Question 3 (a) A two-dimensional flow velocity field in the domain with non-dimensional coordinates x > 0 and y > 0 is defined as: v=-Vox?y i +Voxy?; where i and jare the unit vectors in the x- and y-directions respectively and Ue is a constant with units m/s. O Determine the magnitude and direction of the vclocity at the point (1.1). (3 marks) (ii) Find the equation of the streamlines. (5 marks) (b) A storage tank with base area 40 m is being filled with water through a duct in which the volumetric flow rate is 12 Ls, as shown in Fig. 3. Water is concurrently being extracted from the storage tank through two exit pipes with cross-section arca 150 cm . The inlet of the exit pipes is located at a certain height, denoted h in Fig. 3. above the bottom of the storage tank. Water is assumed to be inviscid and incompressible. exit pipes 12 L/s -150 cm -150 cm? 7 m storage tank (base area 40 m) Figure 3 6) Determine the flow speed V. in each exit pipe when a constant depth of 7 mis maintained in the storage tank. (6 marks) (ii) If the depth of water in the storage tank is initially 7 m and the flow speed in the exit pipes changes to V- 2.4 ms. it takes 1 hour for the water level to coincide with the inlet of the exit pipes. Determine the height h. (6 marks) (Total for question: 20 marks)