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 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. 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