The leading edge of a suspended bridge, when exposed to high wind speeds, may experience harmful periodic forces caused by vortices shed on the back side of the structure. It is known that the frequency of this vortex shedding phenomenon, w, is a function of the wind speed, V, air density and viscosity, (p), dimensions H and D of the structure and the wind angle ie. 0 = f(D, H, V, p, , e)
A) Use the Buckingham theorem (or another method) to determine a set of non- dimensional groups for this problem.
B) For this structure, D = 0.3 m, H = 0.8 m, V-60 km/hr, air is at 20 °C and 101300 Pa, and 0-15°. To determine the shedding frequency, a model with Da = 10 mm will be tested in 10°C water. Determine the model dimension of Hm, the water velocity angle with the model axis (%), and the water velocity at which the test should be performed (I'm).
C) If the water test shows a shedding frequency of 40 Hz, what is the corresponding frequency for the bridge? Gas constant for air, R = 287 J/kg. K, Air viscosity 1.8x103 N. s/m2, Water viscosity 1.31x10 N. s/m.