1) Consider turbulent flow of an incompressible fluid past a flat plate. The boundary layer velocity profile is assumed to be Uu=(y)71fory and u=Ufory This is a reasonable approximation of experimentally observed profiles except very near the plate. (Note the difference between laminar profile and turbulent profile). Also assume the shear stress agrees with the experimentally determined formula w=(501)U2(U)1/4 (Note: In this problem you cannot use the relationship w=dyy=0 since the gradient in velocity is not defined at y=0. That is why the above expression was given to you for the shear stress at the wall). (1) Determine the boundary layer thickness (15 points) and the (2) wall shear stress w as a function of x (5points). Assume that the von Karman relation holds. (3) Determine how the total drag force changes with the length of the plate L ( 15 points)