The Torque and Turbulent Boundary Layer of Rotating Disks with Smooth and Rough Surfaces, and in Drag-Reducing Polymer Solutions

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Abstract
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.