A rotating shaft is mounted in a solid metal bracket using an oil bearing as shown in Figure 1. The shaft has diameter 3.0 cm and rotates at 800 rpm (rotations per minute). The cylindrical hole in the bracket has diameter 3.2 cm and length ("into the paper") 2.4 cm. The gap between the shaft and the recess is filled with oil that has density 875 kg/m3 and dynamic viscosity 0.45 Pa.s. oil-filled gap metal bracket rotating shaft Figure 1 (i) Sketch, with appropriate labels, a suitable model for the motion of the oil in the gap. (3 marks) (ii) State the two main assumptions you have made in your modelling of the bearing. (2 marks) (iii) Calculate the resistive torque experienced by the shaft in the bearing. (7 marks) (iv) Calculate the power lost in the bearing. (3 marks) (v) Calculate the Reynolds number for the flow of oil in the bearing. (3 marks) (vi) What is the meaning and use of the Reynolds number in the characterisation of a fluid flow?