(a) A two-dimensional flow velocity field in the domain with non-dimensional coordinates x > 0 and y> 0 is defined as: v = -Uox i + 2Uoxy j where i and j are the unit vectors in the x- and y-directions respectively and Uo is a constant with units m/s. (i) Determine the magnitude and direction of the velocity at the point (1,1). (ii) Find the equation of the streamlines for this flow and sketch the streamline pattern in the x-y plane. With justification, also indicate the direction of the flow along the streamlines. (b) A flavoured syrup is mixed with water in a mixing unit. Water and syrup are flowing with speed 2 m/s into the mixing unit through circular pipes of cross-section area 9 cm and 2 cm respectively. The homogeneous mixture of water and syrup has density 1200 kg/m. It exits the mixing unit with a speed of 1.25 m/s through a circular pipe of 16 cm and is poured into a tank of base area 6 m, as shown on Figure 3. area 9 cm water 2 m/s area 16 cm mixing unit mixture 1.25 m/s tank base area 6 m area 2 cm syrup 2 m/s Figure 3 (i) Assuming that the mass of fluids inside the mixing unit remains constant, determine the density of the syrup. (ii) If the tank is initially empty, determine the depth h of water-syrup mixture in the tank after 5 hours.