2. To test the aerodynamics of a new prototype automobile, a scale model will be tested...

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2. To test the aerodynamics of a new prototype automobile, a scale model will be tested in a wind tunnel. 1/20 scale model is used to establish a relationship between speed of the automobile, V, and the aerodynamic drag force, FD. The results of the experiment are listed as follows: V, m/s 10 FD, N 15 20 25 30 35 40 45 50 55 0.29 0.64 0.96 1.41 1.55 2.10 2.65 3.28 4.07 4.91 FD can be expressed as FD f(V, h, W, P, H) where h is height of the automobile, W is width of the automobile, p is the fluid density and is the fluid viscosity. There is geometric similarity between model and prototype. The prototype automobile is 4.35 m long, 1.35 m height, and 1.75 m width. Assume that both the wind tunnel air and the air flowing over the prototype automobile are at 25C and atmospheric pressure. (a) Determine a suitable set of dimensionless parameters. One of the dimensionless parameters should be the Reynolds number, Re, where the length scale is the automobile width, W. (b) Plot the dependent pi term (non-dimensional FD) as a function of Re (Re and non-dimensional FD are placed on the x and y axis, respectively.). Is there and dynamic similarity? If there is any Re independency in the experiment, what is its Re range? (c) Using the experimental results, obtain a relationship between the non-dimensional drag force and Re with second degree polynomial curve fitting technique. If there is any Re independence in the experiment, the relationship should not include the results in the Re independent region. (d) Find Fo's on the prototype automobile traveling at 1.2 m/s and 30 m/s, respectively. 2. To test the aerodynamics of a new prototype automobile, a scale model will be tested in a wind tunnel. 1/20 scale model is used to establish a relationship between speed of the automobile, V, and the aerodynamic drag force, FD. The results of the experiment are listed as follows: V, m/s 10 FD, N 15 20 25 30 35 40 45 50 55 0.29 0.64 0.96 1.41 1.55 2.10 2.65 3.28 4.07 4.91 FD can be expressed as FD f(V, h, W, P, H) where h is height of the automobile, W is width of the automobile, p is the fluid density and is the fluid viscosity. There is geometric similarity between model and prototype. The prototype automobile is 4.35 m long, 1.35 m height, and 1.75 m width. Assume that both the wind tunnel air and the air flowing over the prototype automobile are at 25C and atmospheric pressure. (a) Determine a suitable set of dimensionless parameters. One of the dimensionless parameters should be the Reynolds number, Re, where the length scale is the automobile width, W. (b) Plot the dependent pi term (non-dimensional FD) as a function of Re (Re and non-dimensional FD are placed on the x and y axis, respectively.). Is there and dynamic similarity? If there is any Re independency in the experiment, what is its Re range? (c) Using the experimental results, obtain a relationship between the non-dimensional drag force and Re with second degree polynomial curve fitting technique. If there is any Re independence in the experiment, the relationship should not include the results in the Re independent region. (d) Find Fo's on the prototype automobile traveling at 1.2 m/s and 30 m/s, respectively.