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Engineering · Civil Engineering
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1. Show that for ideal gases Speed of horizontal wind near the ground can be approximated using log wind profile as )In where y is the vertical coordinate (y O at the ground surface and positive upwards); ue is the friction velocity; K 0.4 is the von Karman constant; and yo is the roughness length. Assume u*-0.3 m/s, y0 = 10 mnn and T-25 °C (a) At what elevation does the non-slip condition, i.e. u 0, occur for log wind pr (b) What is the shear stress at y yo? (c) Plot the horizontal wind speed u(y) and the shear stress。) versus y for 0 < y < 100 m ofile? 3. A cylinder of diameter d, length I, and density p is falling inside a pipe (diameter D) filled with oil, at a constant velocity Vfatl. The small space between the cylinder and the pipe is lubricated with the oil of viscosity u. Assume a linear velocity profile for a thin film. (a) Find the velocity of descent Vall of the cylinder. (b) Given d 50 mm, D- 50.5 mm, 1-100 mm, ρ= 2400 kg/m3, and μ = 0.1 Ns/m2, compute l fall. Pipe Oil film Cylinder 4. A water bug is suspended on the surface of a pond by surface tension. The bug has six legs, cach in contact with the water over 5 mm. what is the maximum mass of the bug to avoid sinking? Given ơ- 0.073 N/mm. 5 mm 5 mm

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