τw(x). Inte- grate τw(x) and obtain an expression for the drag coefficient, CD, as a function of Rel, where l is length of plate. Compare with results in Table 9.2.
- Repeat, but now consider a turbulent boundary layer for which the velocity profile can be approximated by a power law equation, u/U = (y/δ)1/6.