The resisting torque of disks rotating in an unbounded fluid is analyzed on the basis of three-dimensional boundary-layer theory. Smooth and rough surfaces in ordinary fluids and in drag-reducing polymer solutions are considered. A general logarithmic relation is derived for the torque as a function of Reynolds number for arbitrary roughness and arbitrary drag reduction. Special formulas are obtained for smooth surfaces, fully rough surfaces, polymer solutions with a linear logarithmic drag-reduction characterization, and polymer solutions with maximum drag reduction. Relations are also obtained for boundary-layer parameters such as thickness and wall shearing stress. The computed results are in excellent agreement with experimental data available in the literature.
The Torque and Turbulent Boundary Layer of Rotating Disks with Smooth and Rough Surfaces, and in Drag-Reducing Polymer Solutions
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Granville, Paul S.. "The Torque and Turbulent Boundary Layer of Rotating Disks with Smooth and Rough Surfaces, and in Drag-Reducing Polymer Solutions." J Ship Res 17 (1973): 181–195. doi: https://doi.org/10.5957/jsr.19184.108.40.206
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