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, ι, height, h, and width, b, the air density, ρ, and the air viscosity, μ . (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.
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