A crude but useful approximation for an incompressible boundary layer is a cubic variation from u = 0 at the surface (y = δ) to the freestream velocity, U, at the edge of the boundary layer (y = 0). The equation for the profile is u/U = 3/2(y/δ) – 1/2(y/δ)3, where δ = cx1/2 and c is a constant. Derive the simplest expression for v/U, the y component of velocity ratio. Determine the y/δ location for the maximum value of the ratio v/U. Determine v/U for y = 1 mm, δ = 5 mm and x = 0.87 m. Determine vmax/U for δ = 5 mm and x = 0.87 m.
