3. A fluid flowing uphill can be simplified as shown in Figure 2. Simply speaking, an incompressible Newtonian laminar f

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3 A Fluid Flowing Uphill Can Be Simplified As Shown In Figure 2 Simply Speaking An Incompressible Newtonian Laminar F 1 (244.94 KiB) Viewed 36 times

3. A fluid flowing uphill can be simplified as shown in Figure 2. Simply speaking, an incompressible Newtonian laminar flow with the universal velocity, U., parallelly enters a plate from the leading edge of plate with an angle of 30° of the ground level. If the origin of coordinate (x, y) is at the leading edge of the plate, a steady two- dimensional laminar flow boundary layer with the thickness, d, can be established. The thermal and physical properties of the fluids are assumed to be constant. The velocity in the layer can be written as, > 2 7/3 - --. [e+o(@)+e+a0") 3)1 = , a b + d where a, b, c and d are constant. (a) Determine the coefficient, a, b, c and d using the non-slip boundary conditions at wall, the velocity at free boundary edge, the first-order differential and the second-order differential of velocity at free boundary edge. Applying the von Karman profile method to solve the integral momentum equation, determine the boundary layer thickness, the displacement thickness, the momentum thickness, and local skin friction coefficient.
(b) Point a is illustrated in Figure 2 and we know the distance, L, to the leading edge at the grand level. Please decide the flow boundary layer thickness as a function of L in the coordinate (x, y). Determine the velocity direction at Point a with the reference of ground level. (10 marks) un VE • X 30° Ground Level L Figure 2