  Scrupulous measurements and detailed data analysis of the torque in a
swirling turbulent flow driven by counter-rotating bladed disks reveals an
apparent breaking of the law of similarity. Potentially, such breakdown could
arise from several possible factors, including dependence on dimensionless
numbers other that $Re$ or velocity coupling to other fields such as
temperature. However, careful redesign and calibration of the experiment showed
that this unexpected result was due to background errorscaused by minute
misalignments which lead to a noisy and irreproducible torque signal at low
rotation speeds and prevented correct background subtraction normally ascribed
to frictional losses. An important lesson to be learnt is that multiple minute
misalignments can nonlinearly couple to the torque signal and provide a dc
offset that cannot be removed by averaging. That offset can cause the observed
divergence of the friction coefficient C_f from its constant value observed in
the turbulent regime. To minimize the friction and misalignments, we
significantly modified the experimental setup and carried out the experiment
with one bladed disk where the disk, torque meter and motor shaft axes can be
aligned with significantly smaller error, close to the torque meter resolution.
As a result we made precise measurements with high resolution and sensitivity
of the small torques produced for low rotation speeds for several
water-glycerin solutions of different viscosities and confirmed the similarity
law in a wide range of Re in particular in low viscosity fluids.
