A thin-wall hollow cylinder of 0.5-m inner radius and 2-m length is spinning about the central axis at constant angular

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A Thin Wall Hollow Cylinder Of 0 5 M Inner Radius And 2 M Length Is Spinning About The Central Axis At Constant Angular 1 (66.61 KiB) Viewed 11 times

A thin-wall hollow cylinder of 0.5-m inner radius and 2-m length is spinning about the central axis at constant angular velocity of 4 rad/s. Assume a steady, incompressible, and viscous airflow is generated inside, where the air sticks to the inner surface of the cylinder, and the velocity has only transverse component linearly distributed along the radius, as shown in Figure 1. 2 m 4 rad/s 0.5 m 0.25 m A Figure 1 (a) Determine the stream function of the airflow inside the cylinder. (4 marks) (b) Determine the circulation along the streamline passing through point A. (4 marks) (c) Determine the shear strain rate and vorticity of the airflow. (7 marks) (d) Determine the torque applied by the air on the cylinder. (6 marks) (e) Someone claims that as the air in contact with the cylinder has the highest speed, according to Bernoulli's equation, the pressure in contact with the cylinder is the lowest. Do you agree? Justify your answer. (4 marks)