All Problems

Hydrodynamics

Problem 1.332

A long cylinder of radius R1R_{1} is displaced along its axis with a constant velocity v0v_{0} inside a stationary co-axial cylinder of radius R2R_{2}. The space between the cylinders is filled with viscous liquid. Find the velocity of the liquid as a function of the distance rr from the axis of the cylinders. The flow is laminar.

Reveal Answer
v=v0ln(r/R2)ln(R1/R2)v=v_{0} \frac{\ln \left(r / R_{2}\right)}{\ln \left(R_{1} / R_{2}\right)}