The friction torque versus radius r (bottom axis) and the Reynolds number (top axis) at Ω = 40 π · s − 1 in log-scales. The triangles are simulation results for rotors of β=32° and the circles for the thin disks. The triangles and circles in the regime of small r (or R) are fitted by two solid lines respectively. Both solid lines have slope 3, confirming the pow law Q f ∝ r 3 in the small Reynolds regime. The dotted line is the analytical solution for the thin disk model that is Q f = − 1.94 ρ η Ω r 4 Ω .