Flow patterns that develop as winds blow past a vehicle,

Chapter 7, Problem 7.83

(choose chapter or problem)

Flow patterns that develop as winds blow past a vehicle, such as a train, are often studied in low-speed environmental (meteorological) wind tunnels. (See Video V7.16.) Typically, the air velocities in these tunnels are in the range of 0.1 m/s to 30 m/s. Consider a cross wind blowing past a train locomotive. Assume that the local wind velocity, V, is a function of the approaching wind velocity (at some distance from the locomotive), U, the locomotive length, \(\ell\), height, h, and width, b, the air density, \(\rho\), and the air viscosity, \(\mu\). (a) Establish the similarity requirements and prediction equation for a model to be used in the wind tunnel to study the air velocity, V, around the locomotive. (b) If the model is to be used for cross winds gusting to U = 25 m/s, explain why it is not practical to maintain Reynolds number similarity for a typical length scale 1:50.