A useful approximation for the x component of velocity in an incompressible laminar boundary layer is a parabolic variation from u = 0 at the surface (y = 0) to the freestream velocity, U, at the edge of the boundary layer (y = δ). The equation for the profile is u/U = 2(y/δ) - (y/δ)2, where δ = cx1/2 and c is a constant. (a) Derive the stream function for this flow field. Locate streamlines at (b) "one-quarter" and (c) one-half the total volume flow rate in the boundary layer.