Flow in concentric tubes with an axially moving inner cylinder (see Figure 2B.7). A cylindrical rod of radius KR moves axially with velocity v,= vo along the axis of a cylindrical cavity of radius R as shown in the figure. The pressure at both ends of the cavity is the same, so the fluid moves through the annular region only due to the movement of the rod. a) Find the velocity distribution in the narrow annular region. b) Find the velocity of mass flow through the annular region. C) Obtain the viscous force acting on the rod over the length L. d) Show that the result of part (c) can be written as a formula for "planar slit" multiplied by a "curvature correction". Problems of this type arise in the study of the performance of dies for coated wire.

Figura 2B.7 Flujo en tubos concntricos donde el cilindro interior se mueve axialmente. Respuestas: a) v0vz=lnln(r/R) b) w=2R2v0[ln(1/)(12)22] c) Fz=2Lv0/ln(1/) d) Fz=2Lv0(1211212+) donde =1 (vase el problema 2B.5)