The aerodynamic drag of a new sports car is to be predicted at a speed of...

 

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The aerodynamic drag of a new sports car is to be predicted at a speed of 100 km/h at an air temperature of 25°C. Automotive engineers build a one-fifth scale model of the car to test in a wind tunnel. It is winter and the wind tunnel is located in an unheated building; the temperature of the wind tunnel air is only about 5°C. The wind tunnel has a moving belt to simulate the ground under the car, as in Fig.Q4. (The moving belt is necessary to achieve kinematic similarity everywhere in the flow, in particular underneath the car). a) Assuming that drag force is a function of velocity, density, length of the car, and viscosity, conduct a dimensional analysis based on the drag force. (12 Marks) b) Assuming that the compressibility of the air is negligible, the wind tunnel walls are far enough away to not interfere with the aerodynamic drag on the model car and the model is geometrically similar to the prototype. Determine the velocity of air in which engineers should run the wind tunnel to achieve similarity between the model and the prototype. (6 Marks) c) Assuming that the engineers obtain a drag force value of 500 N, predict the aerodynamic drag force on the prototype (at 25°C). (7 Marks) Properties: For air at atmospheric pressure and at T = 25°C, p = 1.184 kg/m³ and μ = 1.849 x 10-5 kg/m-s. Similarly, at T = 5°C, p = 1.269 kg/m³ and μ = 1.754 x 10-5 kg/m-s. Wind tunnel test section Moving belt Model Drag balance Fig.Q4 FD The aerodynamic drag of a new sports car is to be predicted at a speed of 100 km/h at an air temperature of 25°C. Automotive engineers build a one-fifth scale model of the car to test in a wind tunnel. It is winter and the wind tunnel is located in an unheated building; the temperature of the wind tunnel air is only about 5°C. The wind tunnel has a moving belt to simulate the ground under the car, as in Fig.Q4. (The moving belt is necessary to achieve kinematic similarity everywhere in the flow, in particular underneath the car). a) Assuming that drag force is a function of velocity, density, length of the car, and viscosity, conduct a dimensional analysis based on the drag force. (12 Marks) b) Assuming that the compressibility of the air is negligible, the wind tunnel walls are far enough away to not interfere with the aerodynamic drag on the model car and the model is geometrically similar to the prototype. Determine the velocity of air in which engineers should run the wind tunnel to achieve similarity between the model and the prototype. (6 Marks) c) Assuming that the engineers obtain a drag force value of 500 N, predict the aerodynamic drag force on the prototype (at 25°C). (7 Marks) Properties: For air at atmospheric pressure and at T = 25°C, p = 1.184 kg/m³ and μ = 1.849 x 10-5 kg/m-s. Similarly, at T = 5°C, p = 1.269 kg/m³ and μ = 1.754 x 10-5 kg/m-s. Wind tunnel test section Moving belt Model Drag balance Fig.Q4 FD

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a Dimensional analysis based on drag force Drag force F fveloc... View the full answer