Extension of perturbation series by computer: Viscous flow between two infinite rotating disks*1

A digital computer is used to extend the low-Reynolds-number perturbation series for viscous, incompressible flow between two infinite, concentric, rotating disks. Ten terms are found for the case of contrarotating disks and eight for the case of one disk fixed. Convergence is found to be limited by a square root branch point at R² = -1747.24 and -215.63 for the contrarotating case and the one disk fixed case, respectively. Analytic continuation is used to extend the series for velocity profile and torque to high Reynolds numbers. Comparisons with published numerical solutions show excellent agreement. The link between the low-Reynolds-number perturbation solution and the solution at high-Reynolds-number is discussed.