Reconsider Fig. P4.17 in the following general way, It is known that the boundary layer thickness (x) increases monotonically and that there is no slip

Reconsider Fig. P4.17 in the following general way, It is known that the boundary layer thickness δ(x) increases monotonically and that there is no slip at the wall (y = 0). Further, u(x, y) merges smoothly with the outer stream flow, where u ≈ U = constant outside the layer. Use these facts to prove that
(a) the component υ(x, y) is positive everywhere within the layer,
(b) υ increases parabolically with y very near the wall, and
(c) υ is a maximum at y = δ.