A horizontal flat plate (of length L) exposed to a solvent stream in laminar flow parallel to the plate, with a free-stream velocity of U. The plate is coated with a substrate made of flexible macromolecules that dissolve slowly into the flowing solvent. Consider the momentum boundary layer problem associated with this system. Assume that the velocity distribution inside the boundary layer can be described by a parabolic profile of the form: Vx = a + by + cy^2 where a, b, and care coefficients. Use an appropriate set of boundary conditions to fully specify the velocity profile. What criticisms, if any, can be made against this choice for the velocity profile? ii. Determine the thickness of the hydrodynamic boundary layer as a function of distance along the plate (x)