(See Fluids in the News article titled “Galloping Gertie,” Section 7.8.2.) The Tacoma Na...

(See Fluids in the News article titled “Galloping Gertie,” Section 7.8.2.) The Tacoma Narrows Bridge failure is a dramatic example of the possible serious effects of wind-induced vibrations. As a fluid flows around a body, vortices may be created that are shed periodically creating an oscillating force on the body. If the frequency of the shedding vortices coincides with the natural frequency of the body, large displacements of the body can be induced as was the case with the Tacoma Narrows bridge. To illustrate this type of phenomenon, consider fluid flow past a circular cylinder. Assume the frequency, n, of the shedding vortices behind the cylinder is a function of the cylinder diameter, D, the fluid velocity, V, and the fluid kinematic viscosity, . (a) Determine a suitable set of dimensionless variables for this problem. One of the dimensionless variables should be the Strouhal number, nD/V. (b) Some experiments using small models (cylinders) were performed in which the shedding frequency of the vortices (in Hz) was measured. Results for a particular cylinder in a Newtonian, incompressible fluid are shown in Fig. P7.54. Is this a “universal curve” that can be used to predict the shedding frequency for any cylinder placed in any fluid? Explain. (c) A certain structural component in the form of a 1-in.-diameter, 12-ft-long rod acts as a cantilever beam with a natural frequency of 19 Hz. Based on the data in Fig. P7.54, estimate the wind speed that may cause the rod to oscillate at its natural frequency. Hint: Use a trial-and-error solution.