1. The period of a pendulum T, is assumed (correctly or incorrectly) to depend an its mass, M, the length of the pendulum, e, the acceleration due to gravity, g, and the angle of swing, U. Using dimensional analysis, nondimensionalize the period, 7′, and express its dependence on the other non-dimensional terms. (15 points)
2. Under certain conditions, wind blowing past a rectangular speed lima sign can cause the sign to oscillate with a frequency si Assume that to is a function of the sign width, 0, sign height, h, wind velocity, V. air density p, and an elastic constant, k, for the supporting pole. Hint The constant it has dimensions of /force’, length]
a) How many (nononmensional) n-groups are there? (3 points) b) Find these non-dimensional groups. (10 points) c) Can one of the fl-groups be considered a Reynolds number? (2 points)
3 Consider two different flows over geometrically similar airfoil shapes, one airfoil being Woe the size of the other. Also, assume that the angle of attack is the same in both flows. The airflow over the smaller airfoil has freestream properties given by T.= 200K, p. = 1.23 kg/m., and m = 100 m/s. The airflow over the larger airfoil is described by T.= 800 K, p. = 1.739 kg/m., and V.= 200 m/s. Assume that the viscosity of the air is proportional to TV., while the heat capacities of air is a constant. Are the two flows similar/ (5 points)
