PD&C HW4pA

Problem Statement: 1. Assuming that the viscous damping in a manometer can be expressed in terms of the pressure drop associated with laminar flow, i.e., Fanning friction factor of 16/Re, derive the transfer function relating the height difference between the fluid levels in a manometer to the pressure differential. 2. For a water-filled manometer where the total length of fluid is 1 m, with a tube diameter of 1 cm, determine the gain, damping coefficient, and time constant of the second order system. Simulate the response of the system to a 5000 Pa step change in pressure. 3. Show algebraically that two first order systems in series always has a damping coefficient greater than 1 and thus overdamped. 4. Computationally simulate the behavior of a second order system for different damping coefficients for oscillatory inputs at frequencies below, at, and above the natural frequency.