We defined in class potential flow and learned that the flow in the near vicinity of the boundary is highly affected by shear stress and hence results in a boundary layer. Consider now that a fluid is entering between two parallel plates. After a sufficient distance (Le) from the entrance, the flow will be fully developed, thus Vx will not be a function of x. We want to focus on the region 0xLe, where flow will transit from uniform flow prior to entering the channel, to a transition flow that can be estimated as a potential flow with symmetry at the center. Beyound Le a fully developed flow is formed as shown in the figure below. At the transition stage, the velocity of the core is assumed to be independent of y, while close to the boundary a wall layer develops due to shear stress. Because the wall layer thickness increase with x, the core must accelerate to conserve mass, the flow then fully develops. We are interested in finding an expression of the entrance length (Le), which can be found by integrating the wall layer equation derived from the Karman Integral equation for 0xLe. Show that this expression should be HLe=0.052Re The following steps will be useful: a. Make use of the symmetry of the flow by considering one side only, i.e., 0 yH. b. Reduce the governing equations by order of magnitude arguments. c. In the proposed velocity profile, the velocity at the wall layer can be estimated as the maximum velocity in fully developed flow between two parallel plates. d. It is advisable to put the expression resulting from Karman Integral equation in a dimensionless form before proceeding. e. The following relation, derived from conservation of mass, between u and can be used: UH=u(H3)