Answer Happy

Question 1 A biomedical device allows blood to drain through a straight, vertical tube, as shown in Figure Q1. Ľ u(1) 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: ди, р at aur (1 a + urar + ur, ) - + they - 36 ) . 1] du, дz др - ar a²ur ur дz2 [Eqn. 1] Ouz rauz Plat tur ar อิน; + uz az a²uz др + 4 дz rər duz + дz2 - pg [Eqn.2) 1a ди, (rur) + = 0 тar 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, Q [3 marks]