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 eitherl 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/m' and its absolute viscosityH-1 .00 x 103 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 1.82 x 10-5 Ns/m?, are given below Model length (mm)800800800 1200 1200 1200 Wind Speed V (m/s) 355376 355376 176 404832 192 436 899 Drag D (N/m) Frequency f(Hz) 22.8 34.5 49.4 624.234.1 (a)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.) I4 marksl (b)Using the principle of geometric and dynamic similarity, determine the drag force and the frequency of wake oscillation on the pile with li- 2 m [6 marksl Flow li, 12 Direction Figure 1. Flow around a bridge pile (top view) HINTS: Part a) Because the piles are big and long, surface effects such as waves and surface tension can be neglected. It can be assumed that the piles are smooth and roughness ε can be neglected, then: 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. Part b) The drag measured on the model is in N/m which is a drag per unit length/depth. As a final answer you should calculate overall drag on a bridge pile for actual depth of the river.

Answer 1

In this solution some basic concepts and formulas of Fluid Mechanics are used. For more information, refer to any standard textbook or drop a comment below. Please give a Thumbs Up, if solution is helpful.

Solution :

Solution to both the parts is given below,

Part a.)

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Part b.)

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