5.5 For the laminar boundary layer flow of an incompressible fluid, the x component of velocity can be approximated as a linear variation from u = 0 at the surface to the u = U at the boundary-layer edge,
, where U is the freestream velocity. The equation for the profile is then u=U y

δ

where
=cx1 2 and c is a constant. Show that v is given by v=

Uy 4x

. At a location where x = 0.5 m and d = 5 mm, evaluate the ratio v

U at the wall, at
/2, and at
.