- E The Flow Over A Flat Plate Adheres To The Plate Surface And Forms A Boundary Layer As Depicted In Figure 5 At Both S 1 (136.6 KiB) Viewed 30 times
E The flow over a flat plate adheres to the plate surface and forms a boundary layer, as depicted in Figure 5. At both sections a-b and c-d, the velocity within the boundary layer, y € (0,8), are approximated by a linear profile such that Uy for y < 8; (:r, y) 8(2) U, for y > 8. where U = 3 m/s is the free-stream velocity outside the boundary layer (y > ) and the boundary layer thickness (1) varies in the streamwise r-direction. The boundary layer thickness is measured at section a-b such that dab = 2 mm and Scd = 3 mm at section c-d. The fluid is water with density p= 1000 kg/m3. The plate width perpendicular to the paper is w = 0.2 m. Assume two-dimensional, steady state, and incompressible flow. b. b dcd = 3 mm ey dab = 2 mm a •êz Figure 5: Control volume analysis of a boundary layer. 1. Find the mass flow rate across top surface b-c of control volume a-b-c-d. (10 pts) 2. Outside of the boundary layer, the wall-normal velocity gradient is zero, or Oyu = 0. Hence, no shear stress presents over section b-c. If the pressure at section a-b is equal to that at section c-d, determine the magnitude and direction of the friction force exerted by the wall on the flow over section a-d. (10 pts)