Annular flow with inner cylinder moving axially (see Fig. 2B.7), a cylindrical rod of diameter KR moves axially with velocity v0 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. Fig. 2B.7 annular flow with the inner cylinder moving axially

(a) Find the velocity distribution in the narrow annular region.

(b) Find the mass rate of flow through the annular region.

(c) Obtain the viscous force acting on the rod over the length L.

(d) Show that the result in (c) can be written as a "plane slit" formula multiplied by a "curvature correction." Problems of this kind arise in studying the performance of wire-coatingdies.1

Fluid at modified pressure Po Rod of radius KR moving with velocity v Cylinder of inside radius R Fluid at modified pressure Po