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Question 1 A biomedical device allows blood to drain through a straight, vertical tube, as shown in Figure Q1. Figure Q1: biomedical device in which blood drains downward under the force of gravity. The flow is driven by gravity, and is steady-state, full-developed and axisymmetric. The pressure is constant throughout the tube. The axisymmetric Navier-Stokes and Continuity equations in cylindrical coordinates are: four at aur .+te az turar dur) др -- + ( to a²ur + az2 [Egn. 1] dus + uz az + ar ди, az + + az2 Pg [Eqn. 2] ror (ru) + Top du, =0 дz [Egn. 3] where g = 9.81 m/s2 a) Find the variation in radial velocity, up, as a function of radius (r). Explain any simplifications to the Navier-Stokes equations that you make. (5 marks) b) Find the variation in the axial velocity, uz, as a function of radius (r). Explain any simplifications to the Navier-Stokes equations that you make. [17 marks] c) Find the flow rate, [3 marks]