Question 1 Consider a steady, two dimensional, incompressible flow of a Newtonian fluid with velocity field: u = -2xx v = xx a) Show that this flow model satisfies the continuity relation. (8 marks) b) Obtain expressions for the fluid accelerations in the x and y directions. (12 marks) c) Find the pressure distribution P(x, x), if the pressure at the point x x = 0 is Po. Neglect gravity. (20 marks) Question 2 A reasonable approximation for the two-dimensional incompressible laminar boundary layer on a flat surface in Figure Q2 on the next page is a) b) u = U for < where, 8 = Cx1/2 and C = ccccc Assuming a no-slip condition at the wall, find an expression for the velocity component v(x, x) for x 8. (Hint: - ud uu ) (20 marks) Also, find the maximum value of at the station x = 1 m, for the particular case of air flow, when U = 3 m/s and 8 = 1.1 cm. (10 marks) st Layer thickness 8(x) U U = constant u(x, y) u(x, y) Figure Q2 Question 3 Consider the two-dimensional incompressible velocity potential 0 = xx+xx a) Show that this flow is irrotational. (10 marks) b) Find the stream function (x, x), where (0,0) = 0 (20 marks) Question 4 For pressure-driven laminar flow between two horizontal infinite parallel plates separated by a distance 2h, the velocity components are: u = U (1 - x v = 0 where U is the centreline velocity and the x-axis is located at the centreline. Assume steady, fully developed and incompressible laminar flow. a) b) For the problem above, obtain the final form of the energy equation after applying the given assumptions. (10 marks) Identify the fluid temperature distribution T(y), for a constant wall temperature Tw at each plate. (20 marks) Hint: The incompressible flow energy equation can be written in the following form dT 0T 0T 0T P dt x + y + Oz + where; + 2 + {{( ) + ( ) ( ) ( ) ( ) ( )] - +