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# hw6 - 16.100 Homework Assignment 6 Due Monday October 31...

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16.100 Homework Assignment # 6 Due: Monday, October 31 9am Reading Assignment Anderson, 3 rd edition: Chapter 15, Sections 1-4, 7 Chapter 16, pages 745-751, 781-786 Problem 1 y 0 U Consider an initially stationary, long flat plate. At time t = 0 , the plate is set in motion at velocity U . As time evolves, the air above the plate will begin to move as the viscous effects diffuse the momentum away from the plate. We will define the height of the boundary layer of non-negligible momentum, 0 ) ( t δ , as the y-location at which the velocity is only 1% of the wall velocity. Assume the flow is incompressible. a) Apply the conservation of mass in differential form (i.e. not integral form) to show that the vertical velocity, v , is zero everywhere in the flow for all time. b) Next, show that the conservation of x-momentum can be reduced to the following form: 2 2 y u t u = ν (1) c) Show that the following x-velocity is a solution to Equation (1) and that it satisfies the initial and boundary conditions: () = η ξ π 0 0 2 2 4 1 d

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hw6 - 16.100 Homework Assignment 6 Due Monday October 31...

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