Given:

A model of a high-rise offiice building at 1/500 scale is tested in a wind tunnel to estimate the pressures and forces on the full-scale structure. The wind-tunnel air speed is 20 m/s at (20 degrees C) and atmospheric pressure. The full-scale structure is expected to withstand winds of 200 km/h (10 degrees C).

find:

Show that the model and prototype Reynolds numbers are not equal, but sufficiently large for approximate dynamic similitude. For the length scale in the Reynolds number, does it make a dierence if you choose building height or building width? Which do you think is the more relevant length scale for this problem? (For reference, the Empire State Building is 443 m high to its tip, with average floor area 2048 m^2.)

assume

viscosity at 20 degrees c =1.51*10^-5 and density of air is 1.2

viscosity at 10 degrees=1.3*10-5 and air density is 1.25

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