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A flat plate with sharp leading edge is placed in the test section of a low-speed wind tunnel. The working section of the wind tunnel has been designed to produce a region of constant free stream velocity (i.e., for x S 1.0 m, U = 27.0 m/s), followed by a region of decelerating flow (i.e., for x > 1.0, U. = A (1 - 5m/s, Figure Q1. bres Wind Tunnel Wall yUe = 27.01.for x S 10 m = V. = 4(1-6). m/s, !!! for x 2 1.0 m For 13 1.0 m Flat Plate Figure Q1 U is the freestream air velocity, x is the streamwise position in meter, Lrer is a reference length equal to 10 m and x = 0 corresponds to the leading edge of the flat plate. 1- Determine the constant A and its dimension.
2- Calculate the boundary layer momentum thickness and shape factor at point B immediately before the boundary layer reaches the decelerating section. Physical thickness of the boundary layer (8) for x SXg, is defined as a distance at which "/u. = 0.99425. [10 marks] 3- Determine the boundary layer displacement thickness and shape factor at the point of separation [15 marks] 4- Explain the variation of boundary layer shape factor under the action of adverse pressure gradient. Explain the difference between the values of the shape factor at points B and C. Then explain how a Pitot tube can be used to detect the location of the separation point. Use sketches to illustrate your answer. Please limit your answer to around 50-70 words. [5 marks]