Question

Problem 1 (40 pts): Wind blowing past a flag causes it to \"flutter in the breeze.\" The frequency of this fluttering, $\omega$ (with dimension of T?¹), is assumed to be a function of the wind speed, V, the air density, $\rho$, the acceleration of gravity, g, the length of the flag, l, and the \"area density,\" $\rho_a$, (with dimensions of ML?²) of the flag material. It is desired to predict the flutter frequency of the large l = 40 ft flag in a V = 30 ft/s wind. To do this, a model flag with l = 4 ft is to be tested in a wind tunnel. a) It has been shown that $\omega = f(V, \rho, g, l, \rho_a)$. Express each parameter in terms of its primary dimensions using the MLT system. (3 pts) b) How many nondimensional parameters are expected to fully describe this problem? Show how you arrived at your answer. (2 pts) c) Show that l, g, and $\rho$ meet the criterion of being selected as repeating variables. (4 pts) d) Using l, g, and $\rho$ as repeating variables, and the linear equations method, develop the $\Pi$ term. Make $\Pi_1$ contain the dependent variable ($\omega$). (8 pts)

          Problem 1 (40 pts):
Wind blowing past a flag causes it to \"flutter in the breeze.\" The frequency of this fluttering, $\omega$
(with dimension of T?¹), is assumed to be a function of the wind speed, V, the air density, $\rho$, the
acceleration of gravity, g, the length of the flag, l, and the \"area density,\" $\rho_a$, (with dimensions of
ML?²) of the flag material. It is desired to predict the flutter frequency of the large l = 40 ft flag
in a V = 30 ft/s wind. To do this, a model flag with l = 4 ft is to be tested in a wind tunnel.
a) It has been shown that $\omega = f(V, \rho, g, l, \rho_a)$. Express each parameter in terms of its primary
dimensions using the MLT system. (3 pts)
b) How many nondimensional parameters are expected to fully describe this problem? Show
how you arrived at your answer. (2 pts)
c) Show that l, g, and $\rho$ meet the criterion of being selected as repeating variables. (4 pts)
d) Using l, g, and $\rho$ as repeating variables, and the linear equations method, develop the $\Pi$
term. Make $\Pi_1$ contain the dependent variable ($\omega$). (8 pts)

Problem 1 (40 pts):
Wind blowing past a flag causes it to f̈lutter in the breeze.T̈he frequency of this fluttering, ω
(with dimension of T?¹), is assumed to be a function of the wind speed, V, the air density, ρ, the
acceleration of gravity, g, the length of the flag, l, and the ärea density,$̈, (with dimensions of
ML?²) of the flag material. It is desired to predict the flutter frequency of the large l = 40 ft flag
in a V = 30 ft/s wind. To do this, a model flag with l = 4 ft is to be tested in a wind tunnel.
a) It has been shown thatω= f(V, ρ, g, l, ). Express each parameter in terms of its primary
dimensions using the MLT system. (3 pts)
b) How many nondimensional parameters are expected to fully describe this problem? Show
how you arrived at your answer. (2 pts)
c) Show that l, g, andρmeet the criterion of being selected as repeating variables. (4 pts)
d) Using l, g, andρas repeating variables, and the linear equations method, develop theΠterm. MakeΠ1contain the dependent variable (ω). (8 pts)

Added by Luz P.

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