Answer Happy

4. It is suggested that the air speed near the ground of a landing strip be measured using the anchored balloon shown below. The 0.6-m balloon is filled with helium (PHe = 164.5 g/m?), and the balloon material itself weighs 0.5 N. The density and viscosity of air can be taken as Pair = 1.23 kg/mand = 17.9. 10-6 Pa-s. D U 400 200 100 60 40 20 10 6 6 4 CD -Co - 24 Ср Re Smooth cylinder Rough cylinder 2 1 0.6 0.4 0.2 Smooth sphere 0.1 0.06 10-1 100 101 102 103 104 105 106 Re a) Draw a free body diagram of the balloon, identifying all the forces acting on it. b) Derive a general expression for the angle, 0, between the rope and the ground as a function of the wind velocity, U, the total drag coefficient, CD, the balloon diameter, D, the balloon weight, W, the density of air and helium, the acceleration of gravity, g, and relevant numerical constants. c) Use the accompanying drag coefficient figure to determine 0 for wind velocities of 1, 2, 5, 10, 20, 40, 60, and 80 km/h. Plot the results and connect the individual data points by "eyeballing" the presumed smooth curve between each point. d) For approximately what range of wind speeds would this be an effective measurement device? Explain your reasoning, including why you excluded certain wind speeds from the effective range. Some things to consider when answering this question: • Would you prefer a measurement device to have a large or small change in its output in response to a change in the input? • Would you want a measurement device to provide the same output value for multiple different inputs?