Question

A long cylinder of radius R₁ is displaced along its axis with a constant velocity v_o inside a stationary co-axial cylinder of radius R₂. The space between the cylinders is filled with viscous liquid. Find the velocity of the liquid as a function of the distance r from the axis of the cylinders. The flow is laminar.

Answer 1

Let us consider a coaxial cylinder of radius r and thickness dr. then force of friction or viscous force on this elemental layer

This force must be constant from layer to layer so that steady motion may be possible

Note: The force F is supplied by the agency which tries to carry the inner cylinder with velocity v₀.