Problem 5 The sketch below shows air flow over a flat plate positioned parallel to the oncoming flow. The laminar boundary layer (i.e., the region above the plate in which the flow is influenced by the presence of the plate) forms very close to the flat plate surface. The laminar velocity field is approximately: u(x,y)=u0(2y2y2) v(x,y)=u0x(22y233y3) where is the boundary layer thickness and u0 is the fluid velocity far above the plate. Outside of the boundary layer, u(x,y)u0. For laminar flow, the thickness is a function of position along the plate and is given by: (x)=5u0x where and are the dynamic viscosity and density of air, respectively. a) On one graph, sketch (i) vs. x and (ii) u(y) at three different x locations along the plate. b) Derive an expression for the drag force that acts on the top side of the plate. The plate has length L and a width of b into the page. c) Estimate the drag force when air at 20C,1atm, and u0=3m/s flows over a plate that is 0.5 m long and 2m widc