Fluid Mechanics

i. (20 points) During a high Reynolds number experiment, the total drag force acting on a spherical body of diameter D = 12 cm subjected to airflow at 1 atm and 5°C is measured to be 5.2 N. The pressure drag acting on the body is calculated by integrating the pressure distribution (measured by the use of pressure sensors throughout the surface) to be 4.9 N. Determine the friction drag coefficient of the sphere, and whether the flow is in turbulence.

i. (20 point) During major windstorms, high vehicles such as RVs and semis maybe thrown off the road and boxcars off their tracks, especially when they are empty and in open areas. Consider a 5000-kg semi that is 9 m long, 2.5 m high,and 2 m wide. The distance between the bottom of the truck and the road is 0.75m. Now the truck is exposed to winds from its side surface. Determine the wind velocity that will tip the truck over to its side, and estimate whether the flow will be in laminar or turbulent regime. Take the air density to be 1.1 kg/m3 and assume the weight to be uniformly distributed. (please refer to Figure P11-43)

i. (20 point) The forming section of a plastics plant puts out a continuous sheet of plastic that is 1.2 m wide and 2 mm thick at a rate of 18 m/min. The sheet is subjected to airflow at a velocity of 4 m/s on both top and bottom surfaces normal to the direction of motion of the sheet. The width of the air cooling section is such that a fixed point on the plastic sheet passes through that section in 2 s. Using properties of air at 1 atm and 60 °C, determine the drag force the air exerts on the plastic sheet in the direction of airflow (please refer to the FigureP11-57).

(20 points) Consider an aircraft that takes off at 190 km/h when it is fully loaded. If the weight of the aircraft is increased by 20% as a result of overloading, determine the speed at which the overloaded aircraft will take off.

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