3) A rod of radius R, moves upward with a constant velocity throupl a cylindrical container of inner radius R containing a Neutonian liquid. The liquid circuiates in the eylinder, moving upward along the moving central rod and moving dowuward along the fixed container wall. Find the velocity distribution in the annolar region, far from the end disturbances. Flows similar to this occur in the seals of some reciprocating machinery-for example, in the annular space between piston rings. (3) First consider the problem where the annular region is quite narrow-that is, where K is just slightly less than unity. In that case the annulus may be approximated by a thin plane elit and the curvature can be neglected. Show that in this limit, the velocity distribution is given by v0v2=3(1)24(1)+1(3B.61) where =rR. (b) Next work the problem without the thin-slit assump-tion. Show that the velocity distribution is given by Fig. 3B.6. Circulating fow produced by an axially moving rod in a closed annular region