Annular flow with inner cylinder moving axially (see Fig. 1). A cylindrical rod of radius KR moves axially with velocity v, = vo along the axis of a cylindrical cavity of radius R as seen in the figure. The pressure at both ends of the cavity is the same, so that the fluid moves through the annular region solely because of the rod motion. Obtain an expression for the velocity profile: assuming (1) steady state (2) all physical properties = constant (3) negligible end effects.

Fuid at modified pressure ? Cylinder of inside radius R Fluid at modified pressure Rod of radius R moving with velocity vo Fig. 1 Annular flow with the inner cylinder moving axially