Wind blowing past a flag causes it to flutter in the breeze. The frequency of this fluttering, ω, is assumed to be a function of the wind speed V , the air density ρ, the acceleration due to gravity g, the length of the flag `, and the area density ρA (with dimensions of mass per unit area) of the flag material. It is desired to predict the flutter frequency of a large 12 m flag in a 10 m/s wind. To do this a model flag with ` = 1.2 m is to be tested in a wind tunnel. (a) Express the non-dimensional frequency as a function of the other non-dimensional groups. (b) Determine the required area density of the model flag material if the large flag has ρA = 1 kg/m2 . (c) What wind tunnel velocity is required for testing the model? (d) If the model flag flutters at 6 Hz, predict the frequency for the large flag.
Wind blowing past a flag causes it to flutter in the breeze. The frequency of this fluttering, ω, is assumed to be a function of the wind speed V , the air density ρ, the acceleration due to gravity g, the length of the flag `, and the area density ρA (with dimensions of mass per unit area) of the flag material. It is desired to predict the flutter frequency of a large 12 m flag in a 10 m/s wind. To do this a model flag with ` = 1.2 m is to be tested in a wind tunnel.
(a) Express the non-dimensional frequency as a function of the other non-dimensional groups.
(b) Determine the required area density of the model flag material if the large flag has ρA = 1 kg/m2 .
(c) What wind tunnel velocity is required for testing the model?
(d) If the model flag flutters at 6 Hz, predict the frequency for the large flag.
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