Velocity field of an incompressible flow is given by V = 6xi − 6yj (m/s) a) Find the pathlines in x-y plane. Make a sketch of pathlines for x ≥ 0 and y ≥ 0. b) Find the streamlines. Make a sketch of streamlines for x ≥ 0 and y ≥ 0. c) At time t = 0 s, the position of a rectangular fluid element ABCD is described by the corner points A(1,3), B(2,3), C(1,2) and D(2,2). Determine the new position of the fluid element at time t = 1/6 s

In an experiment to determine the force acting on an oval-shaped body, a model is mounted in the test section of a wind tunnel. The test section itself has rectangular cross section with height 2h and width l (into the page). The model spans the entire width of the test section. The model is subject to a steady, uniform, incompressible flow of velocity V₁. The pressure gauge indicates a pressure difference (Ap) between the test section exit (location 2) and the test section entrance (location 1). The velocity profile downstream of the model is shown in the figure. Use the control volume shown. Find the force acting on the model in terms of given quantities V₁, h, l, Ap, and density, p. Ap V AL

Consider a 2-dimensional incompressible flow field. The vertical component of velocity forthe flow field is given by 2y. The pressure at (x, y) = 0,0 is given by 3 bar absolute. The densityof the fluid is 1.2 Kg/m3 . Find. a) x-component of velocity; b) acceleration at point (x, y) = 2,1;c) pressure gradient at the same point; d) pressure gradient along the x-axis; e) check whetherthe flow is irrotational; f) find the potential function; g) find the stream function; h) equationfor streamline and sketch few streamlines.

Please answer both