How many (non-dimensional) fl-groups are there?


Homework 6

  1. The period of a pendulum, T, is assumed (correctly or incorrectly) to depend on its mass, M, the length of the pendulum. P, the acceleration due to gravity, 9, and the angle of swing, O. Using dimensional analysis, nondimensionalize the period, T, and express its dependence on the other non-dimensional terms.
  2. Under certain conditions, wind blowing past a rectangular speed limit sign can cause the sign to oscillate with a frequency w. Assume that co is a function of the sign width, b, sign height. h, wind velocity. V. air density p, and an elastic constant, k. for the supporting pole. Hint: The constant k has dimensions of [force x length].
  3. a) How many (non-dimensional) fl-groups are there?
  4. b) Find these non-dimensional groups.
  5. c) Can one of the 11-groups be considered a Reynolds number?
  6. Consider two different flows over geometrically similar airfoil shapes. one airfoil being twice 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 71.= 200K. p. = 1.23 kg/m3. and V. = 100 m/s. The airflow over the larger airfoil is described by T. = 800 K. p= 1.739 kg/m3, and V. = 200 m/s. Assume that the viscosity of the air is proportional to T1I2 , while the heat capacities of air is a constant. Are the two flows similar?