Top Section: Two Tables: There are two tables, each with a 5x5 grid. The top left corner of each table has a number (1 or 2). The cells within the tables contain 'X' symbols in various configurations. Equation: There is an equation: w_s = 16.75 rad/s and a calculation: (fs = 2.67 Hz). Text: The phrase "lock in" is written below the equation. Bottom Section: Diagrams: There are multiple diagrams, including: A wave-like pattern with labels like R=20 and R=120. A circular diagram with arrows pointing in different directions and labels like V_s and V_g. A diagram of a boat on a wavy surface with arrows indicating velocity. A diagram of a planet with a curved trajectory around a star. A diagram of a wave with a peak and trough, labeled with V_s and V_g. Part B: a) Terminal Velocity: Drag Force: The drag force (F_D) is modeled as proportional to the square of the velocity: F_D = kρv²A. Buoyancy Force: The buoyancy force (F_B) is equal to the weight of the fluid displaced by the object: F_B = ρ_fgV. Gravitational Force: The gravitational force (F_g) is equal to the weight of the object: F_g = mg. Terminal Velocity Condition: At terminal velocity, the net force is zero: F_D + F_B - F_g = 0. Calculation of Terminal Velocity: Using the expressions for the forces and the condition for terminal velocity, the formula for terminal velocity is derived. Numerical Example: The calculation of terminal velocity is demonstrated with a numerical example, considering different values for the drag coefficient and other parameters. b) Frequency Calculation: Given a velocity u, the frequency f is calculated using the formula f = u / λ, where λ is the wavelength. A numerical example is provided to illustrate the calculation. Part B: 3. Assumption: The flow velocity is assumed to be 0.2 m/s. Top: The drag force (F_D) is calculated as 0.1 * F_p, where F_p is the pressure force. Bottom: The drag force (F_B) is calculated as 0.1 * F_p. F_p: The pressure force is given as 0.4 kg. b) Frequency of Drag: It is stated that the frequency of drag is twice the frequency of vortex shedding. The frequency of lift is equal to the frequency of vortex shedding. Therefore, the flow velocity directly correlates with the frequency of vortex shedding. c) Structural Vibration: The structure is expected to vibrate more at the top due to the higher drag force and lower mass. In both cases (top and bottom), the frequency is low. Shear forces might complicate the shedding and make the flow more three-dimensional. d) Flexible Cylinder: Figure 8 Motion: The cylinder might exhibit a figure-8 motion under certain flow conditions. Higher Velocity, Tension, and Inline Vibration: As the velocity increases, the tension in the cylinder increases, and it might experience inline vibrations.

Solutions to Exam 2 (2004)

Related Documents

Recommended Documents

Description

Related Documents

Want to Download This Document?

Free up your schedule!

Take 5 seconds to unlock