2. In a two dimensional incompressible fluid flow, the velocity components are given by: u=(x-4y) and v=-(y+4x). If possible show that the potential exists and determine its form. Also determine whether the flow is irrotational?

Question 3 Consider the two-dimensional incompressible velocity potential O = xy + x² – y2 a) Show that this flow is irrotational. b) Find the stream function Y(x, y), if Y(0,0) = 0 .

The stream function o in a two-dimensional flow field is given as 9 = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. Find the potential flow function P(x, y) for this flow field with boundary condition 0 = 0 at x = 2, y = 1. (b)

Problem 3: Obtaining the stream function from velocity components The steady state, incompressible flow field for two-dimensional flow is given by the following velocity components: V =16y-x and v, =16x + y %3D Determine the equation for the stream function and make sure continuity is satisfied.