Viscous slow-down motion between coaxial cylinders

An analysis of the viscous tangential motion of a Newtonian fluid in the gap between coaxial cylinders is given for the particular situation in which the inner cylinder, rotating initially with a constant angular velocity, is suddenly left to move with its own inertia and viscous retarding couple alone. The exact solution for the transient angular velocity distribution in the annular space is given in terms of a rapidly converging series in which the use of the sole first term seems to be of sufficient accuracy for most practical calculations. For discrete values of the relevant parameters of the problem, the eigenvalues less than 41 were obtained numerically on a digital computer.