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Hydrodynamics

Problem 1.332

A long cylinder of radius \(R_{1}\) is displaced along its axis with a constant velocity \(v_{0}\) inside a stationary co-axial cylinder of radius \(R_{2}\). 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.

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)}
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