In cylindrical coordinates, a 2-dimensional velocity field in the , plane is given by

( = ) * = 0 + = 0 > 0 *

here is a positive constant. The velocity field would be singular at = 0, this is why there is the restriction that > 0.

5. In cylindrical coordinates, a 2-dimensional velocity field in the r, plane is given by v=rAvr=0vz=0r>0 here A is a positive constant. The velocity field would be singular at r=0, this is why there is the restriction that r>0. (a) Determine the stream function as a function of position and the parameter A, to within an arbitrary constant. Sketch a few streamlines for this flow. (b) Show that the vorticity wz is zero and that 2=0 for this flow. This indicates that this ideal vortex flow is an irrotational flow