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Question: a twodimensional diverging duct is being designed to diffuse...

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( A two-dimensional diverging duct is being designed to diffuse the high-speed air exiting a wind tunnel. The. x-axis is the centerline of the duct (it is symmetric about the. x-axis), and the top and bottom walls are to be curved in such a way that the axial wind speed udecreases approximately linearly from u 1-300 m/s at section 1 to u 2-100 m/s at section 2 (Fig. P9-24) Meanwhile, the air density p is to increase approximately linearly from p 1, 0.85 kg/m 3 at section 1 to ρ 2 = 1.2 kg/m 3 at section 2. The diverging duct is 2.0 m long and is 1.60 m high at section 1 (only the upper half is sketched in Fig, P9-24; the half-height at section 1 is 0.80 m). ( a) Predict the y-component of velocity, v( х. y). in the duct, ( b) Plot the approximate shape of the duct, ignoring friction on the walls, (c) What should be the half-height of the duct at section 2? Ar 2.0 m 0.8 m (2)I

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