In aerodynamics, complicated flow patterns can be synthesised by combining a number of flows that satisfy Laplace's equation. To satisfy Laplace's equation a flow field must satisfy the continuity equation and must be irrotational. A velocity flow field is described by u=2xyi+(x2y2)j (i) Show that the above flow satisfies the continuity equation. [3 marks] (ii) Show that the flow is irrotational. [3 marks] (iii) Determine the scalar potential of the flow. [6 marks] (iv) Confirm that satisfies Laplace's equation. [3 marks]