1) The full mass conservation equation (i.c. continuity equation) can be written in different coordinate systems. For instance, in cylindrical coordinates (r.6.:), you would get: Ta - + .j = (prv.) + (PH) + apv.) = 0 ap ar rar r24 The Burger's vortex is a type of flow that, at steady state, can be described using cylindrical coordinates (r.2.:), by i=(-ar.(1-e-or), Laz) where a and b are constants. The 3D result is represented in the figure below, which includes 5000 velocity vectors. Using this information, explain and justify whether the Burger's vortex flow can be considered incompressible or not. 450 450 500 i 2) In cylindrical coordinates, the vorticity vector (defined as the curl of the velocity vector) is given by the expression below: 1 du, =V x = a 1a r rae 22 10 Ve VE (10v, ovo dv dv, 1 a ae dz' az r rr (rvo) ae Find an expression for the vorticity of the Burger's vortex flow. 3) Determine the angular velocity vector (i.e. rotation speed) of the vortex, D, including the magnitude and the direction. 4) Is the direction of the vorticity equivalent to that of the fluid trajectories? Why or why not