Question

A bridge is supported by two types of rectangular cross-section piles located in a river as shown in Figure 1. The width of the piles is w 0.5 m and their lengths are either l-2 m or 12 = 2.5 m. The river of depth of about 20 m runs at 2 m/s. Water density is ρ = 1000 kg/mand its absolute viscosity 1.00 x 10-3 N.s/m2 You are asked to perform dimensional analysis to find the drag force on the piles, and the frequency of wake oscillations due to vortex shedding from the piles, using experimental data from a wind tunnel experiment. The results from the wind tunnel, collected for models with a width w 200 mm, at air density p-1.20 kg/m3 and air absolute viscosity H- 182 x 10-5 N.s/m2, are given below. Model length (mm)800800800 12001200 1200 Wind Speed V (m/s) 35 5376355376 Drag D (N/m) 176 404 832 192 436 899 Frequency f(Hz)22.8 34.549.416.124.2 34.1 Write a dimensionless expression describing the functional dependence of the drag force on other important parameters. Briefly explain which dimensionless variables are important in this problem. (Note: it is NOT necessary to carry out an analysis using the PI-Theorem. Dimensional analysis by inspection is sufficient.) (a) It can be assumed that the piles are smooth and roughness can be neglected, then: c ) D-f(U, μ , p. 1, w, And number of dimensionless groups can be determined. This should be done by inspection Select standard groups to include Drag Force, Viscous Effects and Characteristic Fluctuations. Use width w as the normalising scale. In this problem you are given drag per unit length of pile (N/m), which means that in Drag Coefficient you should just use the width of pile w for scaling (rather than an area) to obtain a dimensionless parameter

Answer 1

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Solution :

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