QUESTION 1 [50 Marks] PART A (25 Marks) Consider a parallel plate flow problem as illustrated in Fig.1(a) where the normal and tangential stresses acting on an infinitesimal control volume as shown along the Cartesian direction of x are shown in Fig.1(b): Ay: Andy Ou [T+AJAKAY +Az 5 AxAz Surface Forces Figure 1(a) The mass conservation equation is given as: dp (pu) (pv) (pw) = 0 + + + dy Oz =0 Figure 1(b) (i) Provided that the flow is incompressible, reduce the above equation. What physical description of the flow can be concluded based on the reduced equation? [6 Marks] (ii) Based on the finding in (i) and given the fluid is Newtonian with constant fluid properties, and no external body forces, derive the following x-momentum equation: Ju +v+w ax +4 + The normal and tangential viscous stresses are given as: Ou Ou Ov Ow =-p+2- +2 axx ax by + 2 du ov and F = [+] z ax [8 Marks] (iii) Starting from the following two-dimensional x-momentum equation: Non-dimensionalize the above equation using the following scaling factors: and j p (6 Marks] (iv) Provided that there are two separate flows across two parallel plates with different fluid viscosities but sharing the same Reynolds number. Briefly discuss about the outlet velocity profiles. You may use figure to illustrate your answer. [5 Marks)