Hydrodynamic drag versus roughness for rotating disks

Stylus measurements of the microroughness of rotating disks and their significant correlation with hydrodynamic drag measurements were studied. The roughest disks ( R a ≈ 16 μm) were found to have drag coefficients about 30% greater than those of the smoothest disks ( R a ≈ 0.14 μm). For a Reynolds' number of 1.5 × 10 6, the following empirical relationship between the drag coefficient C, the average roughness R a and a parameter designated the peak count wavelength λ pc was obtained: C= bR a λ pc 1 2 + C o where b = 3.85 × 10 −3 μm − 1 2 and C 0 = 6.48 × 10 −3 . Other surface parameters and functions were measured in addition to R a and λ pc; however, it seems that knowledge of an amplitude-sensitive parameter and a wavelength-sensitive parameter is adequate for characterizing increases in the drag of rotating disks due to surface roughness. R a is the preferred amplitude-sensitive parameter because it is the most widely used. We propose λ pc as the wavelength parameter because it is sensitive to the larger profile features rather than to the fine structure. However, there is a need for all workers in the field to standardize on measuring the same parameters so that the results of one group can be easily related to the work of other groups.